Computational complexity theory is a branch of computer science dedicated to classifying computational problems in terms of their difficulty. While computability theory tells us what we can compute in principle, complexity theory informs us regarding our practical limits. In this chapter I argue that the science of \emph{quantum computing} illuminates complexity theory by emphasising that its fundamental concepts are not model-independent, but that this does not, as some suggest, force us to radically revise the foundations of the theory. For model-independence (...) never has been essential to those foundations. The fundamental aim of complexity theory is to describe what is achievable in practice under various models of computation for our various practical purposes. Reflecting on quantum computing illuminates complexity theory by reminding us of this, too often under-emphasised, fact. (shrink)

The inaugural title in the new, Open Access series BSPS Open, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas or rules or a single (...) formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist. The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it. Which that is, and its extent, is determined by the facts prevailing in that domain. Paying close attention to how inductive inference is conducted in science and copiously illustrated with real-world examples, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. (shrink)

The book’s core argument is that an artificial intelligence that could equal or exceed human intelligence—sometimes called artificial general intelligence (AGI)—is for mathematical reasons impossible. It offers two specific reasons for this claim: Human intelligence is a capability of a complex dynamic system—the human brain and central nervous system. Systems of this sort cannot be modelled mathematically in a way that allows them to operate inside a computer. In supporting their claim, the authors, Jobst Landgrebe and Barry Smith, marshal evidence (...) from mathematics, physics, computer science, philosophy, linguistics, and biology, setting up their book around three central questions: What are the essential marks of human intelligence? What is it that researchers try to do when they attempt to achieve "artificial intelligence" (AI)? And why, after more than 50 years, are our most common interactions with AI, for example with our bank’s computers, still so unsatisfactory? Landgrebe and Smith show how a widespread fear about AI’s potential to bring about radical changes in the nature of human beings and in the human social order is founded on an error. There is still, as they demonstrate in a final chapter, a great deal that AI can achieve which will benefit humanity. But these benefits will be achieved without the aid of systems that are more powerful than humans, which are as impossible as AI systems that are intrinsically "evil" or able to "will" a takeover of human society. (shrink)

The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are reviewed and an emerging link between them is outlined. It is shown that these methods employ a wide range of important mathematical concepts like, e.g., Fourier transforms, Galois fields and rings, finite, and related projective geometries, and entanglement, to mention a few. Some applications of the theory to quantum information tasks are also mentioned.

We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via complete tomography of four output states E[ρj] that originate from a set of four linearly independent “test” states ρj (j = 1,2,3,4) at the input of the channel. We study the situation when less than four linearly independent states are transmitted (...) via the channel and measured at the output. We present strategies how to reconstruct the channel when just one, two or three states are transmitted via the channel. In particular, we show that if just one state is transmitted via the channel then the best reconstruction can be achieved when this state is a total mixture described by the density operator ρ = I/2. To improve the reconstruction procedure one has to send via the channel more states. The best strategy is to complement the total mixture with pure states that are mutually orthogonal in the sense of the Bloch-sphere representation. We show that unitary transformations (channels) can be uniquely reconstructed (determined) based on the information of how three properly chosen input states are transformed under the action of the channel. (shrink)

We revisit quantum measurement when the apparatus is initially in a mixed state. We find that, in a particular restriction setup, the amount of entanglement between the system and the apparatus is given by the entropy increasing of the system under the measurement transformation. We show that the information gained is equal to the amount of entanglement under performing perfect measurement. Based on the perfect measurement, we give an upper bound of quantum discord.

There exists a growing literature on the so-called physical Church-Turing thesis in a relativistic spacetime setting. The physical Church-Turing thesis is the conjecture that no computing device that is physically realizable can exceed the computational barriers of a Turing machine. By suggesting a concrete implementation of a beyond-Turing computer in a spacetime setting, Istvan Nemeti and Gyula David have shown how an appreciation of the physical Church-Turing thesis necessitates the confluence of mathematical, computational, physical, and indeed cosmological ideas. In this (...) essay, I will honour Istvan's seventieth birthday, as well as his longstanding interest in, and his seminal contributions to, this field going back to as early as 1987 by modestly proposing how the concrete implementation in Nemeti and D\'avid might be complemented by a quantum-information-theoretic communication protocol between the computing device and the logician who sets the beyond-Turing computer a task such as determining the consistency of Zermelo-Fraenkel set theory. This suggests that even the foundations of quantum theory and, ultimately, quantum gravity may play an important role in determining the validity of the physical Church-Turing thesis. (shrink)

