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arXiv:2304.02295 · Quantum Information Processing

Enabling CV-MDI-QKD for weakly squeezed states using non-Gaussian operations

Farsad Ahmad, Aeysha Khalique, Aeysha Khalique

Published Oct 17, 2024• 0 citations
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Abstract

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.

DOI
10.1007/s11128-024-04565-w

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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.
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.
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.
The method of improving the performance of continuous-variable quantum key distribution protocols by postselection has been recently proposed and verified. In continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocols, the measurement results are obtained from untrusted third party Charlie. There is still not an effective method of improving CV-MDI QKD by the postselection with untrusted measurement. We propose a method to improve the performance of coherent-state CV-MDI QKD protocol by virtual photon subtraction via non-Gaussian postselection. The non-Gaussian postselection of transmitted data is equivalent to an ideal photon subtraction on the two-mode squeezed vacuum state, which is favorable to enhance the performance of CV-MDI QKD. In CV-MDI QKD protocol with non-Gaussian postselection, two users select their own data independently. We demonstrate that the optimal performance of the renovated CV-MDI QKD protocol is obtained with the transmitted data only selected by Alice. By setting appropriate parameters of the virtual photon subtraction, the secret key rate and tolerable excess noise are both improved at long transmission distance. The method provides an effective optimization scheme for the application of CV-MDI QKD protocols.
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.
It has been found that non-Gaussian operations can be applied to increase and distill entanglement between Gaussian entangled states. We show the successful use of the non-Gaussian operation, in particular, photon subtraction operation, on the continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) protocol. The proposed method can be implemented based on existing technologies. Security analysis shows that the photon subtraction operation can remarkably increase the maximal transmission distance of the CV-MDI-QKD protocol, which precisely make up for the shortcoming of the original CV-MDI-QKD protocol, and one-photon subtraction operation has the best performance. Moreover, the proposed protocol provides a feasible method for the experimental implementation of the CV-MDI-QKD protocol.
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.