Necessary condition for information transfer under simulated parity-time-symmetric evolution

TL;DR

This paper investigates the conditions under which information transfer occurs in PT-symmetric quantum evolution, revealing that complex-valued states and measurements are necessary, and linking entanglement to transfer efficiency.

Contribution

It establishes a necessary condition for information transfer in PT-symmetric evolution, emphasizing the role of complex states and measurements, and explores how entanglement influences transfer efficacy.

Findings

Information transfer requires complex density matrices and measurements.

PT-symmetric evolution alone is not sufficient for information transfer.

Higher-dimensional states enhance the efficiency of information transfer.

Abstract

Parity-time (PT) symmetric quantum theory can broaden the scope of quantum dynamics beyond unitary evolution which may lead to numerous counter-intuitive phenomena, including single-shot discrimination of non-orthogonal states, faster evolution of state than the standard quantum speed limit, and violation of no-signaling principle. On the other hand, PT-symmetric evolution can be realized as reduced dynamics of a subsystem in real experiments within the scope of standard quantum theory. In this experimental setup, if one side of a composite system is evolved according to a PT-symmetric way, a non-trivial information transfer can happen, i.e., the operation performed at one side can be gathered by the other side. By considering an arbitrary shared state between two parties situated in two distant locations and arbitrary measurements, we show that the PT-symmetric evolution of the reduced subsystem at one side is not sufficient for this information transfer to occur. Specifically, we prove that the information transfer can only happen when the density matrix and the corresponding measurements contain complex numbers. Moreover, we connect the entanglement content of the shared state with the efficacy of information transfer. We find evidence that the task becomes more efficient with the increase of dimension.