The aim of this paper is to present some basic notions of the theory of quantum computing and to compare them with the basic notions of the classical theory of computation. I am convinced, that the results of quantum computation theory (QCT) are not only interesting in themselves, but also should be taken into account in discussions concerning the nature of mathematical knowledge. The philosophical discussion will however be postponed to another paper. QCT seems not to be well-known among philosophers (...) (at least not to the degree it deserves), so the aim of this paper is to provide the necessary technical preliminaries presented in a way accessible to the general philosophical audience. (shrink)

There is no consensus as to whether a Liar sentence is meaningful or not. Still, a widespread conviction with respect to Liar sentences (and other ungrounded sentences) is that, whether or not they are meaningful, they are useless . The philosophical contribution of this paper is to put this conviction into question. Using the framework of assertoric semantics , which is a semantic valuation method for languages of self-referential truth that has been developed by the author, we show that certain (...) computational problems, called query structures , can be solved more efficiently by an agent who has self-referential resources (amongst which are Liar sentences) than by an agent who has only classical resources; we establish the computational power of self-referential truth . The paper concludes with some thoughts on the implications of the established result for deflationary accounts of truth. (shrink)

The rise of quantum information theory has lent new relevance to experimental tests for non-classicality, particularly in controversial cases such as adiabatic quantum computing superconducting circuits. The Leggett-Garg inequality is a “Bell inequality in time” designed to indicate whether a single quantum system behaves in a macrorealistic fashion. Unfortunately, a violation of the inequality can only show that the system is either (i) non-macrorealistic or (ii) macrorealistic but subjected to a measurement technique that happens to disturb the system. The “clumsiness” (...) loophole (ii) provides reliable refuge for the stubborn macrorealist, who can invoke it to brand recent experimental and theoretical work on the Leggett-Garg test inconclusive. Here, we present a revised Leggett-Garg protocol that permits one to conclude that a system is either (i) non-macrorealistic or (ii) macrorealistic but with the property that two seemingly non-invasive measurements can somehow collude and strongly disturb the system. By providing an explicit check of the invasiveness of the measurements, the protocol replaces the clumsiness loophole with a significantly smaller “collusion” loophole. (shrink)

For many years after Bohr's response to the EPR argument, Bohr was considered to have provided an authoritative rebuttal of the ideas of the paper, and more generally of Einstein's stance on quantum theory. More recently, however, there has been great difficulty even in achieving general agreement on Bohr's meaning. Two recent papers, by Dickson, and by Clifton and Halvorson, have sought to establish the structure of Bohr's argument. In the present paper, the papers of EPR and Bohr are re-assessed (...) in the light of these recent papers, and also in light of the development and presentation of quantum information theory. (shrink)

Although the path-integral formalism is known to be equivalent to conventional quantum mechanics, it is not generally obvious how to implement path-based calculations for multi-qubit entangled states. Whether one takes the formal view of entangled states as entities in a high-dimensional Hilbert space, or the intuitive view of these states as a connection between distant spatial configurations, it may not even be obvious that a path-based calculation can be achieved using only paths in ordinary space and time. Previous work has (...) shown how to do this for certain special states; this paper extends those results to all pure two-qubit states, where each qubit can be measured in an arbitrary basis. Certain three-qubit states are also developed, and path integrals again reproduce the usual correlations. These results should allow for a substantial amount of conventional quantum analysis to be translated over into a path-integral perspective, simplifying certain calculations, and more generally informing research in quantum foundations. (shrink)

This paper examines some common measures of complexity, structure, and information, with an eye toward understanding the extent to which complexity or information‐content may be regarded as objective properties of individual objects. A form of contextual objectivity is proposed which renders the measures objective, and which largely resolves the puzzle of Maxwell's Demon.

