Exploring postselection-induced quantum phenomena with time-bidirectional state formalism

TL;DR

This paper introduces the time-bidirectional state formalism (TBSF), unifying standard quantum mechanics and postselected two-state formalisms, enabling analysis and tomography of quantum states with postselection effects, demonstrated through quantum teleportation experiments.

Contribution

The paper develops the TBSF framework, deriving measurement outcomes, and creating tomography protocols for postselected quantum states, bridging no-postselection and postselected formalisms.

Findings

TBSF unifies standard and postselected quantum formalisms.

Protocols for quantum state tomography using TBSF are proposed.

Experimental tracking of qubit time-reversal in quantum teleportation demonstrates TBSF's capabilities.

Abstract

Here we present the time-bidirectional state formalism (TBSF) unifying in a general manner the standard quantum mechanical formalism with no postselection and the time-symmetrized two-state (density) vector formalism, which deals with postselected states. In the proposed approach, a quantum particle's state, called a time-bidirectional state, is equivalent to a joined state of two particles propagating in opposite time directions. For a general time-bidirectional state, we derive outcome probabilities of generalized measurements, as well as mean and weak values of Hermitian observables. We also show how the obtained expressions reduce to known ones in the special cases of no postselection and generalized two-state (density) vectors. Then we develop tomography protocols based on mutually unbiased bases and a symmetric informationally complete positive operator-valued measure, allowing experimental reconstruction of an unknown single qubit time-bidirectional state. Finally, we employ the developed techniques for tracking of a qubit's time-reversal journey in a quantum teleportation protocol realized with a cloud-accessible noisy superconducting quantum processor. The obtained results justify an existence of a postselection-induced qubit's proper time-arrow, which is different from the time-arrow of a classical observer, and demonstrate capabilities of the TBSF for exploring quantum phenomena brought forth by a postselection in the presence of noise.