Quantum Discrimination of Two Noisy Displaced Number States

TL;DR

This paper investigates the quantum discrimination of noisy displaced number states, deriving their Fock representation, and demonstrates that the Kennedy receiver with threshold detection optimally discriminates these states, reducing error probability.

Contribution

It introduces the Fock representation for noisy displaced number states and proves the Kennedy receiver's optimality for their discrimination.

Findings

Optimal discrimination achieved by Kennedy receiver with threshold detection.

Error probability for displaced number states is lower than for coherent states at same energy.

Simulation results confirm theoretical predictions.

Abstract

The quantum discrimination of two non-coherent states draws much attention recently. In this letter, we first consider the quantum discrimination of two noiseless displaced number states. Then we derive the Fock representation of noisy displaced number states and address the problem of discriminating between two noisy displaced number states. We further prove that the optimal quantum discrimination of two noisy displaced number states can be achieved by the Kennedy receiver with threshold detection. Simulation results verify the theoretical derivations and show that the error probability of on-off keying modulation using a displaced number state is significantly less than that of on-off keying modulation using a coherent state with the same average energy.