Density matrices for mixed state qubits, parametrized by the Bloch vector in the open unit ball of the Euclidean 3-space, are well known in quantum computation theory. We bring the seemingly structureless set of all these density matrices under the umbrella of gyrovector spaces, where the Bloch vector is treated as a hyperbolic vector, called a gyrovector. As such, this article catalizes and supports interdisciplinary research spreading from mathematical physics to algebra and geometry. Gyrovector spaces are mathematical objects that form (...) the setting for the hyperbolic geometry of Bolyai and Lobachevski just as vector spaces form the setting for Euclidean geometry. It is thus interesting, in geometric quantum computation, to realize that the set of all qubit density matrices has rich structure with strong link to hyperbolic geometry. Concrete examples for the use of the gyro-structure to derive old and new, interesting identities for qubit density matrices are presented. (shrink)

Transition Probability (fidelity) for pairs of density operators can be defined as a “functor” in the hierarchy of “all” quantum systems and also within any quantum system. The Introduction of “amplitudes” for density operators allows for a more intuitive treatment of these quantities, also pointing to a natural parallel transport. The latter is governed by a remarkable gauge theory with strong relations to the Riemann-Bures metric.

Order of information plays a crucial role in the process of updating beliefs across time. In fact, the presence of order effects makes a classical or Bayesian approach to inference difficult. As a result, the existing models of inference, such as the belief-adjustment model, merely provide an ad hoc explanation for these effects. We postulate a quantum inference model for order effects based on the axiomatic principles of quantum probability theory. The quantum inference model explains order effects by transforming a (...) state vector with different sequences of operators for different orderings of information. We demonstrate this process by fitting the quantum model to data collected in a medical diagnostic task and a jury decision-making task. To further test the quantum inference model, a new jury decision-making experiment is developed. Using the results of this experiment, we compare the quantum inference model with two versions of the belief-adjustment model, the adding model and the averaging model. We show that both the quantum model and the adding model provide good fits to the data. To distinguish the quantum model from the adding model, we develop a new experiment involving extreme evidence. The results from this new experiment suggest that the adding model faces limitations when accounting for tasks involving extreme evidence, whereas the quantum inference model does not. Ultimately, we argue that the quantum model provides a more coherent account for order effects that was not possible before. (shrink)

The Bayesian approach to quantum mechanics of Caves, Fuchs and Schack is presented. Its conjunction of realism about physics along with anti-realism about much of the structure of quantum theory is elaborated; and the position defended from common objections: that it is solipsist; that it is too instrumentalist; that it cannot deal with Wigner's friend scenarios. Three more substantive problems are raised: Can a reasonable ontology be found for the approach? Can it account for explanation in quantum theory? Are subjective (...) probabilities on their own adequate in the quantum domain? The first question is answered in the affirmative, drawing on elements from Nancy Cartwright's philosophy of science. The second two are not: it is argued that these present outstanding difficulties for the project. A quantum Bayesian version of Moore's paradox is developed to illustrate difficulties with the subjectivist account of pure state assignments. (shrink)

Deutsch and Hayden claim to have provided an account of quantum mechanics which is particularly local, and which clarifies the nature of information transmission in entangled quantum systems. In this paper, a perspicuous description of their formalism is offered and their claim assessed. It proves essential to distinguish, as Deutsch and Hayden do not, between two ways of interpreting the formalism. On the first, conservative, interpretation, no benefits with respect to locality accrue that are not already available on either an (...) Everettian or a statistical interpretation; and the conclusions regarding information flow are equivocal. The second, ontological, interpretation, offers a framework with the novel feature that global properties of quantum systems are reduced to local ones; but no conclusions follow concerning information flow in more standard quantum mechanics. (shrink)

The phase φ of any wave is determined by the ratio x/λ consisting of the distance x propagated by the wave and its wavelength λ. Hence, the dependence of φ on λ constitutes an analogue system for the mathematical operation of division, that is to obtain the hyperbolic function f(ξ)≡1/ξ. We take advantage of this observation to decompose integers into primes and implement this approach towards factorization of numbers in a multi-path Michelson interferometer. This work is part of a larger (...) program geared towards unraveling the connections between quantum mechanics and number theory. We briefly summarize this aspect. (shrink)

Classical physics allows for the existence of pairs of absolutely identical systems. Pairwise application of identical measurements to each of those systems always leads to exactly alike results irrespectively of the choice of measurements. Here we ask a question how the picture looks like in the quantum domain. Surprisingly, we get a counterintuitive outcome. Pairwise application of identical measurements cannot always lead to exactly alike results. We interpret this as quantum uniqueness—a feature that has no classical analog.

