The Two-State Vector Formalism of Quantum Mechanics

Yakir Aharonov, Daniel Rohrlich

Patryk Michalski, Andrzej Dragan

Abstract The two-state vector formalism of quantum mechanics is a time-symmetrized approach to standard quantum theory. In our work, we aim to establish rigorous foundations for the future investigation within this formalism. We introduce the concept of a story—a compatible pair consisting of a two-state vector and an ideal measurement. Using this concept, we examine the structure of the space comprising all two-state vectors. We analyze the problem of distinguishability and confirm that some pairs of two-state vectors or their statistical mixtures cannot be physically distinguished. In particular, we discuss an example of a two-state vector that is indistinguishable from a statistical mixture of separable two-state vectors and provide an example of a two-state vector that can be distinguished from every such mixture. This leads us to formulate the definition of a strictly non-separable two-state vector as a genuine manifestation of entanglement between the past and the future.

Sol Wieder

Lev Vaidman A

The two-state vector formalism (TSVF), the time-symmetric description of the standard quantum mechanics originated by Aharonov, Bergmann and Lebowitz is reviewed. The TSVF describes a quantum system at a particular time by two quantum states: the usual one, evolving forward in time, defined by the results of a complete measurement at the earlier time, and by the quantum state evolving backward in time, defined by the results of a complete measurement at a later time.

Yakir Aharonov, Lev Vaidman A

In this paper we present the two-state vector formalism of quantum mechanics. It is a time-symmetrized approach to standard quantum theory particularly helpful for the analysis of experiments performed on pre- and post-selected ensembles. Several peculiar effects which naturally arise in this approach are considered. In particular, the concept of ``weak measurements'' (standard measurements with weakening of the interaction) is discussed in depth revealing a very unusual but consistent picture. Also, a design of a gedanken experiment which implements a kind of quantum ``time machine'' is described. The issue of time-symmetry in the context of the two-state vector formalism is clarified.

Lampros A. A. Nikolopoulos