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Physical Review A

Quantum-secret-sharing scheme based on local distinguishability of orthogonal multiqudit entangled states

Jingtao Wang, Lixiang Li, Haipeng Peng, Yixian Yang

Published Feb 13, 2017• 110 citations
Publisher

Abstract

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 ($k,n$)-threshold LOCC-QSS scheme, there are two required conditions for the selected quantum states to resist the unambiguous attack: (i) their $k$-level judgment spaces are orthogonal, and (ii) their ($k\ensuremath{-}1$)-level judgment spaces are equal. Practically, if $k<n$ (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 ($k,n$)-threshold LOCC-QSS scheme, and give two specific examples for illustration.

DOI
10.1103/physreva.95.022320

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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−1k\ensuremath{-}1k\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−1k\ensuremath{-}1k\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.
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 $k\ensuremath{\ge}\ensuremath{\lceil}\frac{n}{2}\ensuremath{\rceil}$.
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.
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.
In this work, we construct small sets of bipartite orthogonal pure states that cannot be perfectly distinguished by local operations and classical communication (LOCC). We mention that not all the states within the constructed sets are necessarily entangled. However, such a set contains at least one entangled state which cannot be conclusively identified by LOCC (with nonzero probability). Then, we show that the states of any such set can be perfectly distinguished by LOCC using a minimal-dimensional entangled resource state. Clearly, here the entangled resource state provides an advantage irrespective of the dimension of the given set. Using this result, we also prove that any pure entangled state is useful as a resource to distinguish the states of any present set unambiguously with nonzero probability under LOCC. These sets exist in all two-qudit Hilbert spaces. Furthermore, it is possible to decrease the average entanglement content of such a set or to increase the cardinality of the set without changing certain properties of the same.