Chris Fields, Antonino Marcianò
We show that sharing a quantum reference frame requires sharing measurement operators that identify the reference frame in addition to operators that measure its state. Observers restricted to finite resources cannot, in general, operationally determine that they share such operators. Uncertainty about whether system-identification operators are shared induces decoherence.
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Two qubit operation sharing schemes [J. Phys. B 44 (2011) 165508] are generalized to qutrit ones. Operations to be shared are classified into three different classes in terms of different probabilities (i.e, 1/3, 2/3 and 1). For the latter two classes, ten and three restricted sets of operations are found out, respectively. Moreover, the two generalized schemes are amply compared from four aspects, namely, quantum and classical resource consumption, necessaryoperation complexity, success probability and efficiency. It is found that the second scheme is overall more optimal than the first one a…
A (k,n)-threshold secret-sharing scheme allows for a string to be split into n shares in such a way that any subset of at least k shares suffices to recover the secret string, but such that any subset of at most k-1 shares contains no information about the secret. Quantum secret-sharing schemes extend this idea to the sharing of quantum states. Here we propose a method of performing computation on quantum shared secrets. We introduce a (n,n)-quantum secret sharing scheme together with a set of protocols that allow quantum circuits to be evaluated on the shared secret without the need to decode…
Quantum secret sharing is a method for sharing a secret quantum state among a number of individuals such that certain authorized subsets of participants can recover the secret shared state by collaboration and other subsets cannot. In this paper, we first propose a method for sharing a quantum secret in a basic $(2,3)$ threshold scheme, only by using qubits and the 7-qubit CSS code. Based on this $(2,3)$ scheme, we propose a new $(n, n)$ scheme and we also construct a quantum secret sharing scheme for any quantum access structure by induction. Secondly, based on the techniques of performing qu…
In this work, we generalize the quantum secret sharing scheme of Hillary, Bužek and Berthiaume[Phys. Rev. A59, 1829(1999)] into arbitrary multi-parties. Explicit expressions for the shared secret bit is given. It is shown that in the Hillery-Bužek-Berthiaume quantum secret sharing scheme the secret information is shared in the parity of binary strings formed by the measured outcomes of the participants. In addition, we have increased the efficiency of the quantum secret sharing scheme by generalizing two techniques from quantum key distribution. The favored-measuring-basis Quantum secret shari…
Sharing Bell nonlocality of bipartite high-dimensional pure states using only projective measurements
本文证明仅使用投影测量即可共享任意高维纯两体态的Bell非定域性，推广了已有两量子比特纯态的结果，深化了对高维量子态非定域性共享的理解。
Ouyang et al. proposed an $(n,n)$ threshold quantum secret sharing scheme, where the number of participants is limited to $n=4k+1,k\in Z^+$, and the security evaluation of the scheme was carried out accordingly. In this paper, we propose an $(n,n)$ threshold quantum secret sharing scheme for the number of participants $n$ in any case ( $n\in Z^+$ ). The scheme is based on a quantum circuit, which consists of Clifford group gates and Toffoli gate. We study the properties of the quantum circuit in this paper and use the quantum circuit to analyze the security of the scheme for dishonest particip…
Of late, there has been an upsurge of interest in studying the sequential sharing of various forms of quantum correlations, viz., nonlocality, preparation contextuality, coherence, and entanglement. In this work, we explore the sequential sharing of nonlocality in a quantum network. We first consider the simplest case of the two-input bilocality scenario that features two independent sources and three parties, including two edge parties and a central party. We demonstrate that in the symmetric case when the sharing is considered for both the edge parties, the nonlocality can be shared by at mo…
In this paper, we present an (n, n) threshold quantum secret sharing scheme of secure direct communication using Greenberger-Horne-Zeilinger state. The present scheme is efficient in that all the Greenberger-Horne-Zeilinger states used in the quantum secret sharing scheme are used to generate shared secret messages except those chosen for checking eavesdropper. In our scheme, the measuring basis of communication parties is invariable and the classical information used to check eavesdropping needs only the results of measurements of the communication parties. Another nice feature of our scheme …
Quantum steering as a resource for secure tripartite Quantum State Sharing
针对三方均可能不诚实的量子态共享协议，本文证明量子导引是保障安全共享与重构的必要资源，并给出共享任意单模高斯秘密所需的导引水平以实现资源最优利用。
We propose a quantum secret sharing protocol between multi-party ($m$ members in group 1) and multi-party ($n$ members in group 2) using a sequence of single photons. These single photons are used directly to encode classical information in a quantum secret sharing process. In this protocol, all members in group 1 directly encode their respective keys on the states of single photons via unitary operations, then the last one (the $m^{th}$ member of group 1) sends $1/n$ of the resulting qubits to each of group 2. Thus the secret message shared by all members of group 1 is shared by all members o…
Revocation and Reconstruction of Shared Quantum States
本文提出了一种四量子比特纠缠资源的共享与撤销协议，通过量子份额和额外资源实现对共享量子态的撤销与重建。
Secret sharing of a quantum state, or quantum secret sharing, in which a dealer wants to share certain amount of quantum information with a few players, has wide applications in quantum information. The critical criterion in a threshold secret sharing scheme is confidentiality, with less than the designated number of players, no information can be recovered. Furthermore, in a quantum scenario, one additional critical criterion exists, the capability of sharing entangled and unknown quantum information. Here by employing a six-photon entangled state, we demonstrate a quantum threshold scheme, w…
We present a unified formalism for threshold quantum secret sharing using graph states of systems with prime dimension. We construct protocols for three varieties of secret sharing: with classical and quantum secrets shared between parties over both classical and quantum channels.
