Transceiver designs to attain the entanglement assisted communications capacity

Abstract

Pre-shared entanglement can significantly boost communication rates in the high thermal noise and low-brightness transmitter regime. In this regime, for a lossy-bosonic channel with additive thermal noise, the ratio between the entanglement-assisted capacity and the Holevo capacity - the maximum reliable-communications rate permitted by quantum mechanics without any pre-shared entanglement - scales as $\log(1/{\bar N}_{\rm S})$, where the mean transmitted photon number per mode, ${\bar N}_{\rm S} \ll 1$. Thus, pre-shared entanglement, e.g., distributed by the quantum internet or a satellite-assisted quantum link, promises to significantly improve low-power radio-frequency communications. In this paper, we propose a pair of structured quantum transceiver designs that leverage continuous-variable pre-shared entanglement generated, e.g., from a down-conversion source, binary phase modulation, and non-Gaussian joint detection over a code word block, to achieve this scaling law of capacity enhancement. Further, we describe a modification to the aforesaid receiver using a front-end that uses sum-frequency generation sandwiched with dynamically-programmable in-line two-mode squeezers, and a receiver back-end that takes full advantage of the output of the receiver's front-end by employing a non-destructive multimode vacuum-or-not measurement to achieve the entanglement-assisted classical communications capacity.

Figures (12)

• Figure 1: The ratio $C_{\rm E}/C$ is plotted as a function of ${\bar{N}}_{\rm S}$ and ${\bar{N}}_{\rm B}$ for channel transmissivity, $\eta = 0.01$. Also shown is a plot of $\ln(1/{\bar{N}}_{\rm S})$, which is the scaling of $C_{\rm E}/C$ as ${\bar{N}}_{\rm S} \to 0$ and ${\bar{N}}_{\rm B} \to \infty$.
• Figure 2: Schematic of classical optical communications over a lossy, noisy channel. Each transmitted symbol of a length-$L$ code word is a single bosonic mode excited in a coherent state $|\alpha_{ji}\rangle$, $1 \le i \le L$, $1 \le j \le 2^{nR}$, which results in a displaced thermal state at the channel output: $\hat{\rho}_{\rm th}(\sqrt{\eta}\alpha_{ji}, (1-\eta){\bar{N}}_B)$ of mean field $\sqrt{\eta}\alpha_{ji}$ and mean thermal photon number $(1-\eta){\bar{N}}_B$. The total mean photon number of each received mode is ${\bar{N}}_S^\prime = \eta {\bar{N}}_S+(1-\eta){\bar{N}}_B$. To achieve the Holevo capacity, the ultimate limit to the reliable communication rate, the receiver must perform a joint quantum measurement on a long code word block. Such a receiver is called a joint-detection receiver (JDR).
• Figure 3: Photon information efficiency (bits per photon) plotted as a function of the mean transmitted photon number per mode ${\bar{N}}_S$, for the lossless ($\eta = 1$), noiseless (${\bar{N}}_B=0$) bosonic channel. These plots can be also interpreted as the bits per photon attained for the pure-loss bosonic channel ($\eta \in (0, 1]$), with the x-axis re-labeled $\eta {\bar{N}}_S$. A detailed description of the assumptions on the modulation and receiver choices for the various plots, appear in the main text.
• Figure 4: Schematic of a JDR for BPSK-modulated Hadamard and the 1st order Reed Muller (RM) codes. The Green Machine (GM) receiver front-end transforms $L$ Hadamard code words into $L$-ary pulse-position modulation (PPM) with a single pulse of mean field $\sqrt{L\eta}\alpha$ at one output mode. Single-photon detectors at each of the $L$ outputs of the GM are used to identify the pulse-containing mode. If a RM code is used, the GM transforms the $2L$ RM code words into binary-phase-coded PPM. Single photon detectors are employed at each GM output to identify the pulse-containing mode. An electro-optic switch directs the remaining pulse (in the pulse-containing mode), after the arrival of the first photon click, to a Kennedy receiver Ken73 to identify the binary phase of that pulse.
• Figure 5: Ratios of the entanglement-assisted capacities for specific binary modulation formats and the ultimate classical (Holevo) capacity without pre-shared entanglement $C$, plotted as a function of $\bar{N}_S$ for $\eta=0.1$ and $\bar{N}_B=1$. $M=1$ is assumed for all the $C_E$ plots.