Unified entropic measures of quantum correlations induced by local measurements

We introduce quantum correlations measures based on the minimal change in unified entropies induced by local rank-one projective measurements, divided by a factor that depends on the generalized purity of the system in the case of non-additive entropies. In this way, we overcome the issue of the artificial increasing of the value of quantum correlations measures based on non-additive entropies when an uncorrelated ancilla is appended to the system without changing the computability of our entropic correlations measures with respect to the previous ones. Moreover, we recover as limiting cases the quantum correlations measures based on von Neumann and R\'enyi entropies (i.e., additive entropies), for which the adjustment factor becomes trivial. In addition, we distinguish between total and semiquantum correlations and obtain some relations between them. Finally, we obtain analytical expressions of the entropic correlations measures for typical quantum bipartite systems.Comment: 10 pages, 1 figur

A family of generalized quantum entropies: definition and properties

We present a quantum version of the generalized $(h,\phi)$-entropies, introduced by Salicr\'u \textit{et al.} for the study of classical probability distributions. We establish their basic properties, and show that already known quantum entropies such as von Neumann, and quantum versions of R\'enyi, Tsallis, and unified entropies, constitute particular classes of the present general quantum Salicr\'u form. We exhibit that majorization plays a key role in explaining most of their common features. We give a characterization of the quantum $(h,\phi)$-entropies under the action of quantum operations, and study their properties for composite systems. We apply these generalized entropies to the problem of detection of quantum entanglement, and introduce a discussion on possible generalized conditional entropies as well.Comment: 26 pages, 1 figure. Close to published versio

High intrinsic energy resolution photon number resolving detectors

Transition Edge Sensors (TESs) are characterized by the intrinsic figure of merit to resolve both the energy and the statistical distribution of the incident photons. These properties lead TES devices to become the best single photon detector for quantum technology experiments. For a TES based on titanium and gold has been reached, at telecommunication wavelength, an unprecedented intrinsic energy resolution (0.113 eV). The uncertainties analysis of both energy resolution and photon state assignment has been discussed. The thermal properties of the superconductive device have been studied by fitting the bias curve to evaluate theoretical limit of the energy resolution

Collision entropy and optimal uncertainty

We propose an alternative measure of quantum uncertainty for pairs of arbitrary observables in the 2-dimensional case, in terms of collision entropies. We derive the optimal lower bound for this entropic uncertainty relation, which results in an analytic function of the overlap of the corresponding eigenbases. Besides, we obtain the minimum uncertainty states. We compare our relation with other formulations of the uncertainty principle.Comment: The manuscript has been accepted for publication as a Regular Article in Physical Review

General entropy-like uncertainty relations in finite dimensions

We revisit entropic formulations of the uncertainty principle for an arbitrary pair of positive operator-valued measures (POVM) $A$ and $B$, acting on finite dimensional Hilbert space. Salicr\'u generalized $(h,\phi)$-entropies, including R\'enyi and Tsallis ones among others, are used as uncertainty measures associated with the distribution probabilities corresponding to the outcomes of the observables. We obtain a nontrivial lower bound for the sum of generalized entropies for any pair of entropic functionals, which is valid for both pure and mixed states. The bound depends on the overlap triplet $(c_A,c_B,c_{A,B})$ with $c_A$ (resp. $c_B$) being the overlap between the elements of the POVM $A$ (resp. $B$) and $c_{A,B}$ the overlap between the pair of POVM. Our approach is inspired by that of de Vicente and S\'anchez-Ruiz [Phys.\ Rev.\ A \textbf{77}, 042110 (2008)] and consists in a minimization of the entropy sum subject to the Landau-Pollak inequality that links the maximum probabilities of both observables. We solve the constrained optimization problem in a geometrical way and furthermore, when dealing with R\'enyi or Tsallis entropic formulations of the uncertainty principle, we overcome the H\"older conjugacy constraint imposed on the entropic indices by the Riesz-Thorin theorem. In the case of nondegenerate observables, we show that for given $c_{A,B} > \frac{1}{\sqrt2}$, the bound obtained is optimal; and that, for R\'enyi entropies, our bound improves Deutsch one, but Maassen-Uffink bound prevails when $c_{A,B} \leq\frac12$. Finally, we illustrate by comparing our bound with known previous results in particular cases of R\'enyi and Tsallis entropies

Generalized Entropic Uncertainty Relations with Tsallis' Entropy

A generalization of the entropic formulation of the Uncertainty Principle of Quantum Mechanics is considered with the introduction of the q-entropies recently proposed by Tsallis. The concomitant generalized measure is illustrated for the case of phase and number operators in quantum optics. Interesting results are obtained when making use of q-entropies as the basis for constructing generalized entropic uncertainty measures

Natural Metric for Quantum Information Theory

We study in detail a very natural metric for quantum states. This new proposal has two basic ingredients: entropy and purification. The metric for two mixed states is defined as the square root of the entropy of the average of representative purifications of those states. Some basic properties are analyzed and its relation with other distances is investigated. As an illustrative application, the proposed metric is evaluated for 1-qubit mixed states.Comment: v2: enlarged; presented at ISIT 2008 (Toronto

Graphene edge method for three-dimensional probing of Raman microscopes focal volumes

In this work, a layer of graphene was used as a standard material for the measurement of the dimensions of Raman microscopes focal volumes of different confocal Raman spectrometers equipped with different objectives and excitation laser wavelengths. This method consists in probing the volume near the focal point of the system by using a flat graphene monolayer sheet with a straight edge. Graphene was selected because of its high Raman cross section and mechanically and chemically stability, allowing fast measurements and easy manipulation. In this paper, a method to employ graphene to accurately and precisely measure the three dimensions of the focal volume of a Raman microscope is presented; scanning along the axial and lateral directions, it is possible to reconstruct the three dimensions of the focal volume. Furthermore, these operations can be combined in a single procedure which allows the measurement of projections of the volume on planes parallel to the optical axis. Knowledge of these parameters enable absolute quantification of Raman-active molecules and support high-resolution Raman imaging

Single-photon light detection with transition-edge sensors

Transition-Edge Sensors (TESs) are microcalorimeters that measure the energy of incident single photons by the resistance increase of a superconducting film biased within the superconducting-to-normal transition. TES are able to detect single photons from IR to X-ray with an intrinsic energy resolution and photon-number discrimination capability. Metrology, astronomy and quantum communication are the fields where these properties can be particularly useful. In this work, we report about characterization of different TESs based on Ti films. Single photons have been detected from 200nm to 800 nm working at transition temperature Tc ∼ 100 mK. Using a pulsed laser at 690nm we have demonstrated the capability to resolve up to five photons