Atomic indirect measurement for efficient quantum optical communication using a squeezed binary phase-shift-keying signal

Min Namkung and Jeong San Kim

Phys. Rev. A 108, 012611 – Published 12 July 2023

Abstract

A squeezed-displaced state can be used as an optical signal for efficient binary quantum optical communication. Here, we consider quantum optical communication where an atomic indirect measurement is used to decide the message encoded in a binary phase-shift-keying signal composed of squeezed-displaced states, and show that the incorrect decision probability of an atomic indirect measurement can be less than that of a homodyne measurement. We further show that an atomic indirect measurement can lower the incorrect decision probability even when the quantum channel is exposed to weak phase-diffusion noise.

Received 24 March 2023
Accepted 29 June 2023

DOI:https://doi.org/10.1103/PhysRevA.108.012611

Physics Subject Headings (PhySH)

Quantum communication Quantum communication, protocols & technology Quantum information processing Quantum measurements

Quantum Information, Science & Technology

Authors & Affiliations

Min Namkung^1,2 and Jeong San Kim ^2,*

¹Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
²Department of Applied Mathematics and Institute of Natural Sciences, Kyung Hee University, Yongin 17104, Korea

^*freddie1@khu.ac.kr

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Issue

Vol. 108, Iss. 1 — July 2023

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Images

Figure 1
Schematic of a binary communication including the preparation of the optical signal composed of squeezed-displaced states. In preparation of the signal, Alice performs a squeezing process on the vacuum state, and encodes her binary message $x \in {0, 1}$ on the optical signal by performing the displacement process on the squeezed vacuum. She sends the optical signal to Bob through a quantum channel exposed to phase-diffusion noise, which transforms a squeezed-displaced state $| z, α_{x} 〉$ to a noisy quantum state $τ_{z, x}$ . Then, Bob obtains an outcome $y \in {0, 1}$ by measuring the transmitted optical signal with a quantum measurement, and decides Alice's binary message from this outcome.
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Figure 2
Schematic of atomic indirect measurement. Here, $τ_{r, x}$ is the transmitted squeezed-displaced state with respect to the binary message $x$ , $| g 〉$ is the ground state of the two-level atom, $U (Φ)$ is the unitary operator describing the Jaynes-Cummings interaction, $Π$ is the projective measurement on the atomic system, and $y$ is the measurement outcome.
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Figure 3
The incorrect decision probability of deciding an encoded binary message when the equiprobable BPSK signal with a squeezing operation is transmitted through an ideal quantum channel. We consider $0 \leq \bar{n} \leq 1.0$ in both figures, and the squeezing parameter $r = 0.1$ and $r = 0.2$ in (a) and (b), respectively. The thick solid red lines show the minimum incorrect decision probability over all possible atomic indirect measurements. The dashed red lines show the minimum incorrect decision probability in the case of $r = 0$ . The dotted black lines show the incorrect decision probability from the homodyne measurement. The solid blue lines show the Helstrom bound of the ideal squeezed-displaced states.
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Figure 4
The incorrect decision probability of deciding an encoded binary message when the equiprobable BPSK signal with a squeezing operation is transmitted through a phase-diffusion quantum channel with $0 \leq σ \leq 1.2$ . In (a) and (b), the mean photon number is $\bar{n} = 3$ , and the squeezing parameter, respectively, $r = 0.1$ and $r = 0.2$ . In (c) and (d), we consider $\bar{n} = 0.5$ , and $r = 0.1$ and $r = 0.2$ , respectively. The thick solid red lines show the minimum incorrect decision probability over all possible atomic indirect measurements. The dashed red lines show the minimum incorrect decision probability in the case of $r = 0$ . The dotted black lines show the incorrect decision probability from the homodyne measurement. The solid blue lines show the Helstrom bound of the squeezed-displaced states exposed to phase-diffusion noise.
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