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Continuous-Variable Ramp Quantum Secret Sharing with Gaussian States and Operations

Habibi Davijani, Masoud

Published Jan 1, 2019• 11 citations
Publisher

Abstract

Our aim is to formulate continuous-variable quantum secret-sharing as a continuous-variable ramp quantum secret-sharing protocol, provide a certification procedure for it and explain the criteria for the certification. Here we introduce a technique for certifying continuous-variable ramp quantum secret-sharing schemes in the framework of quantum interactive-proof systems. We devise pseudocodes in order to represent the sequence of steps taken to solve the certification problem. Furthermore, we derive the expression for quantum mutual information between the quantum secret extracted by any multi-player structure and the share held by the referee corresponding to the Tyc-Rowe-Sanders continuous-variable quantum secret-sharing scheme. We solve by converting the Tyc-Rowe-Sanders position representation for the state into a Wigner function from which the covariance matrix can be found, then insert the covariance matrix into the standard formula for continuous-variable quantum mutual information to obtain quantum mutual information in terms of squeezing. Our quantum mutual information result quantifies the leakage of the ramp quantum secret-sharing schemes.

DOI
10.11575/prism/36415

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Abstract We aim to quantify and mitigate quantum-information leakage in continuous-variable quantum secret sharing (CV QSS). Here we introduce a technique for certifying CV ramp quantum secret-sharing (RQSS) schemes in the framework of quantum interactive-proof systems. We devise pseudocodes in order to represent the sequence of steps taken to solve the certification problem. Furthermore, we derive the expression for quantum mutual information between the quantum secret extracted by any multi-player structure and the share held by the referee corresponding to the Tyc–Rowe–Sanders CV QSS scheme. We solve by converting the Tyc–Rowe–Sanders position representation for the state into a Wigner function from which the covariance matrix can be found, then insert the covariance matrix into the standard formula for CR quantum mutual information to obtain quantum mutual information in terms of squeezing. Our quantum mutual information result quantifies the leakage of the RQSS schemes.
We extend the formalism of cluster-state quantum secret sharing, as presented by Markham and Sanders [Phys. Rev. A 78, 042309 (2008)] and Keet et al. [Phys. Rev. A 82, 062315 (2010)], to the continuous-variable regime. We show that both classical and quantum information can be shared by distributing continuous-variable cluster states through either public or private channels. We find that the adversary structure is completely denied from the secret if the cluster state is infinitely squeezed, but some secret information would be leaked if a realistic finitely squeezed state is employed. We suggest benchmarks to evaluate the security in the finitely squeezed cases. For the sharing of classical secrets, we borrow techniques from the continuous-variable quantum key distribution to compute the secret-sharing rate. For the sharing of quantum states, we estimate the amount of entanglement distilled for teleportation from each cluster state.
The need for secrecy and security is essential in communication. Secret sharing is a conventional protocol to distribute a secret message to a group of parties, who cannot access it individually but need to cooperate in order to decode it. While several variants of this protocol have been investigated, including realizations using quantum systems, the security of quantum secret sharing schemes still remains unproven almost two decades after their original conception. Here we establish an unconditional security proof for entanglement-based continuous-variable quantum secret sharing schemes, in the limit of asymptotic keys and for an arbitrary number of players. We tackle the problem by resorting to the recently developed one-sided device-independent approach to quantum key distribution. We demonstrate theoretically the feasibility of our scheme, which can be implemented by Gaussian states and homodyne measurements, with no need for ideal single-photon sources or quantum memories. Our results contribute to validating quantum secret sharing as a viable primitive for quantum technologies.
The dishonest participants have many advantages to gain others’ shares by cheating in quantum secret sharing (QSS) protocols. However, the traditional methods such as identity authentication and message authentication can not resolve this problem due to the reason that the share has already been released to dishonest participants before realizing the deception. In this paper, a continuous variable QSS (CVQSS) scheme is proposed with fairness which ensures all participants can acquire or can not acquire the secret simultaneously. The quantum channel based on two-mode squeezing states provides secure communications through which it can send shares successfully, as long as setting the squeezing and modulation parameters according to the quantum channel transmission efficiency and the Shannon information of shares. In addition, the Chinese Remainder Theorem (CRT) can provides tunable threshold structures according to demands of the complex quantum network and the strategy for fairness can be incorporated with other sharing schemes, resulting in perfect compatibility for practical implementations.
We propose a continuous-variable quantum secret sharing (CV-QSS) protocol in which the quantum states are prepared passively using a thermal source. In our protocol, one player splits the output of a thermal source into two spatial modes with the help of a beam splitter, then he (or she) measures one of the correlated thermal states and sends the others to the secure station of the adjacent player in sequence after using appropriate optical attenuation, which waives the necessity of employment of high extinction ratio modulators with good stability. Therefore, the proposed protocol provides convenient implementation in QSS framework. Moreover, our scheme is immune to Trojan horse attacks. We derive the security bounds for our protocol against both eavesdroppers and dishonest players. Furthermore, we can achieve tighter bound of QSS distance by considering the finite-size effect, which is more practical than that obtained in the asymptotic limit.
We consider a protocol for sharing quantum states using continuous variable systems. Specifically we introduce an encoding procedure where bosonic modes in arbitrary secret states are mixed with several ancillary squeezed modes through a passive interferometer. We derive simple conditions on the interferometer for this encoding to define a secret sharing protocol and we prove that they are satisfied by almost any interferometer. This implies that, if the interferometer is chosen uniformly at random, the probability that it may not be used to implement a quantum secret sharing protocol is zero. Furthermore, we show that the decoding operation can be obtained and implemented efficiently with a Gaussian unitary using a number of single-mode squeezers that is at most twice the number of modes of the secret, regardless of the number of players. We benchmark the quality of the reconstructed state by computing the fidelity with the secret state as a function of the input squeezing.