Coherence measures based on sandwiched Rényi relative entropy

Coherence is a fundamental ingredient for quantum physics and a key resource for quantum information theory.Baumgratz, Cramer and Plenio established a rigorous framework(BCP framework) for quantifying coherence [Baumgratz T, Cramer M and Plenio M B Phys. Rev. Lett. 113 140401(2014)]. In the present paper, under the BCP framework we provide two classes of coherence measures based on the sandwiched Rényi relative entropy. We also prove that we cannot get a new coherence measure f(C(·)) by a function f acting on a given coherence measure C.     

A Strengthened Monotonicity Inequality of Quantum Relative Entropy: A Unifying Approach Via Rényi Relative Entropy

We derive a strengthened monotonicity inequality for quantum relative entropy by employing properties of \({\alpha}\)-Rényi relative entropy. We develop a unifying treatment toward the improvement of some quantum entropy inequalities. In particular, an emphasis is put on a lower bound of quantum conditional mutual information (QCMI) as it gives a Pinsker-like lower bound for the QCMI. We also give some improved entropy inequalities based on Rényi relative entropy. The inequalities obtained, thus, extend some well-known ones. We also obtain a condition under which a tripartite operator becomes a Markov state. As a by-product we provide some trace inequalities of operators, which are of independent interest.     

Beam propagation factor based on the Rényi entropy

A beam width measure based on Rényi entropy was introduced by Luis [Opt. Lett31, 3644 (2006)]. That one-dimensional analysis was limited to beam profiles with rectangular symmetry. In this Letter, we derive a general Rényi beam width measure that accounts for the diffraction properties of beams with profiles of arbitrary symmetry. We also show that the square of this measure has a quadratic dependence as a function of the propagation coordinate, so that it can be applied to propagation through arbitrary ABCD paraxial systems. The Rényi beam propagation factor, here introduced, is discussed in examples where the M(2) factor seems to have a limited effectiveness in describing the beam spreading.     

Quantum Key Distribution Based on Coherent States

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Trapping of continuous-time quantum walks on Erdös–Rényi graphs

We consider the coherent exciton transport, modeled by continuous-time quantum walks, on Erdös–Rény graphs in the presence of a random distribution of traps. The role of trap concentration and of the substrate dilution is deepened showing that, at long times and for intermediate degree of dilution, the survival probability typically decays exponentially with a (average) decay rate which depends non-monotonically on the graph connectivity; when the degree of dilution is either very low or very high, stationary states, not affected by traps, get more likely giving rise to a survival probability decaying to a finite value. Both these features constitute a qualitative difference with respect to the behavior found for classical walks.     

Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT

We calculate the contributions of a general non-vacuum conformal family to R′enyi entropy in twodimensional conformal field theory(CFT). The primary operator of the conformal family can be either non-chiral or chiral, and we denote its scaling dimension by ?. For the case of two short intervals on a complex plane, we expand the R′enyi mutual information by the cross ratio x to order x~(2?+2). For the case of one interval on a torus with low temperature, we expand the R′enyi entropy by q = exp(-2πβ/L), with β being the inverse temperature and L being the spatial period, to order q~(?+2). To make the result meaningful, we require that the scaling dimension ? cannot be too small. For two intervals on a complex plane we need ? 1, and for one interval on a torus we need ? 2.We work in the small Newton constant limit on the gravity side and so a large central charge limit on the CFT side,and find matches of gravity and CFT results.     

Strong Converse for the Classical Capacity of Entanglement-Breaking and Hadamard Channels via a Sandwiched Rényi Relative Entropy

A strong converse theorem for the classical capacity of a quantum channel states that the probability of correctly decoding a classical message converges exponentially fast to zero in the limit of many channel uses if the rate of communication exceeds the classical capacity of the channel. Along with a corresponding achievability statement for rates below the capacity, such a strong converse theorem enhances our understanding of the capacity as a very sharp dividing line between achievable and unachievable rates of communication. Here, we show that such a strong converse theorem holds for the classical capacity of all entanglement-breaking channels and all Hadamard channels (the complementary channels of the former). These results follow by bounding the success probability in terms of a “sandwiched” Rényi relative entropy, by showing that this quantity is subadditive for all entanglement-breaking and Hadamard channels, and by relating this quantity to the Holevo capacity. Prior results regarding strong converse theorems for particular covariant channels emerge as a special case of our results.     

Quantum MIMO Communication Scheme Based on Quantum Teleportation with Triplet States

A novel quantum MIMO communication scheme is proposed by generalizing the wireless communication technique to the quantum field. The MIMO quantum teleportation can be implemented with triplet states in order to enhance the capacity and fidelity of the quantum channel, in which an n-qubit sequence of quantum signals can be transmitted through the MIMO quantum channel by applying the diversity technique. The quantum noise filtering is involved before the quantum signals are outputted. The analysis and discussions demonstrate that the quantum MIMO teleportation can be performed securely with high capacity and fidelity.     

An Estimation for the Power-Law Distribution Parameter Based on Entropy

A new estimation based on the Shannon entropy for the power-law distribution parameter is presented, The maximum likelihood estimation （MLE） of the parameter is discussed and the relation between the MLE and the moment estimation of the parameter is given out. It is shown that the minimum Shannon entropy estimation is equivalent to the MLE giving the log expectation.     

Multiparty Simultaneous Quantum Identity Authentication Based on Entanglement Swapping

We present a multiparty simultaneous quantum identity authentication protocol based on entanglement swapping. In our protocol, the multi-user can be authenticated by a trusted third party simultaneously.     

Universal Quantum Gates Based on Both Geometric and Dynamic Phases in Quantum Dots

A large-scalable quantum computer model,whose qubits are represented by the subspace subtended by the ground state and he single exciton state on semiconductor quantum dots,is proposed.A universal set of quantum gates in this system may be achieved by a mixed approach,composed of dynamic evolution and nonadiabatic geometric phase.     

Quantum Private Comparison Based on χ-Type Entangled States

A two-party quantum private comparison (QPC) protocol is constructed with χ-type entangled states in this paper. The proposed protocol employs a semi-honest third party (TP) that is allowed to misbehave on his own but cannot conspire with the adversary. The proposed protocol need perform Bell basis measurements and single-particle measurements but neither unitary operations nor quantum entanglement swapping technology. The proposed protocol possesses good security toward both the outside attack and the participant attack. TP only knows the comparison result of the private information from two parties in the proposed protocol.