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IEEE Middle East and North Africa Communications Conference (MENACOMM)

Optimal detection with squeezed state for quantum communication in thermal noise channel

Yaoyao Wang, Rong Zhang, Bin Feng Lu, Xiaoguang Chen

Published Dec 6, 2022• 0 citations
Publisher

Abstract

Pulse position modulation (PPM) is widely adopted in free space optical transmission, and is a candidate for deep space transmission, also in quantum form. The change of signal photon number probability distribution is caused by thermal noise in quantum PPM format. We prove that squeezing improves state discrimination at fixed channel energy, and also in the presence of thermal noise. Then we compare the difference between coherent state and squeezed state in thermal noise and reveal that the squeezed state has better robustness. It is shown that for the fixed channel energy, the larger the squeezed parameter is not the better. For some given total channel energies, we further study and get the optimal squeezed parameter. Finally, combined with the actual situation, the simulation results show that, as a resource for noisy quantum communication channels, the squeezing operation can improve the quality of deep space quantum communication system with PPM.

DOI
10.1109/menacomm57252.2022.9998300

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•Nov 11, 2010•1 citation
Pulse position modulation (PPM) is widely adopted in free space optical transmission, and is a candidate for deep space transmission, also in quantum form. The change of signal photon number probability distribution is caused by thermal noise in quantum PPM format. We prove that squeezing improves state discrimination at fixed channel energy, and also in the presence of thermal noise. Then we compare the difference between coherent state and squeezed state in thermal noise and reveal that the squeezed state has better robustness. It is shown that for the fixed channel energy, the larger the squeezed parameter is not the better. For some given total channel energies, we further study and get the optimal squeezed parameter. Finally, combined with the actual situation, the simulation results show that, as a resource for noisy quantum communication channels, the squeezing operation can improve the quality of deep space quantum communication system with PPM.
Pulse position modulation(PPM) is an excellent modulation form that is widely used for deep-space information transmission and also in quantum modulation form. Lots of related work proved that the squeezed state is superior to the traditional coherent state modulation in 3-PPM modulation. In this paper, a new modulation method is proposed, that is, two squeezed states are applied to 3-PPM modulation. Compared with one squeezed state modulation, it is found that the two squeezed state modulation has lower error probability.
The paper deals with quantum pulse position modulation (PPM), both in the absence (pure states) and in the presence (mixed states) of thermal noise, using the Glauber representation of coherent laser radiation. The objective is to find optimal (or suboptimal) measurement operators and to evaluate the corresponding error probability. For PPM, the correct formulation of quantum states is given by the tensorial product of m identical Hilbert spaces, where m is the PPM order. The presence of mixed states, due to thermal noise, generates an optimization problem involving matrices of huge dimensions, which already for 4-PPM, are of the order of ten thousand. To overcome this computational complexity, the currently available methods of quantum detection, which are based on explicit results, convex linear programming and square root measurement, are compared to find the computationally less expensive one. In this paper a fundamental role is played by the geometrically uniform symmetry of the quantum PPM format. The evaluation of error probability confirms the vast superiority of the quantum detection over its classical counterpart.
We consider the discrimination of lossy bosonic channels and focus on the case when one of the values for the loss parameter is zero, i.e., we address the detection of a possible loss against the alternative hypothesis of an ideal lossless channel. This discrimination is performed by inputting one- or two-mode squeezed thermal states with fixed total energy. By optimizing over this class of states, we find that the optimal inputs are pure, thus corresponding to single- and two-mode squeezed vacuum states. In particular, we show that, for any value of the damping rate smaller than a critical value, there is a threshold on the energy that makes the two-mode squeezed vacuum state more convenient than the corresponding single-mode state, whereas for damping larger than this critical value, two-mode squeezed vacua are always better. We then consider the discrimination in realistic conditions, where it is unlikely to have pure squeezing. Thus, by fixing both input energy and squeezing, we show that two-mode squeezed thermal states are always better than their single-mode counterpart when all the thermal photons are directed into the dissipative channel. Aside from that, this result also holds approximately for unbalanced distribution of the thermal photons. Finally, we also investigate the role of correlations in the improvement of detection. For fixed input squeezing (single mode or two mode), we find that the reduction of the quantum Chernoff bound is a monotone function of the two-mode entanglement as well as the quantum mutual information and the quantum discord. We thus verify that employing squeezing in the form of correlations (quantum or classical) is always a resource for loss detection whenever squeezed thermal states are taken as input.
This paper introduces the use of photon-added squeezed states (PASSs) for quantum pulse position modulation (QPPM). It is shown that the use of PASSs in QPPM communication systems can reduce the symbol error probability (SEP) with respect to the use of different classes of quantum states with the same energy, including squeezed states and photon-added coherent states. The impact of thermal noise and phase diffusion on the SEP is also evaluated. The findings of this paper show the utility of PASSs in quantum communication systems.
We introduce a squeezed-state pulse-position modulation (S-PPM) format, where the empty slots are squeezed vacuum states and the pulse slot is a displaced squeezed state. Based on this property, we propose an inverse-squeezing conditional pulse-nulling (IS-CPN) receiver. In the ideal case, inverse squeezing maps S-PPM into an equivalent coherent-state PPM signal with a large pulse energy, leading to a closed-form expression for the receiver error probability. We further analyze IS-CPN under common phase diffusion using a finite-path MAP formulation with phase-averaged likelihoods. Numerical results show that IS-CPN outperforms conventional CPN under the same energy constraint and remains advantageous under phase noise and finite photon-number resolution. These results demonstrate that combining squeezed-state modulation with inverse-squeezing conditional nulling can improve photon-efficient optical communication.
We consider the discrimination of lossy bosonic channels and focus to the case when one of the values for the loss parameter is zero, i.e., we address the detection of a possible loss against the alternative hypothesis of an ideal lossless channel. This discrimination is performed by inputting one-mode or two-mode squeezed thermal states with fixed total energy. By optimizing over this class of states, we find that the optimal inputs are pure, thus corresponding to single- and two-mode squeezed vacuum states. In particular, we show that for any value of the damping rate smaller than a critical value there is a threshold on the energy that makes the two-mode squeezed vacuum state more convenient than the corresponding single-mode state, whereas for damping larger than this critical value two-mode squeezed vacua are always better. We then consider the discrimination in realistic conditions, where it is unlikely to have pure squeezing. Thus by fixing both input energy and squeezing, we show that two-mode squeezed thermal states are always better than their single- mode counterpart when all the thermal photons are directed into the dissipative channel. Besides, this result also holds approximately for unbalanced distribution of the thermal photons. Finally, we also investigate the role of correlations in the improvement of detection. For fixed input squeezing (single-mode or two-mode), we find that the reduction of the quantum Chernoff bound is a monotone function of the two-mode entanglement as well as the quantum mutual information and the quantum discord. We thus verify that employing squeezing in the form of correlations (quantum or classical) is always a resource for loss detection whenever squeezed thermal states are taken as input.