Bennett and Schumacher’s postselected quantum teleportation is a model of closed timelike curves (CTCs) that leads to results physically different from Deutsch’s model. We show that even a single qubit passing through a postselected CTC (P-CTC) is sufficient to do any postselected quantum measurement with certainty, and we discuss an important difference between “Deutschian” CTCs (D-CTCs) and P-CTCs in which the future existence of a P-CTC might affect the present outcome of an experiment. Then, based on a suggestion of Bennett (...) and Smith, we explicitly show how a party assisted by P-CTCs can distinguish a set of linearly independent quantum states, and we prove that it is not possible for such a party to distinguish a set of linearly dependent states. The power of P-CTCs is thus weaker than that of D-CTCs because the Holevo bound still applies to circuits using them, regardless of their ability to conspire in violating the uncertainty principle. We then discuss how different notions of a quantum mixture that are indistinguishable in linear quantum mechanics lead to dramatically differing conclusions in a nonlinear quantum mechanics involving P-CTCs. Finally, we give explicit circuit constructions that can efficiently factor integers, efficiently solve any decision problem in the intersection of NP and coNP, and probabilistically solve any decision problem in NP. These circuits accomplish these tasks with just one qubit traveling back in time, and they exploit the ability of postselected closed timelike curves to create grandfather paradoxes for invalid answers. (shrink)

Weak values are average quantities, therefore investigating their associated variance is crucial in understanding their place in quantum mechanics. We develop the concept of a position-postselected weak variance of momentum as cohesively as possible, building primarily on material from Moyal and Sonego :1135, 1991) . The weak variance is defined in terms of the Wigner function, using a standard construction from probability theory. We show this corresponds to a measurable quantity, which is not itself a weak value. It also leads (...) naturally to a connection between the imaginary part of the weak value of momentum and the quantum potential. We study how the negativity of the Wigner function causes negative weak variances, and the implications this has on a class of ‘subquantum’ theories. We also discuss the role of weak variances in studying determinism, deriving the classical limit from a variational principle. (shrink)

In the context of a discussion of time symmetry in the quantum mechanical measurement process, Aharonov et al. (1964) derived an expression concerning probabilities for the outcomes of measurements conducted on systems which have been pre- and postselected on the basis of both preceding and succeeding measurements. Recent literature has claimed that a resulting "time-symmetrized" interpretation of quantum mechanics has significant implications for some basic issues, such as contextuality and determinateness, in elementary, nonrelativistic quantum mechanics. Bub and Brown (1986) have (...) shown that under the standard interpretation of the aforementioned expression, these claims employ ensembles which are not well defined. It is argued here that under a counterfactual interpretation of the expression, these claims may be understood as employing well-defined ensembles; it is shown, however, that such an interpretation cannot be reconciled with the standard interpretation of quantum mechanics. (shrink)

Recently various gedankenexperiments have been formulated which argue that the assumption that “elements of reality” are Lorentz invariant cannot be reconciled with standard quantum mechanics. Two of these gedankenexperiments were subsequently analyzed using the notion of pre- and postselected quantum systems, and it was claimed that elements of reality can be made Lorentz invariant if the “product rule” of standard quantum mechanics is abandoned. In this paper we show that the apparent violations of the product rule in these gedankenexperiments are (...) not as significant as they appeared to be in the previous analysis. We conclude that the problems with Lorentz invariance which arise in these gedankenexperiments are essentially unrelated to the product rule violations. (shrink)

Proposed models of closed timelike curves have been shown to enable powerful information-processing protocols. We examine the simulation of models of CTCs both by other models of CTCs and by physical systems without access to CTCs. We prove that the recently proposed transition probability CTCs are physically equivalent to postselection CTCs, in the sense that one model can simulate the other with reasonable overhead. As a consequence, their information-processing capabilities are equivalent. We also describe a method for quantum computers (...) to simulate Deutschian CTCs. In cases for which the overhead is reasonable, it might be possible to perform the simulation in a table-top experiment. This approach has the benefit of resolving some ambiguities associated with the equivalent circuit model of Ralph et al. Furthermore, we provide an explicit form for the state of the CTC system such that it is a maximum-entropy state, as prescribed by Deutsch. (shrink)

A novel description of quantum systems is employed for constructing a “time machine” capable of shifting in time the wave function of a quantum system. This device uses gravitational time dilations and a peculiar quantum interference effect due to preselection and postselection. In most trials this time machine fails to operate but when it does succeed it accomplishes tasks which no other machine can.

Entangled states provide the necessary tools for conceptual tests of quantum mechanics and other alternative theories. These tests include local hidden variables theories, pre- and postselective quantum mechanics, QND measurements, complementarity, and tests of quantum mechanics itself against, e.g., the so-called causal communication constraint. We show how to produce various nonlocal entangled states of multiple cavity fields that are useful for these tests, using cavity QED techniques. First, we discuss the generation of the Bell basis states in two entangled cavities, (...) when there is at most one photon in either of the cavities, and then a straightforward generalization to similar N-cavity states. We then show how to produce a nonlocal entangled state when there is precisely one photon hiding in three cavities. These states can be produced by sending appropriately prepared atoms through the cavities. As applications we briefly review two proposals: one to test quantum mechanics against the causal communication constraint using a two-cavity entangled state and the other to test pre- and postselective quantum mechanics using a three-cavity entangled state. The outcome of the latter experiment can be discussed from the viewpoint of the consistent histories interpretation of quantum mechanics and therefore provides an opportunity to subject quantum cosmological ideas to laboratory tests. Finally, we point out the relation between these schemes and the schemes suggested for quantum computing, teleportation, and quantum copying. (shrink)

We investigate the thesis of Aharonov, Bergmann, and Lebowitz that time-symmetry holds in ensembles defined by both an initial and a final condition, called preand postselected ensembles. We distinguish two senses of time symmetry and show that the first one, concerning forward directed and time reversed measurements, holds if the measurement process is ideal, but fails if the measurement process is non-ideal, i.e., violates Lüders's rule. The second kind of time symmetry, concerning the interchange of initial and final conditions, fails (...) even in the case of ideal measurements. Bayes's theorem is used as a primary tool for calculating the relevant probabilities. We are critical of the concept that a pair of vectors in Hilbert space, characterizing the initial and final conditions, can be considered to constitute a generalized quantum state. (shrink)