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Quantum Discrimination of Noisy Photon-Subtracted Squeezed States

Andrea Giani, Moe Z. Win, Andrea Conti

Published Dec 4, 2022• 5 citations
Publisher

Abstract

Quantum state discrimination (QSD) is crucial for various applications of quantum sensing, communications, and computing. This paper characterizes the binary QSD with photon-subtracted squeezed states (PSSSs) affected by thermal noise during state preparation. First, noisy PSSSs are charac-terized and their Fock representation is given. Then, the binary QSD problem with noisy PSSSs affected by phase diffusion is presented. Finally, it is shown the suitability of PSSSs for QSD-based applications, especially when employing quantum states with unbalanced prior probabilities.

DOI
10.1109/globecom48099.2022.10001626

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Quantum state discrimination (QSD) is crucial for various applications of quantum sensing, communications, and computing. This paper characterizes the binary QSD with photon-subtracted squeezed states (PSSSs) affected by thermal noise during state preparation. First, noisy PSSSs are charac-terized and their Fock representation is given. Then, the binary QSD problem with noisy PSSSs affected by phase diffusion is presented. Finally, it is shown the suitability of PSSSs for QSD-based applications, especially when employing quantum states with unbalanced prior probabilities.
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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.
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 the photon-subtracted squeezed coherent state (PSSCS), which is theoretically constructed by repeatedly subtracting photons from the squeezed coherent state (SCS) with squeezing parameter r and displacement amplitude α=|α|eiφ. Employing the normal ordering form of density operator of the SCS, we study the nonclassicality of the PSSCS by analyzing Mandel’s Q-parameter, quadratures squeezing, photon-number distribution (PND), and Wigner function (WF). We find that the PND in a PSSCS is a periodic function of φ with a period π and exhibits more remarkable oscillations than that of a SCS in the case of strong squeezing. The partial negative region of the WF is sensitive to r and |α|. The fidelity between PSSCS and SCS is analyzed, which manifests that larger photon subtraction number may result in lower fidelity. By virtue of the thermal entangled state representation the decoherence of the PSSCS in thermal environment is studied through the time evolution of the WF. The negative volume of the WF gradually diminishes with the increase of evolution time and thermal photon number, respectively. The study of the PSSCS shows that generating new photon-number-controllable nonclassical states from a weak coherent light may be realized by subtracting suitable photons from a SCS.
The so-called quasi-Bell entangled coherent states in a thermal environment are studied. In the analysis, we assume thermal noise affects only one of the two modes of each state. First the matrix representation of the density operators of the quasi-Bell entangled coherent states in a thermal environment is derived. Secondly we investigate the entanglement property of one of the quasi-Bell entangled coherent states with thermal noise. At that time a lower bound of the entanglement of formation for the state is computed. Thirdly the minimax discrimination problem for two cases of the binary set of the quasi-Bell entangled coherent states with thermal noise is considered, and the error probabilities of the minimax discrimination for the two cases are computed with the help of Helstrom's algorithm for finding the Bayes optimal error probability of binary states.