Continuity bounds on the quantum relative entropy

The quantum relative entropy is frequently used as a distance, or distinguishability measure between two quantum states. In this paper we study the relation between this measure and a number of other measures used for that purpose, including the trace norm distance. More precisely, we derive lower and upper bounds on the relative entropy in terms of various distance measures for the difference of the states based on unitarily invariant norms. The upper bounds can be considered as statements of continuity of the relative entropy distance in the sense of Fannes. We employ methods from optimisation theory to obtain bounds that are as sharp as possible.Comment: 13 pages (ReVTeX), 3 figures, replaced with published versio

Binegativity and geometry of entangled states in two qubits

We prove that the binegativity is always positive for any two-qubit state. As a result, as suggested by the previous works, the asymptotic relative entropy of entanglement in two qubits does not exceed the Rains bound, and the PPT-entanglement cost for any two-qubit state is determined to be the logarithmic negativity of the state. Further, the proof reveals some geometrical characteristics of the entangled states, and shows that the partial transposition can give another separable approximation of the entangled state in two qubits.Comment: 5 pages, 3 figures. I made the proof more transparen

Universal quantum Controlled-NOT gate

An investigation of an optimal universal unitary Controlled-NOT gate that performs a specific operation on two unknown states of qubits taken from a great circle of the Bloch sphere is presented. The deep analogy between the optimal universal C-NOT gate and the `equatorial' quantum cloning machine (QCM) is shown. In addition, possible applications of the universal C-NOT gate are briefly discussed.Comment: 18 reference

On Hastings' counterexamples to the minimum output entropy additivity conjecture

Hastings recently reported a randomized construction of channels violating the minimum output entropy additivity conjecture. Here we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact probability distribution of the Schmidt coefficients of a random bipartite pure state, as in the original proof, but rather derive the necessary large deviation bounds by a concentration of measure argument. Furthermore, we prove non-additivity for the overwhelming majority of channels consisting of a Haar random isometry followed by partial trace over the environment, for an environment dimension much bigger than the output dimension. This makes Hastings' original reasoning clearer and extends the class of channels for which additivity can be shown to be violated.Comment: 17 pages + 1 lin

Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination

We consider the multiple hypothesis testing problem for symmetric quantum state discrimination between r given states \sigma_1,...,\sigma_r. By splitting up the overall test into multiple binary tests in various ways we obtain a number of upper bounds on the optimal error probability in terms of the binary error probabilities. These upper bounds allow us to deduce various bounds on the asymptotic error rate, for which it has been hypothesised that it is given by the multi-hypothesis quantum Chernoff bound (or Chernoff divergence) C(\sigma_1,...,\sigma_r), as recently introduced by Nussbaum and Szko{\l}a in analogy with Salikhov's classical multi-hypothesis Chernoff bound. This quantity is defined as the minimum of the pairwise binary Chernoff divergences min_{j<k}C(\sigma_j,\sigma_k). It was known already that the optimal asymptotic rate must lie between C/3 and C, and that for certain classes of sets of states the bound is actually achieved. It was known to be achieved, in particular, when the state pair that is closest together in Chernoff divergence is more than 6 times closer than the next closest pair. Our results improve on this in two ways. Firstly, we show that the optimal asymptotic rate must lie between C/2 and C. Secondly, we show that the Chernoff bound is already achieved when the closest state pair is more than 2 times closer than the next closest pair. We also show that the Chernoff bound is achieved when at least $r-2$ of the states are pure, improving on a previous result by Nussbaum and Szko{\l}a. Finally, we indicate a number of potential pathways along which a proof (or disproof) may eventually be found that the multi-hypothesis quantum Chernoff bound is always achieved.Comment: 50 pages. v3: Slightly restructured, main results unchanged, connection to Barnum and Knill's result (arXiv:quant-ph/0004088) clarified. Accepted for JM

Ischiofemoral impingement: the evolutionary cost of pelvic obstetric adaptation.

