The Two-State Vector Formalism: An Updated Review

Abstract

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.

Can the two-time interpretation of quantum mechanics solve the measurement problem?

“…The two-state vector formalism (TVSF) [4,1] alters the traditional formalism of QM by assigning an additional state vector Φ| to a system, as well as the usual state vector, |Ψ . The latter state vector |Ψ(t 0 ) unitarily evolves according to the Schrödinger equation, under U .…”

“…In section 3, I outline the key tenets of the TTI as well as its proposed solution to the measurement problem. 1 The two papers cited explicitly expound the TTI, but other papers such as [3] and [4] hint at it, since -as will become apparent shortly -the TTI naturally arises out of a wider research programme. 2 As usual, we model a measurement by a composite unitary operator U that takes the measuring device to one of several distinguishable (orthogonal) states depending on the system's state.…”

Extension of Information Geometry to Non-statistical Systems: Some Examples

“…Ref. [12] discusses the notions of pre and post selected states. The density matrix σ = |ψ ψ| of the present paper describes the preselected state.…”

“…The present paper tries to situate some recent insights in the context of quantum conditional expectations. In particular, weak measurement theory [11,12] is considered.…”

Protective Measurements

“…The protective measurements method can be extended to pre-and postselected systems described by a two-state vector Φ| |Ψ [14]. It requires separate different protections for the forward and backward evolving quantum states which are achieved by pre-and post-selection of quantum states of systems which provide the protection [15].…”