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.     

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.     

A generalized complexity measure based on Rényi entropy

Phase drift is an inherent problem in one-way phase-encoded quantum key distribution (QKD) systems. Although combining passive with active phase compensation (APC) processes can effectively compensate for the phase drift, the security problems brought about by these processes are rarely considered. In this paper, we point out a security hole in the APC process and put forward a corresponding attack scheme. Under our proposed attack, the quantum bit error rate (QBER) of the QKD can be close to zero for some conditions. However, under the same conditions the ratio r of the key “0” and the key “1” which Bob (the legal communicators Alice and Bob) gets is no longer 1:1 but 2:1, which may expose Eve (the eavesdropper). In order to solve this problem, we modify the resend strategy of the attack scheme, which can force r to reach 1 and the QBER to be lower than the tolerable QBER.     

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.     

The minimum Rényi entropy output of a quantum channel is locally additive

We show that the minimum Rényi entropy output of a quantum channel is locally additive for Rényi parameter \(\alpha >1\). While our work extends the results of Gour and Friedland (IEEE Trans. Inf. Theory 59(1):603, 2012) (in which local additivity was proven for \(\alpha =1\)), it is based on several new techniques that incorporate the multiplicative nature of \(\ell _p\)-norms, in contrast to the additivity property of the von-Neumann entropy. Our results demonstrate that the counterexamples to the Rényi additivity conjectures exhibit purely global effects of quantum channels. Interestingly, the approach presented here cannot be extended to Rényi entropies with parameter \(\alpha <1\).     

Superinsulator–superconductor duality in two dimensions

For nearly a half century the dominant orthodoxy has been that the only effect of the Cooper pairing is the state with zero resistivity at finite temperatures, superconductivity. In this work we demonstrate that by the symmetry of the Heisenberg uncertainty principle relating the amplitude and phase of the superconducting order parameter, Cooper pairing can generate the dual state with zero conductivity in the finite temperature range, superinsulation. We show that this duality realizes in the planar Josephson junction arrays (JJA) via the duality between the Berezinskii–Kosterlitz–Thouless (BKT) transition in the vortex–antivortex plasma, resulting in phase-coherent superconductivity below the transition temperature, and the charge-BKT transition occurring in the insulating state of JJA and marking formation of the low-temperature charge-BKT state, superinsulation. We find that in disordered superconducting films that are on the brink of superconductor–insulator transition the Coulomb forces between the charges acquire two-dimensional character, i.e. the corresponding interaction energy depends logarithmically upon charge separation, bringing the same vortex-charge-BKT transition duality, and realization of superinsulation in disordered films as the low-temperature charge-BKT state. Finally, we discuss possible applications and utilizations of superconductivity–superinsulation duality.     

Consequences of Rényi entropy on the thermal geometries and Hawking evaporation of topological dyonic dilaton black hole

The thermodynamics of black holes(BHs) has had a profound impact on theoretical physics,providing insight into the nature of gravity, the quantum structure of spacetime and the fundamental laws governing the Universe. In this study, we investigate thermal geometries and Hawking evaporation of the recently proposed topological dyonic dilaton BH in anti-de Sitter(Ad S) space. We consider Rényi entropy and obtain the relations for pressure, heat capacity and Gibbs free energy and observe that the R...     

Some Properties of the kth-partial Rényi Entropy

The kth-partial Rényi entropies for both classical and quantum cases are defined and some properties of them are given. Also, we study the stability of kth-partial Rényi entropy for two states which satisfy majorization condition.     

Quantifying the quantumness of ensembles via generalized α-z-relative rényi entropy

International Journal of Theoretical Physics - Quantifying the quantumness of ensembles is a vital and practical task in quantum information theory. In this paper, we quantify the quantumness of...     

Heterotic σ-models and conformal supergravity in two dimensions

The (1, 0) and (2, 0) type heterotic σ-models with Wess-Zumino term are coupled to conformal supergravity in two dimensions. There are no new restrictions on the σ-model manifolds in addition to those which arise in the globally supersymmetric cases. In the (1, 0) case possible isometries of the scalar manifold are gauged. A derivation of d = 2 conformal supergravity based on the super Lie algebra OSp(2, N)⊕OSp(2, N) (N = 1, 2) is given.