We extend the formalism of cluster-state quantum secret sharing, as presented by Markham and Sanders [Phys. Rev. A 78, 042309 (2008)] and Keet et al. [Phys. Rev. A 82, 062315 (2010)], to the continuous-variable regime. We show that both classical and quantum information can be shared by distributing continuous-variable cluster states through either public or private channels. We find that the adversary structure is completely denied from the secret if the cluster state is infinitely squeezed, but some secret information would be leaked if a realistic finitely squeezed state is employed. We suggest benchmarks to evaluate the security in the finitely squeezed cases. For the sharing of classical secrets, we borrow techniques from the continuous-variable quantum key distribution to compute the secret-sharing rate. For the sharing of quantum states, we estimate the amount of entanglement distilled for teleportation from each cluster state.
We extend the formalism of cluster-state quantum secret sharing, as presented by Markham and Sanders [Phys. Rev. A 78, 042309 (2008)] and Keet et al. [Phys. Rev. A 82, 062315 (2010)], to the continuous-variable regime. We show that both classical and quantum information can be shared by distributing continuous-variable cluster states through either public or private channels. We find that the adversary structure is completely denied from the secret if the cluster state is infinitely squeezed, but some secret information would be leaked if a realistic finitely squeezed state is employed. We suggest benchmarks to evaluate the security in the finitely squeezed cases. For the sharing of classical secrets, we borrow techniques from the continuous-variable quantum key distribution to compute the secret-sharing rate. For the sharing of quantum states, we estimate the amount of entanglement distilled for teleportation from each cluster state.
Quantum secret sharing (QSS), as a quantum extension of classical secret sharing, uses the basic principles of quantum mechanics to share information safely among multiple parties, providing a new paradigm for information security. As a key foundation for secure multiparty quantum communication and distributed quantum computing, QSS has attracted considerable attention since its emergence. Currently, research in this field includes both classical and quantum scenarios, and continuous progress has been made in both theoretical and experimental aspects. This paper first reviews the current development of QSS for classical information. In this regard, significant and parallel progress has been made in both discrete-variable QSS and continuous-variable QSS. The QSS protocols for sharing classical information, from entangled states to single photons and then to coherent light, have been continuously optimized to better utilize available resources and achieve more efficient implementation under current technological conditions. Meanwhile, round-robin, measurement-device-independent, and other protocols have been steadily improving the security of QSS. Next, one will focus on QSS scheme for quantum secrets, which begins with the symmetry of access structures and introduces basic (k, n) threshold protocols, dynamic schemes that support adaptive agent groups, and symmetric quantum information splitting through entanglement. It further introduces hierarchical quantum secret sharing schemes for asymmetric splitting of quantum information. Considering practical laboratory conditions of quantum states as resources, an overall discussion is conducted on quantum secret sharing with graph states. Afterwards, the design of a continuous-variable scheme for quantum secret sharing is outlined, and entanglement state sharing and quantum teleportation between multiple senders and receivers are introduced. Finally, this review discusses and outlines the future development directions of QSS, thereby inspiring readers to further study and explore the relevant subjects.
The one-to-multiparty quantum secret sharing scheme [Phys. Rev. A 71 (2005) 044301] proposed recently is extended to a multiparty-to-multiparty case. Furthermore, the continuous variable operations are employed in the extended scheme to replace the specific discrete unitary operations used in the original scheme. The complete randomicity of the continuous variable characterizing the unitary operations can ensure the security of secret sharing. Moreover, the present scheme is compared with the recent similar scheme [Phys. Rev. A 72 (2005) 012304]. It is found that the efficiency of the present scheme is n times of that of the previous one.
While the objective of conventional quantum key distribution (QKD) is to secretly generate and share the classical bits concealed in the form of maximally mixed quantum states, that of private quantum channel (PQC) is to secretly transmit individual quantum states concealed in the form of maximally mixed states using shared one-time pad and it is called Gaussian private quantum channel (GPQC) when the scheme is in the regime of continuous variables. We propose a GPQC enhanced with squeezed coherent states (GPQCwSC), which is a generalization of GPQC with coherent states only (GPQCo) [Phys. Rev. A 72, 042313 (2005)]. We show that GPQCwSC beats the GPQCo for the upper bound on accessible information. As a subsidiary example, it is shown that the squeezed states take an advantage over the coherent states against a beam splitting attack in a continuous variable QKD. It is also shown that a squeezing operation can be approximated as a superposition of two different displacement operations in the small squeezing regime.
A study of the entanglement properties of Gaussian cluster states, proposed as a universal resource for continuous variable (CV) quantum computing is presented in this paper. The central aim is to compare mathematically idealized cluster states defined using quadrature eigenstates, which have infinite squeezing and cannot exist in nature, with Gaussian approximations that are experimentally accessible. Adopting widely used definitions, we first review the key concepts, by analysing a process of teleportation along a CV quantum wire in the language of matrix product states. Next we consider the bipartite entanglement properties of the wire, providing analytic results. We proceed to grid cluster states, which are universal for the qubit case. To extend our analysis of the bipartite entanglement, we adopt the entropic-entanglement width, a specialized entanglement measure introduced recently by Van den Nest et al (2006 Phys. Rev. Lett. 97 150504), adapting their definition to the CV context. Finally, we consider the effects of photonic loss, extending our arguments to mixed states. Cumulatively our results point to key differences in the properties of idealized and Gaussian cluster states. Even modest loss rates are found to strongly limit the amount of entanglement. We discuss the implications for the potential of CV analogues for measurement-based quantum computation.
We propose here a quantum secret sharing scheme that works for both quantum and classical secrets. The proposed scheme is based on both entanglement swapping and teleportation together. It allows sender to encrypt his/her secret and simultaneously distribute decryption information of the encrypted secret among distant parties where decryption shares are nonlocally correlated with each other. Two-fold quantum non-local correlations, generated through entanglement swapping and then teleporting quantum states over swapped maximally entangled pairs, guarantee both authentication and secrecy of the secret from internal as well as external eavesdroppers. For classical secrets, we demonstrate a direct (2,2) quantum secret sharing scheme where neither pre-shared key nor physically secure quantum/classical channel are required. The same scheme turns out to be a (5,5) quantum secret sharing scheme for quantum secrets if sender and receivers have private quantum/classical channels among them.
Secret sharing is a multiparty cryptographic primitive that can be applied to a network of partially distrustful parties for encrypting data that is both sensitive (it must remain secure) and important (it must not be lost or destroyed).When sharing classical secrets (as opposed to quantum states), one can distinguish between protocols that leverage bipartite quantum key distribution (QKD) and those that exploit multipartite entanglement.The latter class are known to be vulnerable to so-called participant attacks and, while progress has been made recently, there is currently no analysis that quantifies their performance in the composable, finite-size regime, which has become the gold standard for QKD security.Given this-and the fact that distributing multipartite entanglement is typically challenging-one might well ask is there any virtue in pursuing multipartite entanglement-based schemes?Here, we answer this question in the affirmative for a class of secret-sharing protocols based on continuous-variable graph states.We establish security in a composable framework and identify a network topology, specifically a bottleneck network of lossy channels, and parameter regimes within the reach of present-day experiments for which a multipartite scheme outperforms the corresponding QKD-based method in the asymptotic and finite-size setting.Finally, we establish experimental parameters where the multipartite schemes outperform any possible QKD-based protocol.This is one of the first concrete compelling examples of multipartite entangled resources achieving a genuine advantage over point-to-point protocols for quantum communication and represents a rigorous, operational benchmark to assess the usefulness of such resources.