We characterize the algebraic structure of semi-direct product of cyclic groups, $Z_{N}rtimesZ_{p}$, where $p$ is an odd prime number which does not divide $q-1$ for any prime factor $q$ of $N$, and provide a polynomial-time quantum computational algorithm solving hidden symmetry subgroup problem of the groups.
We propose replacing concurrence by convex-roof extended negativity (CREN) for studying monogamy of entanglement (MoE). We show that all proven MoE relations using concurrence can be rephrased in terms of CREN. Furthermore we show that higher-dimensional (qudit) extensions of MoE in terms of CREN are not disproven by any of the counterexamples used to disprove qudit extensions of MoE in terms of concurrence. We further test the CREN version of MoE for qudits by considering fully or partially coherent mixtures of a qudit W-class state with the vacuum and show that the CREN version of MoE for qudits is satisfied in this case as well. The CREN version of MoE for qudits is thus a strong conjecture with no obvious counterexamples.
In this work, we investigate what kinds of quantum states are feasible to perform perfectly secure secret sharing, and present its necessary and sufficient conditions. We also show that the states are bipartite distillable for all bipartite splits, and hence the states could be distillable into the Greenberger-Horne-Zeilinger state. We finally exhibit a class of secret-sharing states, which have an arbitrarily small amount of bipartite distillable entanglement for a certain split.
Quantum correlations as the resource for quantum communication can be distributed over long distances by quantum repeaters. In this Letter, we introduce the notion of a noisy quantum repeater, and examine its role in quantum communication. Quantum correlations shared through noisy quantum repeaters are then characterized and their secrecy properties are studied. Remarkably, noisy quantum repeaters naturally introduce private states in the key distillation scenario, and consequently key distillation protocols are demonstrated to be more tolerant.
We develop a three-party quantum secret sharing protocol based on arbitrary dimensional quantum states. In contrast to the previous quantum secret sharing protocols, the sender can always control the state, just using local operations, for adjusting the correlation of measurement directions of three parties and thus there is no waste of resource due to the discord between the directions. Moreover, our protocol contains the hidden value which enables the sender to leak no information of secret key to the dishonest receiver until the last steps of the procedure.
