International Journal of Quantum Information

Quantum secret sharing techniques allow two parties or more to securely share a key, while the same number of parties or less can efficiently deduce the secret key. In this paper, we propose an authenticated quantum secret sharing protocol, where a quantum dialogue protocol is adopted to authenticate the identity of the parties. The participants simultaneously authenticate the identity of each other based on parts of a prior shared key. Moreover, the whole prior shared key can be reused for deducing the secret data. Although the proposed scheme does not significantly improve the efficiency performance, it is more secure compared to some existing quantum secret sharing scheme due to the identity authentication process. In addition, the proposed scheme can stand against participant attack, man-in-the-middle attack, impersonation attack, Trojan-horse attack as well as information leaks.

Multi-valued quantum operations have several advantages over binary operators. They decrease the number of essential data sending lines dramatically, which reduces the internal connections and thus can improve the circuit efficiency. In this paper, new reversible quaternary flip-flops are proposed which decrease the number of internal connectors and complexity of the circuits. So, the speed of circuits is increased. The implementation of synchronous sequential circuits requires memory elements. The proposed flip-flops need solely one memory element.

We construct the tripartite Bell-type inequalities of product states for $l_1$-norm of coherence, relative entropy of coherence and skew information. We give examples of three-qubit entangled states that violate these inequalities. Particularly, the tripartite Bell-type inequality for relative entropy of coherence is always violated by the W class pure or mixed states as well as the GHZ class pure or mixed states, being used as entanglement witness.

We investigate small geometric configurations that furnish observable-based proofs of the Kochen–Specker theorem. Assuming that each context consists of the same number of observables and each observable is shared by two contexts, it is proved that the most economical proofs are the famous Mermin–Peres square and the Mermin pentagram featuring, respectively, 9 and 10 observables, there being no proofs using less than 9 observables. We also propose a new proof with 14 observables forming a “magic” heptagram. On the other hand, some other prominent small-size finite geometries, like the Pasch configuration and the prism, are shown not to be contextual.

We put forward a measure for evaluating quantum speed limit for arbitrary mixed states of open systems by means of trace distance. Compared with some present measures, it can provide an optimal bound to the speed of the evolution. The dynamical crossover from no speedup region to speedup region happens during the spontaneous decay of an atom. The evolution is characteristic of the alternating behavior between quantum acceleration and deceleration in the strong coupling case. Under the condition of detuning, the evolution can be initially accelerated and then decelerated to a normal process either in the weak or strong coupling regime. In accordance with the uncertainty relation, we demonstrate that the potential capacity for quantum speedup evolution is closely related to the energy feedback from the reservoir to the system. The negative decay rate for the evolution results in the speedup process where the photons previously emitted by the atom are reabsorbed at a later time. The values of the spontaneous decay rate become positive after a long enough time, which results in the evolution with no speedup potential.

Generation of Aharonov–Bohm (AB) phase has achieved a state-of-the-art in mesoscopic systems with manipulation and control of the AB effect. The possibility of transfer information encoded in such systems to nonclassical states of light increases the possible scenarios where the information can be manipulated and transferred. In this paper, we propose a quantum transfer of the AB phase generated in a spintronic device, a topological spin transistor (TST), to an quantum optical device, a coherent state superposition in high-Q cavity and discuss optical and spin-optical superpositions in the presence of an AB phase. We demonstrate that the AB phase generated in the TST can be transferred to the coherent state superposition, considering the interaction with the spin state and the quantum optical manipulation of the coherent state superposition. We show that these cases provide examples of two-qubit states modulated by AB effect and that the phase parameter can be used to control the degree of rotation of the qubit state. We also show under a measurement on the spin basis, an optical one-qubit state that can be modulated by the AB effect. In these cases, we consider a dispersive interaction between a coherent state and a spin state with an acquired AB phase and also discuss a dissipative case where a given Lindblad equation is achieved and solved.

We revisit the problem of finding the Naimark extension of a probability operator-valued measure (POVM), i.e. its implementation as a projective measurement in a larger Hilbert space. In particular, we suggest an iterative method to build the projective measurement from the sole requirements of orthogonality and positivity. Our method improves existing ones, as it may be employed also to extend POVMs containing elements with rank larger than one. It is also more effective in terms of computational steps.

In this paper, we extend existing variance-based sum uncertainty relations for pure states to those for mixed states by a mathematical approach. Furthermore, we show that the monotonicity of the standard deviation of observables induces a variance-based sum uncertainty relation. Finally, the multiobservable case is also discussed.