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arXiv:quant-ph/0311015 · Physical Review Letters

Tripartite Quantum State Sharing

Andrew M. Lance, Thomas Symul, Warwick P. Bowen, Barry C. Sanders, Ping Koy Lam

Published Apr 29, 2004• 521 citations
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Abstract

We demonstrate a multipartite protocol to securely distribute and reconstruct a quantum state. A secret quantum state is encoded into a tripartite entangled state and distributed to three players. By collaborating, any two of the three players can reconstruct the state, while individual players obtain nothing. We characterize this (2,3) threshold quantum state sharing scheme in terms of fidelity, signal transfer, and reconstruction noise. We demonstrate a fidelity averaged over all reconstruction permutations of 0.73+/-0.04, a level achievable only using quantum resources.

DOI
10.1103/physrevlett.92.177903

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We demonstrate a multipartite protocol to securely distribute and reconstruct a quantum state. A secret quantum state is encoded into a tripartite entangled state and distributed to three players. By collaborating, any two of the three players can reconstruct the state, while individual players obtain nothing. We characterize this (2,3) threshold quantum state sharing scheme in terms of fidelity, signal transfer, and reconstruction noise. We demonstrate a fidelity averaged over all reconstruction permutations of 0.73+/-0.04, a level achievable only using quantum resources.
We demonstrate a multipartite protocol that utilizes entanglement to securely distribute and reconstruct a quantum state. A secret quantum state is encoded into a tripartite entangled state and distributed to three players. By collaborating together, a majority of the players can reconstruct the state, whilst the remaining player obtains nothing. This (2,3) threshold quantum state sharing scheme is characterized in terms of fidelity (F), signal transfer (T) and reconstruction noise (V). We demonstrate a fidelity averaged over all reconstruction permutations of 0.73 ± 0.04, a level achievable only using quantum resources.
Superconducting microwave quantum networks is a rapidly developing field, enabling distributed quantum computing and holding a promise for hybrid architectures in quantum internet. Quantum secret sharing (QSS) is one of the key protocols for multipartite quantum networks and can provide an unconditionally secure way to share quantum states among nnn players. Using microwave two-mode squeezed states as an entanglement resource, we experimentally implement a QSS protocol with n=3n = 3n=3, where a subset of at least k=2k = 2k=2 players must collaborate to faithfully reconstruct the original secret state. We demonstrate reconstructed-state fidelities that surpass the asymptotic no-cloning threshold of Fnc=2/3F_\textrm{nc} = 2/3Fnc​=2/3 and identify a parameter regime that allows for unconditionally secure communication in the presence of an omnipotent dishonest player. Furthermore, we experimentally explore inherent connections between QSS and other important quantum information processing tasks, such as quantum dense coding and elementary quantum error correction of channel erasures. Finally, we discuss extensions of QSS and its relation to the concept of blind quantum computing.
Quantum-state sharing is a protocol where perfect reconstruction of quantum states is achieved with incomplete or partial information in a multipartite quantum network. Quantum-state sharing allows for secure communication in a quantum network where partial information is lost or acquired by malicious parties. This protocol utilizes entanglement for the secret-state distribution and a class of ``quantum disentangling'' protocols for the state reconstruction. We demonstrate a quantum-state sharing protocol in which a tripartite entangled state is used to encode and distribute a secret state to three players. Any two of these players can collaborate to reconstruct the secret state, while individual players obtain no information. We investigate a number of quantum disentangling processes and experimentally demonstrate quantum-state reconstruction using two of these protocols. We experimentally measure a fidelity, averaged over all reconstruction permutations, of $\mathcal{F}=0.73\ifmmode\pm\else\textpm\fi{}0.02$. A result achievable only by using quantum resources.
Quantum state sharing (QSS) is a protocol by which a (secret) quantum state may be securely split into shares, shared between multiple potentially-dishonest players, and reconstructed. Crucially, the players are each assumed to be dishonest, and so QSS requires that only a collaborating authorized subset of players can access the original secret state; any dishonest unauthorized conspiracy cannot reconstruct it. We analyze a QSS protocol involving three untrusted players and demonstrate that quantum steering is the required resource enabling the protocol to proceed securely. We analyze the level of steering required to share any single-mode Gaussian secret which enables the states to be shared with the optimal use of resources.
Quantum state sharing, an important protocol in quantum information, can enable secure state distribution and reconstruction when part of the information is lost. In (k, n) threshold quantum state sharing, the secret state is encoded into n shares and then distributed to n players. The secret state can be reconstructed by any k players (k > n / 2), while the rest of the players get nothing. In the continuous variable regime, the implementation of quantum state sharing needs the feedforward technique, which involves optic-electro and electro-optic conversions. These conversions limit the bandwidth of the quantum state sharing. Here, to avoid the optic-electro and electro-optic conversions, we experimentally demonstrate (2, 3) threshold deterministic all-optical quantum state sharing. A low-noise phase-insensitive amplifier based on the four-wave mixing process is utilized to replace the feedforward technique. We experimentally demonstrate that any two of three players can cooperate to implement the reconstruction of the secret state, while the rest of the players cannot get any information. Our results provide an all-optical platform to implement arbitrary (k, n) threshold deterministic all-optical quantum state sharing and pave the way to construct the all-optical broadband quantum network.
In this article we present a benchmark for resource characterization in the process of controlled quantum state reconstruction and secret sharing for general three-qubit states. This is achieved by providing a closed expression for the reconstruction fidelity, which relies on the genuine tripartite correlation and the bipartite channel between the dealer and the reconstructor characterized by the respective correlation parameters. We formulate the idea of quantum advantage in approximate state reconstruction as surpassing the classical limit set at 23\frac{2}{3}32​. This article introduces new interoperability between teleportation and state reconstruction. This is detailed through a case-by-case analysis of relevant correlation matrices. We reformulate the idea of quantum secret sharing by setting up additional constraints on the teleportation capacity of the bipartite channels between dealer and shareholders by ensuring that, individually, the shareholders cannot reconstruct the secret. We believe that this will give us an ideal picture of how quantum secret sharing should be.