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Scientific Reports

Quantum secret sharing via local operations and classical communication

Ying‐Hui Yang, Fei Gao, Xia Wu, Su-Juan Qin, Hui-Juan Zuo, Qiaoyan Wen

Published Nov 20, 2015• 75 citations
Publisher

Abstract

We investigate the distinguishability of orthogonal multipartite entangled states in d-qudit system by restricted local operations and classical communication. According to these properties, we propose a standard (2, n)-threshold quantum secret sharing scheme (called LOCC-QSS scheme), which solves the open question in [Rahaman et al., Phys. Rev. A, 91, 022330 (2015)]. On the other hand, we find that all the existing (k, n)-threshold LOCC-QSS schemes are imperfect (or "ramp"), i.e., unauthorized groups can obtain some information about the shared secret. Furthermore, we present a (3, 4)-threshold LOCC-QSS scheme which is close to perfect.

DOI
10.1038/srep16967

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We investigate the distinguishability of orthogonal multipartite entangled states in d-qudit system by restricted local operations and classical communication. According to these properties, we propose a standard (2, n)-threshold quantum secret sharing scheme (called LOCC-QSS scheme), which solves the open question in [Rahaman et al., Phys. Rev. A, 91, 022330 (2015)]. On the other hand, we find that all the existing (k, n)-threshold LOCC-QSS schemes are imperfect (or "ramp"), i.e., unauthorized groups can obtain some information about the shared secret. Furthermore, we present a (3, 4)-threshold LOCC-QSS scheme which is close to perfect.
In this paper, we analyze the (im)possibility of the exact distinguishability of orthogonal multipartite entangled states under restricted local operation and classical communication. Based on this local distinguishability analysis, we propose a quantum secret sharing scheme (which we call LOCC-QSS). Our LOCC-QSS scheme is quite general and cost efficient compared to other schemes. In our scheme, no joint quantum operation is needed to reconstruct the secret. We also present an interesting (2,n)(2,n)(2,n)-threshold LOCC-QSS scheme, where any two cooperating players, one from each of two disjoint groups of players, can always reconstruct the secret. This LOCC-QSS scheme is quite uncommon, as most (k,n)(k,n)(k,n)-threshold quantum secret sharing schemes have the restriction $k\ensuremath{\ge}\ensuremath{\lceil}\frac{n}{2}\ensuremath{\rceil}$.
In this study, we propose the concept of judgment space to investigate the quantum-secret-sharing scheme based on local distinguishability (called LOCC-QSS). Because of the proposing of this conception, the property of orthogonal mutiqudit entangled states under restricted local operation and classical communication (LOCC) can be described more clearly. According to these properties, we reveal that, in the previous (k,nk,nk,n)-threshold LOCC-QSS scheme, there are two required conditions for the selected quantum states to resist the unambiguous attack: (i) their kkk-level judgment spaces are orthogonal, and (ii) their ($k\ensuremath{-}1$)-level judgment spaces are equal. Practically, if k<nk<nk<n (this is almost always true in the LOCC-QSS scheme), it is very difficult to satisfy the two conditions simultaneously. In the current study, we further establish a simple encoding method, which can concurrently ease the selection of quantum states and ensure the scheme's security, i.e., even if the ($k\ensuremath{-}1$)-level judgment spaces of the selected quantum states are not equal, these states can still be used for defeating the unambiguous attack. With this encoding method, we propose a more secure (k,nk,nk,n)-threshold LOCC-QSS scheme, and give two specific examples for illustration.
Maintaining confidentiality and reliability in distributed quantum environments remains a significant challenge. To this end, we propose a quantum secret sharing (QSS) scheme based on the local distinguishability of orthogonal eight-qudit entangled states. Compared to the previous seven-particle model, this scheme significantly expands the quantum state space, enhances security, and improves flexibility. We systematically construct 22 types of eight-qudit entangled states, define their corresponding judgment spaces, and introduce a new distinction rule to simplify the local discrimination process. Based on this framework, we develop a general ( k , n )-threshold quantum synchronization sharing protocol and verify its effectiveness using a (7, 8)-threshold example on the IBM Qiskit platform. Results show that this scheme is resilient to multiple attack types and provides a scalable approach for secure quantum information sharing in future distributed quantum systems, with potential applications in fields such as quantum-enhanced edge computing.
(t,n)(t,n)(t,n) -Threshold Quantum Secret Sharing Based on One-Way Local Distinguishability
We propose a quantum secret sharing protocol with a set of orthogonal generalized Bell states and one-way local distinguishability. In the proposed protocol, the participants use local projective measurements and one-way classical communication to distinguish among four Bell states, and we combine with the Shamir (t,n) -threshold scheme to realize (t,n) -threshold access structure. Compared to the existing schemes, the practical communication costs are dramatically improved as there is need for one-way classic communication between the two participants in our protocol. In addition, the efficiency in the process of information transmission will also be improved, as the number of communications will be reduced. At last, we demonstrate our protocol to be secure against both eavesdropping and dishonest participants.
Quantum secret sharing (QSS) is a cryptographic protocol in which a quantum secret is distributed among a number of parties where some subsets of the parties are able to recover the secret while some subsets are unable to recover the secret. In the standard ((k, n)) quantum threshold secret sharing scheme, any subset of k or more parties out of the total n parties can recover the secret while other subsets have no information about the secret. But recovery of the secret incurs a communication cost of at least k qudits for every qudit in the secret. Recently, a class of communication efficient QSS schemes were proposed which can improve this communication cost to dd−k+1\frac{d}{{d - k + 1}}d−k+1d​ by contacting d ≥ k parties where d is fixed prior to the distribution of shares. In this paper, we propose a more general class of ((k, n)) quantum secret sharing schemes with low communication complexity. In these schemes the combiner can contact any d parties at the time of recovery where k ≤ d ≤ n. This is the first such class of universal communication efficient quantum threshold schemes.
We demonstrate a new construction for perfect quantum secret sharing (QSS) schemes based on imperfect “ramp” secret sharing combined with classical encryption, in which the individual parties' shares are split into quantum and classical components, allowing the former to be of lower dimension than the secret itself. We show that such schemes can be performed with smaller quantum components and lower overall quantum communication than required for existing methods. We further demonstrate that one may combine both imperfect quantum and imperfect classical secret sharing to produce an overall perfect QSS scheme, and that examples of such schemes (which we construct) can have the smallest quantum and classical share components possible for their access structures, something provably not achievable using perfect underlying schemes. Our construction has significant potential for being adapted to other QSS schemes based on stabilizer codes.