We consider the concept of entanglement for pure cases of finite dimensional state spaces. The criterion of unentangled states is related to demanding rank one of an associated eigenvalue problem. In addition to the conventional procedure based on the Schmidt decomposition, we devise a method based on the spectral resolution of unsymmetric matrices. In particular, we consider the case when all eigenvalues are zero, and find that the method still works.

Costa and Shrapnel have recently proposed an interventionist theory of quantum causation. The formalism generalizes the classical methods of Pearl and allows for the discovery of quantum causal structure via localized interventions. Classical causal structure is presented as a special case of this more general framework. I introduce the account and consider whether this formalism provides a causal explanation for the Bell correlations.

The ideas of quantum simulation and advances in quantum algorithms to solve quantum chemistry problems have been discussed. Theoretical proposals and experimental investigations both have been studied to gauge the extent to which quantum computation has been applied to solve quantum chemical problems till date. The distinctive features and limitations of the application of quantum simulation on chemical systems and current approaches to define and improve upon standard quantum algorithms have been studied in detail. The possibility and consequences of designing (...) an efficient quantum computer that can address chemical problems have been assessed. The experimental realization of quantum supremacy defies the conventional belief of chemists, that millions of qubits would be required to solve fundamental chemistry problems. It is predicted that quantum simulation of quantum chemistry problems will radically revolutionize this field. (shrink)

Unlike the standard Quantum Computational Logic, where the carrier of information is conventionally assumed to be only the last qubit over a sequence of many qubits, here we propose an extended version of the QCL where the number and the position of the target qubits are arbitrary.

Motivated by the question what it is that makes quantum mechanics a holistic theory, I try to define for general physical theories what we mean by `holism'. For this purpose I propose an epistemological criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if it is impossible in principle to infer the global properties, as assigned in the theory, by local resources available to an agent. I propose that these (...) resources include at least all local operations and classical communication. This approach is contrasted with the well-known approaches to holism in terms of supervenience. The criterion for holism proposed here involves a shift in emphasis from ontology to epistemology. I apply this epistemological criterion to classical physics and Bohmian mechanics as represented on a phase and configuration space respectively, and for quantum mechanics using the formalism of general quantum operations as completely positive trace non-increasing maps. Furthermore, I provide an interesting example from which one can conclude that quantum mechanics is holistic in the above mentioned sense, although, perhaps surprisingly, no entanglement is needed. (shrink)

A longstanding issue in attempts to understand the Everett (Many-Worlds) approach to quantum mechanics is the origin of the Born rule: why is the probability given by the square of the amplitude? Following Vaidman, we note that observers are in a position of self-locating uncertainty during the period between the branches of the wave function splitting via decoherence and the observer registering the outcome of the measurement. In this period it is tempting to regard each branch as equiprobable, but we (...) argue that the temptation should be resisted. Applying lessons from this analysis, we demonstrate (using methods similar to those of Zurek's envariance-based derivation) that the Born rule is the uniquely rational way of apportioning credence in Everettian quantum mechanics. In doing so, we rely on a single key principle: changes purely to the environment do not affect the probabilities one ought to assign to measurement outcomes in a local subsystem. We arrive at a method for assigning probabilities in cases that involve both classical and quantum self-locating uncertainty. This method provides unique answers to quantum Sleeping Beauty problems, as well as a well-defined procedure for calculating probabilities in quantum cosmological multiverses with multiple similar observers. (shrink)

Reception of the Bohm-Hiley interpretation of quantum mechanics has a curiously Janus faced quality. On the one hand, it is frequently derided as a conservative throwback to outdated classical patterns of thought. On the other hand, it is equally often taken to task for encouraging a wild quantum mysticism, often regarded as anti-scientific. I will argue that there are reasons for this reception, but that a proper appreciation of the dual scientific and philosophical aspects of the view reveals a powerful (...) and extremely interesting metaphysical view of the world. This view is akin to that of Russellian Monism, in which the empirical world studied by science is restricted to relational features that stand in need of some background intrinsic properties to ground their reality. This allows for a theory that can embrace a world which exhibits a reasonable and plausible sort of emergence (especially of domains that fall under classical concepts) while also making room for distinctive and scientifically intransigent properties such as consciousness. (shrink)

From the structure of quantum dynamics for closed and open systems, we describe several general results about information flow between interacting systems, which can be expressed in diagrammatic form. Conditions on information flow (e.g., that no information is transferred from system A to system B) imply that the overall dynamical evolution has a particular structure. We also remark that one simple type of two-qubit interaction, the unitary CNOT gate, cannot be represented by local operations and a single simultaneous information exchange.

