Weak measurement devices resemble band pass filters: they strengthen average values in the state space or equivalently filter out some ‘frequencies’ from the conjugate Fourier transformed vector space. We thereby adjust a principle of classical communication theory for the use in quantum computation. We discuss some of the computational benefits and limitations of such an approach, including complexity analysis, some simple examples and a realistic not-so-weak approach.

A so called “weak value” of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM paradoxes (e.g., the so called Three-Box Paradox and Hardy’s Paradox). This requires the weak value to be interpreted as a bona fide property of the system considered, a par with entities like operator mean values and eigenvalues. I question such an (...) interpretation; it has no support in the basic axioms of quantum mechanics and it leads to unreasonable results in concrete situations. (shrink)

A relation is obtained between weak values of quantum observables and the consistency criterion for histories of quantum events. It is shown that “strange” weak values for projection operators always correspond to inconsistent families of histories. It is argued that using the ABL rule to obtain probabilities for counterfactual measurements corresponding to those strange weak values gives inconsistent results. This problem is shown to be remedied by using the conditional weight, or pseudo-probability, obtained from the multiple-time application of Lüders’ Rule. (...) It is argued that an assumption of reverse causality implies that weak values obtain, in a restricted sense, at the time of the weak measurement as well as at the time of post-selection. Finally, it is argued that weak values are more appropriately characterized as multiple-time amplitudes than expectation values, and as such can have little to say about counterfactual questions. (shrink)

ABSTRACT: A relation is obtained between weak values of quantum observables and the consistency criterion for histories of quantum events. It is shown that ``strange'' weak values for projection operators always correspond to inconsistent families of histories. It is argued that using the ABL rule to obtain probabilities for counterfactual measurements corresponding to those strange weak values gives inconsistent results. This problem is shown to be remedied by using the conditional weight, or pseudo-probability, obtained from the multiple-time application of Luders' (...) Rule. It is argued that an assumption of reverse causality implies that weak values obtain, in a restricted sense, at the time of the weak measurement as well as at the time of post-selection. Finally, it is argued that weak values are more appropriately characterised as multiple-time amplitudes than expectation values, and as such can have little to say about counterfactual questions. (shrink)

An apparent paradox proposed by Aharonov and Vaidman in which a single particle can be found with certainty in two (or more) boxes is analyzed by way of a simple thought experiment. It is found that the apparent paradox arises from an invalid counterfactual usage of the Aharonov-Bergmann-Lebowitz (ABL) rule and effectively attributes conflicting properties not to the same particle but no different particles. A connection is made between the present analysis and the consistent histories formulation of Griffiths. Finally, a (...) critique is given of some recent counterarguments by Vaidman against the rejection of the counterfactual usage of the ABL rule. (shrink)

It is proposed that the recent controversy over "time-symmetric quantum counterfactuals" (TSQCs), based on the Aharonov-Bergmann-Lebowitz Rule for measurements of pre- and post-selected systems, can be clarified by taking TSQCs to be counterfactuals with a specific type of compound antecedent. In that case, inconsistency proofs such as that of Sharp and Shanks (1993) are not applicable, and the main issue becomes not whether such statements are true, but whether they are nontrivial. The latter question is addressed and answered in the (...) negative. Thus it is concluded that TSQCs, understood as counterfactuals with a compound antecedent, are true but only trivially so, and provide no new contingent information about specific quantum systems (except in special cases already identified in literature). (shrink)

A large literature has grown up around the proposed use of 'weak measurements' to allegedly provide information about hidden ontological features of quantum systems. This paper attempts to clarify the fact that 'weak measurements' are simply strong measurements on one member of an entangled pair, and that all such measurements thus effect complete disentanglement of the pair. The only thing 'weak' about them is that the correlation established via the entanglement does not correspond to eigenstates of the 'weakly measured observable' (...) for the component system that is subject to the weak measurement. It is observed that complete disentanglement always occurs, whether post-­‐selection is performed before or after the pointer detection. Assertions in the literature that weak measurements leave a system negligibly disturbed are therefore inaccurate, and claims based on those assertions need to be critically reassessed. (shrink)

In combination with post-selection, weak measurements can lead to surprising results known as anomalous weak values. These lie outside the bounds of the spectrum of the relevant observable, as in the canonical example of measuring the spin of an electron (along some axis) to be 100. We argue that the disturbance caused by the weak measurement, while small, is sufficient to significantly affect the measurement result, and that this is the most reasonable explanation of anomalous weak values.

A large literature has grown up around the proposed use of ‘weak measurements’ to allegedly provide information about hidden ontological features of quantum systems. This paper attempts to clarify the fact that ‘weak measurements’ involve strong measurements on one member of an entangled system. The only thing ‘weak’ about such measurements is that the correlation established via the entanglement does not correspond to eigenstates of the ‘weakly measured observable’ for the remaining component system subject to the weak measurement. All observed (...) statistics are straightforwardly and easily predicted by standard quantum mechanics. Specifically, it is noted that measurement of the pointer steers the remaining degree of freedom into new states with new statistical properties—constituting a non-trivial disturbance. In addition, standard quantum mechanics readily allows us to conditionalize on a final state if we choose, so the ‘post-selection’ that features prominently in time-symmetric formulations is also equipment from standard quantum theory. Assertions in the literature that weak measurements leave a system negligibly disturbed, and/or that standard quantum theory is cumbersome for computing the predicted measurement results, are therefore unsupportable, and ontological claims based on such assertions need to be critically reassessed. (shrink)

An attempt to solve the collapse problem in the framework of a time-symmetric quantum formalism is reviewed. Although the proposal does not look very attractive, its concept - a world defined by two quantum states, one evolving forwards and one evolving backwards in time - is found to be useful in modifying the many-worlds picture of Everett’s theory.