On the equivalence of lossy evolution and POVM generalized quantum measurements

TL;DR

This paper establishes a complete equivalence between lossy quantum evolution and a broad class of POVM measurements, including those used for state discrimination and entanglement concentration, with implications for quantum measurement schemes.

Contribution

It extends the concept of loss-induced measurements to show a full equivalence with certain POVMs, including those for unambiguous state discrimination.

Findings

Lossy evolution can implement a wide class of POVMs.

PT-symmetric and non-Hermitian Hamiltonian schemes have equivalent performance to standard POVMs.

Theoretical and physical realizations demonstrate the equivalence.

Abstract

Loss induced generalized measurements have been introduced years ago as a mean to implement generalized quantum measurements (POVM). Here the original idea is extended to a complete equivalence of lossy evolution and a certain widely used class of POVM. This class includes POVM used for unambiguous state discrimination and entanglement concentration. One implication of this equivalence is that unambiguous state discrimination schemes based on PT-symmetric and non-Hermitian Hamiltonians have the same performance as those of standard POVM. After discussing several key points of this equivalence we illustrate our findings in two elementary physical realizations. Finally, we discuss several implications of this equivalence.