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arXiv:2406.17727 · Optics Express

Re-examination of the role of displacement and photon catalysis operation in continuous variable measurement device-independent quantum key distribution

Chandan Kumar, Arvind

Published Nov 8, 2024• 3 citations
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Abstract

We investigate the benefits of using m -photon catalyzed two-mode squeezed coherent ( m -PCTMSC) state in continuous variable measurement device-independent quantum key distribution (CV-MDI-QKD). To that end, we derive the Wigner characteristic function of the m -PCTMSC state and show that the 0-PCTMSC state is a Gaussian state and is an inferior choice as compared to the zero photon catalyzed two-mode squeezed vacuum state for CV-MDI-QKD. We carry out the optimization of the secret key rate with respect to all state parameters, namely variance, transmissivity, and displacement. Contrary to many recent proposals, the results show that zero- and single-photon catalysis operation provides only a marginal benefit in improving the maximum transmission distance. Secondly, we find that displacement offers no benefit in improving CV-MDI-QKD.

DOI
10.1364/oe.546946

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We investigate the benefits of using m -photon catalyzed two-mode squeezed coherent ( m -PCTMSC) state in continuous variable measurement device-independent quantum key distribution (CV-MDI-QKD). To that end, we derive the Wigner characteristic function of the m -PCTMSC state and show that the 0-PCTMSC state is a Gaussian state and is an inferior choice as compared to the zero photon catalyzed two-mode squeezed vacuum state for CV-MDI-QKD. We carry out the optimization of the secret key rate with respect to all state parameters, namely variance, transmissivity, and displacement. Contrary to many recent proposals, the results show that zero- and single-photon catalysis operation provides only a marginal benefit in improving the maximum transmission distance. Secondly, we find that displacement offers no benefit in improving CV-MDI-QKD.
Non-Gaussian operations, in particular, photon subtraction (PS), have been shown to enhance the performance of various quantum information processing tasks including continuous variable measurement device independent quantum key distribution (CV-MDI-QKD). This work investigates the role of non-Gaussian resource states, namely, the photon subtracted two-mode squeezed coherent (PSTMSC) (which include photon subtracted two-mode squeezed vacuum (PSTMSV) as a special case) states in CV-MDI-QKD. To this end, we derive the Wigner characteristic function for the resource states, from which the covariance matrix and, finally, the secret key rate expressions are extracted. The optimization of the state parameters is undertaken to find the most suitable resource states in this family of states. There have been previous studies on the PSTMSV and PSTMSC states in CV-MDI-QKD that make use of PS operation. We evaluate such proposals and find to our surprise that both PSTMSC and PSTMSV resource states underperform as compared to the TMSV state rendering PS operation and displacement undesirable.
We critically analyze the role of single photon subtraction (SPS) and displacement in improving the performance of continuous variable measurement device independent quantum key distribution (CV-MDI-QKD). We consider CV-MDI-QKD with resource states generated by SPS on a displaced two-mode squeezed vacuum state. Optimizing the secret key rate with state parameters reveals that implementing SPS yields no benefits in improving the loss tolerance of CV-MDI-QKD. Additionally, we find that displacement too is not useful in improving the performance of CV-MDI-QKD. While our result is in contradistinction with the widely held belief in the field regarding the utility of SPS and displacement in CV-MDI-QKD, it also calls for a reexamination of the role of non-Gaussian operations in increasing the efficiency of various quantum information processing protocols.
Non-Gaussian operations in continuous variable (CV) quantum key distribution (QKD) have been limited to photon subtraction on squeezed vacuum states only. This is mainly due to the ease of calculating the covariance matrix representation of such states. In this paper we study the effects of general non-Gaussian operations corresponding to photon addition, catalysis, and subtraction on squeezed coherent states on CV measurement-device-independent (MDI) QKD. We find that non-Gaussianity coupled with coherence can yield significantly longer transmission distances than without. Particularly we observe that zero photon catalysis on the two-mode squeezed coherent state (TMSC) is an optimal choice for CV MDI QKD, while single photon subtraction is also a good candidate; both of them offer nearly 70 km of transmission distances. We also derive a single generalized covariance matrix for the aforementioned states which will be useful in several other aspects of CV quantum information processing.
Non-Gaussian operations on two-mode squeezed vacuum states in continuous-variable (CV) measurement-device-independent (MDI) quantum key distribution (QKD) protocols have been shown to effectively increase the total transmission distances drastically. In this paper we show that photon subtraction on a two-mode squeezed coherent (PSTMSC) state can further improve the transmission distances remarkably. To that end we also provide a generalized covariance matrix corresponding to the PSTMSC state. We show that coherence, defined as the amount of displacement of the vacuum state, along with non-Gaussianity can help improve the performance of prevalent CV MDI QKD protocols. Furthermore, since we use realistic parameters, our technique is experimentally feasible and can be readily implemented.
Abstract Discrete modulation can make up for the shortage of transmission distance in measurement-device-independent continuous-variable quantum key distribution (MDI-CVQKD), providing a unique advantage against all side-channel attacks but also creating a challenge for further performance improvement. Here we suggest a quantum catalysis (QC) approach for enhancing the performance of the discrete-modulated (DM) MDI-CVQKD in terms of the achievable secret key rate and lengthening the maximal transmission distance. The numerical simulation results show that the QC-based MDI-CVQKD with discrete modulation, involving a zero-photon catalysis (ZPC) operation, can not only obtain a higher secret key rate than the original DM protocol, but also contribute to a reasonable increase of the corresponding optimal variance. As for the extreme asymmetric and symmetric cases, the secret key rate and maximal transmission distance of the ZPC-involved DM MDI-CVQKD system can be further improved under the same parameters. This approach enables the system to tolerate lower reconciliation efficiency, which may provide excellent potential for practical implementations with state-of-art technology.
The measurement-device-independent quantum key distribution (MDI-QKD) protocol is immune to imperfect measurement devices. However, its practicality and performance when implemented in continuous-variable (CV) mode are still not satisfactory. We propose a CV-MDI-QKD protocol based on modulated squeezed states, and analyze its security against two-mode Gaussian attack. The results show that the protocol can achieve a higher secret key rate and transmission distance than previous coherent-state and squeezed-state protocols. A method to compensate the imperfection of a practical homodyne detector using phase-sensitive optical amplifiers is also presented. By setting an appropriate optical amplification gain, realistic detectors with ordinary quantum efficiency can be employed. In addition, we discuss the impact of finite-size effects on the secret key rate of the protocol. The methods presented may aid in the practical application of the CV-MDI-QKD protocol.