Secret sharing is a multiparty cryptographic task in which some secret information is splitted into several pieces which are distributed among the participants such that only an authorized set of participants can reconstruct the original secret. Similar to quantum key distribution, in quantum secret sharing, the secrecy of the shared information relies not on computational assumptions, but on laws of quantum physics. Here, we present an experimental demonstration of four-party quantum secret sharing via the resource of four-photon entanglement.
Revocation and Reconstruction of Shared Quantum States
本文研究共享量子态的撤销问题，提出让分发者持有量子份额以增强控制，并基于四量子比特纠缠资源给出共享与撤销协议，同时确定了协议成功的参数范围。
We investigate the approximate quantum state sharing protocol based on random unitary channels, which is secure against any exterior or interior attackers in principle. Although the protocol leaks small information for a security parameter $ε$, the scheme still preserves its information-theoretic secrecy, and reduces some pre-shared classical secret keys for a private quantum channel between a sender and two receivers. The approximate private quantum channels constructed via random unitary channels play a crucial role in the proposed quantum state sharing protocol.
Given an ensemble of n spins, at least some of which are partially polarized, we investigate the sharing of this polarization within a subspace of k spins. We assume that the sharing results in a pseudopure state, characterized by a single purity parameter which we call the bias. As a concrete example we consider ensembles of spin-1/2 nuclei in liquid-state nuclear magnetic resonance (NMR) systems. The shared bias levels are compared with some current entanglement bounds to determine whether the reduced subspaces can give rise to entangled states.
Two tripartite schemes are put forward with shared entanglements and LOCC for sharing an operation on a remote target sate. The first scheme uses a Bell and a symmetric W states as quantum channels, while the second replaces the symmetric W state by an asymmetric one. Both schemes are treated and compared from the aspects of quantum resource consumption, operation complexity, classical resource consumption, success probability and efficiency. It is found that, the latter scheme is better than the former one. Particularly, the sharing can be achieved only probabilistically with the first scheme…
Sharing correlated random variables is a resource for a number of information theoretic tasks such as privacy amplification, simultaneous message passing, secret sharing and many more. In this article, we show that to establish such a resource called shared randomness, quantum systems provide an advantage over their classical counterpart. Precisely, we show that appropriate albeit fixed measurements on a shared two-qubit state can generate correlations which cannot be obtained from any possible state on two classical bits. In a resource theoretic set-up, this feature of quantum systems can be …
We present a new protocol in which a secret multiqubit quantum state $\ketΨ$ is shared by $n$ players and $m$ controllers, where $\ketΨ$ is the encoding state of a quantum secret sharing scheme. The players may be considered as field agents responsible for carrying out a task, using the secret information encrypted in $\ketΨ$, while the controllers are superiors who decide if and when the task should be carried out and who to do it. Our protocol only requires ancillary Bell states and Bell-basis measurements.
Entanglement is a key resource of quantum science for tasks that require it to be shared among participants. Within atomic, condensed matter and photonic many-body systems the distribution and sharing of entanglement is of particular importance for information processing by progressively larger and larger quantum networks. Here we report a singly-bipartitioned qubit entanglement inequality that applies to any N-party qubit pure state and is completely tight. It provides the first prescription for a direct calculation of the amount of entanglement sharing that is possible among N qubit parties.…
Sharing Asymmetric Einstein-Podolsky-Rosen Steering with Projective Measurements
提出基于投影测量的 EPR 导引共享协议，理论与实验证明无共享随机性时任意多方可共享单向导引，仅靠局部随机性还可共享不对称双向导引。
Maximally entangled states--a resource for quantum information processing--can only be shared through noiseless quantum channels, whereas in practice channels are noisy. Here we ask: Given a noisy quantum channel, what is the maximum attainable purity (measured by singlet fraction) of shared entanglement for single channel use and local trace preserving operations? We find an exact formula of the maximum singlet fraction attainable for a qubit channel and give an explicit protocol to achieve the optimal value. The protocol distinguishes between unital and nonunital channels and requires no loc…
Quantum secret sharing is one of the most important and interesting quantum information processing task. In quantum secret sharing, information is split among several parties such that only one of them is able to recover the qubit exactly provided all the other parties agree to cooperate. To achieve this task, all the parties need to share entangled state. As far as my knowledge, all the previous quantum secret sharing protocol used either pure tripartite or pure bipartite entangled state. In this work we use for the first time bipartite two qubit mixed state (formed due to noisy environment) …
A resilient secret sharing scheme is supposed to generate the secret correctly even after some shares are damaged. In this paper, we show how quantum error correcting codes can be exploited to design a resilient quantum secret sharing scheme, where a quantum state is shared among more than one parties.
We develop a connection between tripartite information $I_3$, secret sharing protocols and multi-unitaries. This leads to explicit ((2,3)) threshold schemes in arbitrary dimension minimizing tripartite information $I_3$. As an application we show that Page scrambling unitaries simultaneously work for all secrets shared by Alice. Using the $I_3$-Ansatz for imperfect sharing schemes we discover examples of VIP sharing schemes.
Sharing quantum nonlocality and teleportation over long distance using optical hybrid states
本文提出利用单光子偏振与多光子相干态构成的光学混合态，经中间站纠缠交换在长距离共享违反 CHSH 不等式的偏振纠缠，并验证其可支持未知偏振量子比特的忠实隐形传态。
Split-State Non-Malleable Codes and Secret Sharing Schemes for Quantum Messages
本文首次针对量子消息提出分裂状态不可延展码与秘密共享方案，构造了可抵抗拥有共享纠缠的量子敌手、保持外部纠缠且错误率极低的高效编码方案，并在平均情况下实现接近1/11的编码速率。
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