Quantum secret sharing based on local distinguishability

Abstract

In this paper we analyze the (im)possibility of the exact distinguishability of orthogonal multipartite entangled states under {\em restricted local operation and classical communication}. Based on this local distinguishability analysis we propose a new scheme for quantum secret sharing (QSS). Our 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 $(2,n)$-threshold QSS scheme, where any two cooperating players, one from each of two disjoint groups of players, can always reconstruct the secret. This QSS scheme is quite uncommon, as most $(k,n)$-threshold schemes have the restriction $k\ge \lceil \frac{n}{2}\rceil$.

7 pages, Comments are welcome

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• Quantum secret sharing
• How to share a quantum secret
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• Local Distinguishability of Multipartite Orthogonal Quantum States
• Multiparty Quantum Secret Sharing
• Multiparty Quantum Secret Sharing Based on Entanglement Swapping
• Distinguishability of the Bell states
• Generalized Quantum Secret Sharing
• LOCC distinguishability of unilaterally transformable quantum states
• Reducing the quantum communication cost of quantum secret sharing
• Accessing quantum secrets via local operations and classical communication
• Stochastic local operations and classical communication properties of the n-qubit symmetric Dicke states

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• Strong quantum nonlocality without entanglement in $n$-partite system with even $n$
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• Local discrimination of generalized Bell states via commutativity
• Strongest nonlocal sets with minimum cardinality in tripartite systems
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• Genuinely nonlocal sets without entanglement in multipartite systems
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• Strongest quantum nonlocality in $N$-partite systems
• Information locking and its resource efficient extraction
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• The construction of sets with strong quantum nonlocality using fewer states
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• Annihilating and creating nonlocality without entanglement by postmeasurement information
• The existence of distinguishable bases in three-dimensional subspaces of qutrit-qudit systems under one-way local operations and classical communication
• Novel methods to construct nonlocal sets of orthogonal product states in arbitrary bipartite high-dimensional system
• Application of Ramsey theory to localization of set of product states via multicopies
• Graph connectivity based strong quantum nonlocality with genuine entanglement
• Nonlocal sets of orthogonal multipartite product states with less members
• Quantum Access Structure and Secret Sharing
• Locking and unlocking of quantum nonlocality without entanglement in local discrimination of quantum states
• Trade-off between Information Gain and Disturbance in Local Discrimination of Entangled Quantum States
• A secret sharing scheme on p^2 -dimensional quantum system
• A Hybrid Quantum Secret Sharing Scheme based on Mutually Unbiased Bases
• Efficient decoding of stabilizer code by single-qubit local operations and classical communication
• Activate genuine nonlocality from distinguishable sets in tripartite systems