Near-optimal coherent state discrimination via continuously labelled non-Gaussian measurements

Abstract

Quantum state discrimination plays a central role in quantum information and communication. For the discrimination of optical quantum states, the two most widely adopted measurement techniques are photon detection, which produces discrete outcomes, and homodyne detection, which produces continuous outcomes. While various protocols using photon detection have been proposed for optimal and near-optimal discrimination between two coherent states, homodyne detection is known to have higher error rates, with its minimum achievable error rate often referred to as the Gaussian limit. In this work, we demonstrate that, despite the fundamental differences between discretely labelled and continuously labelled measurements, continuously labelled non-Gaussian measurements can also achieve near-optimal coherent state discrimination. We design two discrimination protocols that surpass the Gaussian limit: one using non-Gaussian unitary operations with homodyne detection, and another based on orthogonal polynomials. Our results show that photon detection is not required for near-optimal coherent state discrimination and that we can achieve error rates close to the Helstrom bound at low energies with continuously labelled measurements. We also find that our schemes maintain an advantage over the photon detection-based Kennedy receiver for a moderate range of coherent state amplitudes.

Figures (10)

• Figure 1: A pictorial representation of the two types of continuously labelled non-Gaussian measurement schemes considered in this work. Type A refers to a non-Gaussian unitary preprocessing of the coherent states followed by Gaussian detection. Type B refers to a continuously labelled non-Gaussian measurement which is unitarily inequivalent to type A.
• Figure 2: Comparison of the two best performing near-optimal continuously labelled receivers in Tab. \ref{['POVMtab']} versus the homodyne, Kennedy and Helstrom limits in the energy range $0<\abs{\alpha}^2<0.7$. Here we find that the cat state rotation and coherent state rotation perform best
• Figure 3: Comparison of the two best performing near-optimal continuously labelled receivers in Tab. \ref{['POVMtab']} versus the homodyne, Kennedy and Helstrom limits in the energy range $0.5<\abs{\alpha}^2<3$. Here we find that the coherent state rotation and Legendre states perform best
• Figure 4: Performance of the $\textrm{DFS}_n$-based receivers $\hat{\Pi}_{\beta;1}$ and $\hat{\Pi}_{\beta;2}$, and CPG-based receivers for $\gamma=0.1$ and $\gamma=1$ versus homodyne detection.
• Figure 5: Error rates for Fock state rotation based receivers, $\hat{\Pi}^{(N)}_{\left\{\ket{k}\right\}}$, for different values of $N$ with $\abs{\mathcal{S}_1}=1, \abs{\mathcal{S}_2}=3$, and $\abs{\mathcal{S}_3}=5$ corresponding to the sets in \ref{['focksets']}. We find that the error rate decreases with increasing $N$. The performance of the receiver in PhysRevA.51.1702 based on a Kerr gate combined with homodyne detection is also shown.

Theorems & Definitions (3)

• Definition 1
• Definition 2
• Definition 3