Funder: Flemmish research foundationThe risk for ischiofemoral impingement has been mainly related to a reduced ischiofemoral distance and morphological variance of the femur. From an evolutionary perspective, however, there are strong arguments that the condition may also be related to sexual dimorphism of the pelvis. We, therefore, investigated the impact of gender-specific differences in anatomy of the ischiofemoral space on the ischiofemoral clearance, during static and dynamic conditions. A random sampling Monte-Carlo experiment was performed to investigate ischiofemoral clearance during stance and gait in a large (n = 40 000) virtual study population, while using gender-specific kinematics. Subsequently, a validated gender-specific geometric morphometric analysis of the hip was performed and correlations between overall hip morphology (statistical shape analysis) and standard discrete measures (conventional metric approach) with the ischiofemoral distance were evaluated. The available ischiofemoral space is indeed highly sexually dimorphic and related primarily to differences in the pelvic anatomy. The mean ischiofemoral distance was 22.2 ± 4.3 mm in the females and 29.1 ± 4.1 mm in the males and this difference was statistically significant (P < 0.001). Additionally, the ischiofemoral distance was observed to be a dynamic measure, and smallest during femoral extension, and this in turn explains the clinical sign of pain in extension during long stride walking. In conclusion, the presence of a reduced ischiofemroal distance and related risk to develop a clinical syndrome of ischiofemoral impingement is strongly dominated by evolutionary effects in sexual dimorphism of the pelvis. This should be considered when female patients present with posterior thigh/buttock pain, particularly if worsened by extension. Controlled laboratory study

Maximally entangled mixed states of two qubits

We consider mixed states of two qubits and show under which global unitary operations their entanglement is maximized. This leads to a class of states that is a generalization of the Bell states. Three measures of entanglement are considered: entanglement of formation, negativity and relative entropy of entanglement. Surprisingly all states that maximize one measure also maximize the others. We will give a complete characterization of these generalized Bell states and prove that these states for fixed eigenvalues are all equivalent under local unitary transformations. We will furthermore characterize all nearly entangled states closest to the maximally mixed state and derive a new lower bound on the volume of separable mixed states

BRDF characterization of Al-coated thermoplastic polymer surfaces

In this paper, we present a combined morphological and optical characterization of aluminum-coated thermoplastic polymer surfaces. Flat plastic substrates, obtained by means of an injection molding process starting from plastic granules, were coated with ultra-thin aluminum films evaporated in vacuo, on top of which a silicon-based protective layer was plasma deposited in order to prevent oxidation of the metal reflective surface. Different sample treatments were studied to unravel the influence of substrate chemistry, substrate thickness, aluminum and protective layer thickness, and surface roughness on the actual optical reflectance properties. Bidirectional reflectance distribution function measurements, corroborated by surface morphological information obtained by means of atomic force microscopy, correlate reflectance characteristics with the root-mean-square surface roughness, providing evidence for\ua0the role of the substrate and the thin films\u2019 morphology. The results unravel information of interest within many applicative fields involving metal coating processes of plastic substrates as an example in the case of automotive lighting

A Quantum Broadcasting Problem in Classical Low Power Signal Processing

We pose a problem called ``broadcasting Holevo-information'': given an unknown state taken from an ensemble, the task is to generate a bipartite state transfering as much Holevo-information to each copy as possible. We argue that upper bounds on the average information over both copies imply lower bounds on the quantum capacity required to send the ensemble without information loss. This is because a channel with zero quantum capacity has a unitary extension transfering at least as much information to its environment as it transfers to the output. For an ensemble being the time orbit of a pure state under a Hamiltonian evolution, we derive such a bound on the required quantum capacity in terms of properties of the input and output energy distribution. Moreover, we discuss relations between the broadcasting problem and entropy power inequalities. The broadcasting problem arises when a signal should be transmitted by a time-invariant device such that the outgoing signal has the same timing information as the incoming signal had. Based on previous results we argue that this establishes a link between quantum information theory and the theory of low power computing because the loss of timing information implies loss of free energy.Comment: 28 pages, late