PT and Anti-PT Symmetry Arising in Time Dependent Weak Value Measurements

TL;DR

This paper explores how time-dependent weak value measurements reveal PT and anti-PT symmetries in Hamiltonians, providing insights into non-Hermitian quantum mechanics and potential implications for quantum interpretations.

Contribution

It extends the formalism of time-dependent weak values to demonstrate PT and anti-PT symmetries in Hamiltonians during measurements, linking weak measurement theory with non-Hermitian quantum mechanics.

Findings

Hamiltonians exhibit PT or anti-PT symmetry during weak measurements

Pointer translations reflect these symmetries via real or imaginary parts

Potential to distinguish quantum interpretations based on symmetry properties

Abstract

Parks introduced a formulation of time dependent weak values in 2008, which is the formalism we use in this paper. In this paper we extend notions from time dependent weak values to show that Hamiltonians associated with weak value measurements can be shown to exhibit even or odd symmetric properties. They exhibit PT or anti-PT symmetry, respectively. These symmetries are manifested during the measurement process as pointer translations, which have vanishing imaginary or vanishing real parts. The consequence of this that one can characterize some of the aspects of these symmetries of the time dependent Hamiltonians that arise from time dependent weak values. This allows one to generalize some work on non-Hermitian variables in quantum mechanics (QM) due to Bender related to weak values and weak measurement. We also speculate how these symmetries might apply to distinguishing between the various two-time interpretations of QM in the Conclusions of this paper.