If operations in a quantum computer were conditioned on the results of a subsequent post-selection measurement, then NP-complete problems could be solved in polynomial time. Using the natural connection between post-selection and NP, we... more
If operations in a quantum computer were conditioned on the results of a subsequent post-selection measurement, then NP-complete problems could be solved in polynomial time. Using the natural connection between post-selection and NP, we show that this result is un-physical by considering constraints on new kinds of measurements which depend on the future post-selection in a non-trivial way. We review
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We introduce a new type of weak measurement which yields a quantum average of weak values that is robust, outside the range of eigenvalues, extends the valid regime for weak measurements, and for which the probability of obtaining the... more
We introduce a new type of weak measurement which yields a quantum average of weak values that is robust, outside the range of eigenvalues, extends the valid regime for weak measurements, and for which the probability of obtaining the pre- and post-selected ensemble is not exponentially rare. This result extends the applicability of weak values, shifts the statistical interpretation previously
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A review of new aspects concerning time-symmetry in Quantum Mechanics.
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Weak values are the outcomes of weak measurements and were discovered by studying the time-symmetric aspects of quantum mechanics. This resulted in new approaches to quantum cryptography and new resources for quantum information. In this... more
Weak values are the outcomes of weak measurements and were discovered by studying the time-symmetric aspects of quantum mechanics. This resulted in new approaches to quantum cryptography and new resources for quantum information. In this article, new non-statistical aspects of weak measurements are introduced. Contary to past results, this outcome is not rare, suggesting that weak values are a property
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Systems evolving according to effective non-Hermitian Hamiltonians are considered. To each eigenvalue of the effective Hamiltonian is associated two eigenstates which evolve backward and forward in time, respectively. Adiabatic... more
Systems evolving according to effective non-Hermitian Hamiltonians are considered. To each eigenvalue of the effective Hamiltonian is associated two eigenstates which evolve backward and forward in time, respectively. Adiabatic measurements on such systems are analyzed. The outcome of the adiabatic measurement of an observable A is the weak value / associated with the two-state vector . The possibility of performing
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We have establish a more rigorous formulation of the AV-formula by illustrating how it can be derived from the Projection Theorem. This connection with the Projection Theorem enables us to establish an additional formula as well as show... more
We have establish a more rigorous formulation of the AV-formula by illustrating how it can be derived from the Projection Theorem. This connection with the Projection Theorem enables us to establish an additional formula as well as show how to calculate the higher powers of the observable in terms of the formulas for Â|Psi> and Â|Psi⊥>. Additionally discussed the relevance
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We discuss color transparency in the nuclear QCD context from the perspective of pre- and post-selected ensembles. We show that the small size of the hadronic states can be explained by the peculiar 'force of... more
We discuss color transparency in the nuclear QCD context from the perspective of pre- and post-selected ensembles. We show that the small size of the hadronic states can be explained by the peculiar 'force of post-selection', in contrast to the more standard explanation based on external forces.
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We develop an approach to quantum interference phenomenon which makes the characteristics of the problem more conspicuous and brings out more physical concepts. We do this by discussing the idea of deterministic quantum experiments using... more
We develop an approach to quantum interference phenomenon which makes the characteristics of the problem more conspicuous and brings out more physical concepts. We do this by discussing the idea of deterministic quantum experiments using the Heisenberg picture. The variables that are relevant for describing interference are modular variables. These variables obey non-local equations of motion and can be used to follow the time evolution of a system without disturbing it. We present a physical explanation for the different behaviors of a single particle when the distant slit is open or closed: instead of having a quantum wave that passes through all slits, we have a localized particle with non-local interactions with the other slit(s). While the Heisenberg picture and the Schrodinger pictures are equivalent formulations of quantum mechanics, nevertheless, the results discussed here support a new approach to quantum mechanics which has led to new insights, new intuitions, new experiments, and even the possibility of new devices that were missed from the old perspective.
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Classical-realistic analysis of entangled systems have lead to retrodiction paradoxes, which ordinarily have been dismissed on the grounds of counter-factuality. Instead, we claim that such paradoxes point to a deeper logical structure... more
Classical-realistic analysis of entangled systems have lead to retrodiction paradoxes, which ordinarily have been dismissed on the grounds of counter-factuality. Instead, we claim that such paradoxes point to a deeper logical structure inherent to quantum mechanics, which is naturally described in the language of weak values, and which is accessible experimentally via weak measurements. Using as an illustration, a gedanken-experiment due to Hardy\cite{hardy}, we show that there is in fact an exact numerical coincidence between a) a pair of classically contradictory assertions about the locations of an electron and a positron, and b) the results of weak measurements of their location. The internal consistency of these results is due to the novel way by which quantum mechanics "resolves" the paradox: first, by allowing for two distinguishable manifestations of how the electron and positron can be at the same location: either as single particles or as a pair; and secondly, by allowing these properties to take either sign. In particular, we discuss the experimental meaning of a {\em negative} number of electron-positron pairs.