We propose a new way of looking at the quantum Maxwell’s demon problem in terms of conditional action. A “conditional action” on a system is a unitary time evolution, selected according to the result of a previous measurement, which can reduce the entropy of the system. However, any conditional action can be realized by an unitary time evolution of a larger system and a subsequent Lüders measurement, whereby the entropy of the entire system is either increased or remains constant. We (...) give some examples that illustrate and confirm our proposal, including the erasure of N qubits and the Szilard engine, thus relating the present approach to the Szilard principle and the Landauer principle that have been discussed as possible solutions of the Maxwell’s demon problem. (shrink)

According to quantum mechanics, the informational content of isolated systems does not change in time. Considering composite systems, it would be very useful to identify suitable indicators able to quantify the informational content of the single parts and to describe their evolution through balance equations, as it happens in the case of energy. Reasoning on the basic concepts of quantum mechanics, we show that there is an intrinsic quantum information encoded in the coherence of quantum states. Such information is measured (...) by a function, called here coherent entropy, which turns out to be complementary to the von-Neumann entropy. We show that the total quantum information of multipartite systems is determined by the coherent entropy of the single subsystems plus their mutual information. Interestingly, the coherent entropy is found to be equal to the information conveyed in the future by quantum states, providing a further inspiring interpretation to this quantity. The vision proposed in this paper also suggests a natural and simple definition of an indicator for nonlocal correlations. (shrink)

Spekkens has introduced a toy theory (Spekkens in Phys. Rev. A 75(3):032110, 2007) in order to argue for an epistemic view of quantum states. I describe a notation for the theory (excluding certain joint measurements) which makes its similarities and differences with the quantum mechanics of stabilizer states clear. Given an application of the qubit stabilizer formalism, it is often entirely straightforward to construct an analogous application of the notation to the toy theory. This assists calculations within the toy theory, (...) for example of the number of possible states and transformations, and enables superpositions to be defined for composite systems. (shrink)

Classical (Bayesian) probability (CP) theory has led to an influential research tradition for modeling cognitive processes. Cognitive scientists have been trained to work with CP principles for so long that it is hard even to imagine alternative ways to formalize probabilities. However, in physics, quantum probability (QP) theory has been the dominant probabilistic approach for nearly 100 years. Could QP theory provide us with any advantages in cognitive modeling as well? Note first that both CP and QP theory share the (...) fundamental assumption that it is possible to model cognition on the basis of formal, probabilistic principles. But why consider a QP approach? The answers are that (1) there are many well-established empirical findings (e.g., from the influential Tversky, Kahneman research tradition) that are hard to reconcile with CP principles; and (2) these same findings have natural and straightforward explanations with quantum principles. In QP theory, probabilistic assessment is often strongly context- and order-dependent, individual states can be superposition states (that are impossible to associate with specific values), and composite systems can be entangled (they cannot be decomposed into their subsystems). All these characteristics appear perplexing from a classical perspective. However, our thesis is that they provide a more accurate and powerful account of certain cognitive processes. We first introduce QP theory and illustrate its application with psychological examples. We then review empirical findings that motivate the use of quantum theory in cognitive theory, but also discuss ways in which QP and CP theories converge. Finally, we consider the implications of a QP theory approach to cognition for human rationality. (shrink)

This paper intends to contribute to the emerging literature on the ethical problems posed by quantum computing and quantum technologies in general. The key ethical questions are as follows: Does quantum computing pose new ethical problems, or are those raised by quantum computing just a different version of the same ethical problems raised by other technologies, such as nanotechnologies, nuclear plants, or cloud computing? In other words, what is new in quantum computing from an ethical point of view? The paper (...) aims to answer these two questions by (a) developing an analysis of the existing literature on the ethical and social aspects of quantum computing and (b) identifying and analyzing the main ethical problems posed by quantum computing. The conclusion is that quantum computing poses completely new ethical issues that require new conceptual tools and methods. (shrink)

