Distinguishability of Gaussian States in Quantum Cryptography using Post-Selection

TL;DR

This paper analyzes how well Gaussian states can be distinguished in quantum cryptography using post-selection, showing that mixed states do not provide more information to eavesdroppers than pure states, and exploring the effects of squeezing on information rates.

Contribution

It demonstrates that mixed symmetric Gaussian states do not increase eavesdropper advantage over pure states and examines how squeezing affects information distinguishability.

Findings

Mixed symmetric Gaussian states do not give more information than pure states.

Varying squeezing alters the information rates, causing squeezing and anti-squeezing effects.

Distinguishability depends on the type of Gaussian states and squeezing parameters.

Abstract

We consider the distinguishability of Gaussian states from the view point of continuous-variable quantum cryptography using post-selection. Specifically, we use the probability of error to distinguish between two pure coherent (squeezed) states and two particular mixed symmetric coherent (squeezed) states where each mixed state is an incoherent mixture of two pure coherent (squeezed) states with equal and opposite displacements in the conjugate quadrature. We show that the two mixed symmetric Gaussian states (where the various components have the same real part) never give an eavesdropper more information than the two pure Gaussian states. Furthermore, when considering the distinguishability of squeezed states, we show that varying the amount of squeezing leads to a "squeezing" and "anti-squeezing" of the net information rates.