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arXiv:2406.04270

Optimization of state parameters in displacement assisted photon subtracted measurement-device-independent quantum key distribution

Chandan Kumar, Sarbani Chatterjee, Arvind

Published Jun 6, 2024• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2406.04270

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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.
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.
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.
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.
We present a detailed phase-space analysis of continuous-variable quantum teleportation using a photon-subtracted two-mode squeezed Fock state (PS-TMSFS) as an entangled resource. We investigate the performance of PS-TMSFS within the Braunstein-Kimble teleportation protocol. The resource-state preparation is described and the success probability related to the photon-subtraction process is derived analytically. The Wigner characteristic function of PS-TMSFS is calculated and then employed to determine the fidelity for input Gaussian and non-Gaussian states. The dependence of the success probability and the teleportation fidelity on the squeezing parameter and the beam-splitter transmissivity is analyzed for both symmetric and asymmetric photon-subtraction scenarios. This results that the symmetric photon subtraction consistently outperforms the corresponding asymmetric configurations with the (2,2)(2,2)(2,2) configuration providing the highest teleportation fidelity among the considered PS-TMSFS resources. A significant improvement over the Gaussian two-mode squeezed vacuum (TMSV) resource is observed for teleporting Gaussian input states, particularly in the low-squeezing regime, whereas the relative advantage for non-Gaussian input states depends on the functioning resource parameters and gradually diminishes as squeezing increases.
Abstract We propose a new non-Gaussian version of the continuous variables measurement device independent quantum key distribution (CV-MDI-QKD) protocol by utilizing a photon added-then-subtracted (PAS) state. We report that our single and two-mode PAS-CV-MDI-QKD protocols outperform pure state CV-MDI-QKD protocol when considering weak squeezing and high noise, which is the practical regime. With such resources, CV-MDI-QKD is inaccessible when using a pure TMSV state, while PAS-CV-MDI-QKD can generate a useful key rate in this regime. We also compare PAS-CV-MDI-QKD with a two-mode photon replaced (2PR) state, which was not studied in low squeezing for MDI-QKD before.