This article defends a modest version of the Physical Church-Turing thesis (CT). Following an established recent trend, I distinguish between what I call Mathematical CT—the thesis supported by the original arguments for CT—and Physical CT. I then distinguish between bold formulations of Physical CT, according to which any physical process—anything doable by a physical system—is computable by a Turing machine, and modest formulations, according to which any function that is computable by a physical system is computable by a Turing machine. (...) I argue that Bold Physical CT is not relevant to the epistemological concerns that motivate CT and hence not suitable as a physical analog of Mathematical CT. The correct physical analog of Mathematical CT is Modest Physical CT. I propose to explicate the notion of physical computability in terms of a usability constraint, according to which for a process to count as relevant to Physical CT, it must be usable by a finite observer to obtain the desired values of a function. Finally, I suggest that proposed counterexamples to Physical CT are still far from falsifying it because they have not been shown to satisfy the usability constraint. (shrink)

We propose partial measurements as a conceptual tool to understand how to operate with counterfactual claims in quantum physics. Indeed, unlike standard von Neumann measurements, partial measurements can be reversed probabilistically. We first analyze the consequences of this rather unusual feature for the principle of superposition, for the complementarity principle, and for the issue of hidden variables. Then we move on to exploring non-local contexts, by reformulating the EPR paradox, the quantum teleportation experiment, and the entanglement-swapping protocol for the situation (...) in which one uses partial measurements followed by their stochastic reversal. This leads to a number of counter-intuitive results, which are shown to be resolved if we give up the idea of attributing reality to the wavefunction of a single quantum system. (shrink)

The recently established universal uncertainty principle revealed that two nowhere commuting observables can be measured simultaneously in some state, whereas they have no joint probability distribution in any state. Thus, one measuring apparatus can simultaneously measure two observables that have no simultaneous reality. In order to reconcile this discrepancy, an approach based on quantum logic is proposed to establish the relation between quantum reality and measurement. We provide a language speaking of values of observables independent of measurement based on quantum (...) logic and we construct in this language the state-dependent notions of joint determinateness, value identity, and simultaneous measurability. This naturally provides a contextual interpretation, in which we can safely claim such a statement that one measuring apparatus measures one observable in one context and simultaneously it measures another nowhere commuting observable in another incompatible context. (shrink)

Quantum mechanics is one of the most successful theories of physics. But the creators of quantum mechanics had to reject realism in order to describe some paradoxical quantum phenomena. Einstein considered the rejection of realism unacceptable, since according to his understanding, realism is the presupposition of every kind of physical thinking. The dispute about the permissibility of rejecting realism has largely determined the modern understanding of quantum theory and even led to the emergence new quantum information technologies. Many modern authors (...) are sure that realism can be refute experimentally. Some authors are sure even that real technologies can be created on the basis of this refutation. The well-known GHZ theorem is considered critically in this work the authors of which are sure that realism can be refute experimentally. (shrink)

For over a decade, the hypercomputation movement has produced computational models that in theory solve the algorithmically unsolvable, but they are not physically realizable according to currently accepted physical theories. While opponents to the hypercomputation movement provide arguments against the physical realizability of specific models in order to demonstrate this, these arguments lack the generality to be a satisfactory justification against the construction of any information-processing machine that computes beyond the universal Turing machine. To this end, I present a more (...) mathematically concrete challenge to hypercomputability, and will show that one is immediately led into physical impossibilities, thereby demonstrating the infeasibility of hypercomputers more generally. This gives impetus to propose and justify a more plausible starting point for an extension to the classical paradigm that is physically possible, at least in principle. Instead of attempting to rely on infinities such as idealized limits of infinite time or numerical precision, or some other physically unattainable source, one should focus on extending the classical paradigm to better encapsulate modern computational problems that are not well-expressed/modeled by the closed-system paradigm of the Turing machine. I present the first steps toward this goal by considering contemporary computational problems dealing with intractability and issues surrounding cyber-physical systems, and argue that a reasonable extension to the classical paradigm should focus on these issues in order to be practically viable. (shrink)

In this paper we describe some first steps for bringing the framework of branching space-times to bear on quantum information theory. Our main application is quantum error correction. It is shown that branching space-times offers a new perspective on quantum error correction: as a supplement to the orthodox slogan, ``fight entanglement with entanglement'', we offer the new slogan, ``fight indeterminism with indeterminism''.

