PT-symmetric quantum state discrimination

TL;DR

This paper explores how PT-symmetric Hamiltonians can redefine the inner product in quantum mechanics, enabling perfect discrimination between non-orthogonal states with a single measurement, which is impossible in standard quantum theory.

Contribution

It introduces a method using PT-symmetric Hamiltonians to achieve perfect quantum state discrimination for non-orthogonal states.

Findings

PT-symmetric Hamiltonians can orthogonalize non-orthogonal states

Single-measurement discrimination becomes possible

Redefines the inner product in quantum state space

Abstract

Suppose that a system is known to be in one of two quantum states, $|\psi_1 > $ or $|\psi_2 >$. If these states are not orthogonal, then in conventional quantum mechanics it is impossible with one measurement to determine with certainty which state the system is in. However, because a non-Hermitian PT-symmetric Hamiltonian determines the inner product that is appropriate for the Hilbert space of physical states, it is always possible to choose this inner product so that the two states $|\psi_1 > $ and $|\psi_2 > $ are orthogonal. Thus, quantum state discrimination can, in principle, be achieved with a single measurement.