¿Cómo se nos presenta, fenomenológicamente la realidad humana? Es la que vemos diariamente en nuestra vida personal y social. Estamos hechos de materia, formamos parte del universo evolutivo. Además, está formada en nosotros una vida psíquica: la sensación, un sistema de percepciones, una conciencia integrada, una condición de sujeto psicológico; producimos conocimiento, emociones, motivaciones; pero, sobre todo, tenemos una mente que discurre racionalmente y nos instala en un mundo de emociones humanas; esta razón emocional está en la base de la (...) búsqueda de la verdad del universo, del sentido de la vida y de la responsabilidad moral, en la vida personal y social. Nuestra realidad humana es, pues, una realidad personal. Somos personas. Ahora bien, ¿cómo explica hoy la ciencia, la neurología, el hecho de que nuestra realidad humana posea estas propiedades que nos hacen personas? Esto debería poder explicarse desde el mundo físico-biológico. Ahora bien, en concreto, ¿cómo la ciencia hace posible explicar que la evolución nos haya producido a nosotros en nuestra condición de personas? Es decir, ¿cuál es el soporte físico que hace inteligible la ontología psico-bio-física que produce evolutivamente nuestra experiencia personal fenomenológica? Esta es, en último término, todavía hoy la cuestión fundamental de las ciencias humanas. Lo que la ciencia, a saber, la neurología, debe explicar es obvio: el hecho de que haya emergido la sensibilidad-conciencia, nuestra condición de sujetos psíquicos, el conocimiento y la razón emocional; de tal manera que, una vez emergida la razón emocional, lleve por sí misma a constituir la actividad racional y las emociones propias de la persona humana encaminada a construir el sentido de su vida. Estas son las cuestiones que abordamos en este artículo. (shrink)

Quantum measurement is a physical process. A system and an apparatus interact for a certain time period, and during this interaction, information about an observable is transferred from the system to the apparatus. In this study, we quantify the energy fluctuation of the quantum apparatus required for this physical process to occur autonomously. We first examine the so-called standard model of measurement, which is free from any non-trivial energy–time uncertainty relation, to find that it needs an external system that switches (...) on the interaction between the system and the apparatus. In such a sense this model is not closed. Therefore to treat a measurement process in a fully quantum manner we need to consider a “larger” quantum apparatus which works also as a timing device switching on the interaction. In this setting we prove that a trade-off relation, \, holds between the energy fluctuation \ of the quantum apparatus and the measurement time \. We use this trade-off relation to discuss the spacetime uncertainty relation concerning the operational meaning of the microscopic structure of spacetime. In addition, we derive another trade-off inequality between the measurement time and the strength of interaction between the system and the apparatus. (shrink)

I describe a pedagogical scheme devised to teach efficiently to computer scientists just enough quantum mechanics to permit them to understand the theoretical developments of the last decade going under the name of “quantum computation.” I then note that my offbeat approach to quantum mechanics, designed to be maximally efficacious for this specific educational purpose, is nothing other than the Copenhagen interpretation.

In this article I raise a new problem for quantum mechanics, which I call the control problem. Like the measurement problem, the control problem places a fundamental constraint on quantum theories. The characteristic feature of the problem is its focus on state preparation. In particular, whereas the measurement problem turns on a premise about the completeness of the quantum state ('no hidden variables'), the control problem turns on a premise about our ability to prepare or control quantum states. After raising (...) the problem, I discuss some applications. I suggest that it provides a useful new lens through which to view existing theories or interpretations, in part because it draws attention to aspects of those theories that the measurement problem does not. I suggest that it also helps clarify the physical significance of the well-known no-go result—the no-cloning theorem—on which it is based. (shrink)

We point out a fundamental problem that hinders the quantization of general relativity: quantum mechanics is formulated in terms of systems, typically limited in space but infinitely extended in time, while general relativity is formulated in terms of events, limited both in space and in time. Many of the problems faced while connecting the two theories stem from the difficulty in shoe-horning one formulation into the other. A solution is not presented, but a list of desiderata for a quantum theory (...) based on events is laid out. (shrink)