Entropic Bell inequalities

We derive entropic Bell inequalities from considering entropy Venn diagrams. These entropic inequalities, akin to the Braunstein-Caves inequalities, are violated for a quantum-mechanical Einstein-Podolsky-Rosen pair, which implies that the conditional entropies of Bell variables must be negative in this case. This suggests that the satisfaction of entropic Bell inequalities is equivalent to the non-negativity of conditional entropies as a necessary condition for separability

On the von Neumann capacity of noisy quantum channels

We discuss the capacity of quantum channels for information transmission and storage. Quantum channels have dual uses: they can be used to transmit known quantum states which code for classical information, and they can be used in a purely quantum manner, for transmitting or storing quantum entanglement. We propose here a definition of the von Neumann capacity of quantum channels, which is a quantum mechanical extension of the Shannon capacity and reverts to it in the classical limit. As such, the von Neumann capacity assumes the role of a classical or quantum capacity depending on the usage of the channel. In analogy to the classical construction, this capacity is defined as the maximum von Neumann mutual entropy processed by the channel, a measure which reduces to the capacity for classical information transmission through quantum channels (the "Kholevo capacity") when known quantum states are sent. The quantum mutual entropy fulfills all basic requirements for a measure of information, and observes quantum data-processing inequalities. We also derive a quantum Fano inequality relating the quantum loss of the channel to the fidelity of the quantum code. The quantities introduced are calculated explicitly for the quantum "depolarizing" channel. The von Neumann capacity is interpreted within the context of superdense coding, and an "extended" Hamming bound is derived that is consistent with that capacity.Comment: 15 pages RevTeX with psfig, 13 figures. Revised interpretation of capacity, added section, changed titl

Prolegomena to a non-equilibrium quantum statistical mechanics

We suggest that the framework of quantum information theory, which has been developing rapidly in recent years due to intense activity in quantum computation and quantum communication, is a reasonable starting point to study non-equilibrium quantum statistical phenomena. As an application, we discuss the non-equilibrium quantum thermodynamics of black hole formation and evaporation.Comment: 20 pages, LaTeX with elsart.cls, 8 postscript figures. Special issue on quantum computation of Chaos, Solitons, and Fractal

Photometric redshifts as a tool to study the Coma cluster galaxy populations

We investigate the Coma cluster galaxy luminosity function (GLF) at faint magnitudes, in particular in the u* band by applying photometric redshift techniques applied to deep u*, B, V, R, I images covering a region of ~1deg2 (R 24). Global and local GLFs in the B, V, R and I bands obtained with photometric redshift selection are consistent with our previous results based on a statistical background subtraction. In the area covered only by the u* image, the GLF was also derived after applying a statistical background subtraction. The GLF in the u* band shows an increase of the faint end slope towards the outer regions of the cluster (from alpha~1 in the cluster center to alpha~2 in the cluster periphery). This could be explained assuming a short burst of star formation in these galaxies when entering the cluster. The analysis of the multicolor type spatial distribution reveals that late type galaxies are distributed in clumps in the cluster outskirts, where X-ray substructures are also detected and where the GLF in the u* band is steeper.Comment: 14 pages, 2 figures in jpeg format, accepted in A&

On the nature of faint Low Surface Brightness galaxies in the Coma cluster

This project is the continuation of our study of faint Low Surface Brightness Galaxies (fLSBs) in one of the densest nearby galaxy regions known, the Coma cluster. Our goal is to improve our understanding of the nature of these objects by comparing the broad band spectral energy distribution with population synthesis models. The data were obtained with the MEGACAM and CFH12K cameras at the CFHT. We used the resulting photometry in 5 broad band filters (u*, B, V, R, and I), that included new u*-band data, to fit spectral models. With these spectral fits we inferred a cluster membership criterium, as well as the ages, dust extinctions, and photometric types of these fLSBs. We show that about half of the Coma cluster fLSBs have a spectral energy distribution well represented in our template library while the other half present a flux deficit at ultraviolet wavelengths. Among the well represented, ~80% are probably part of the Coma cluster based on their spectral energy distribution. They are relatively young (younger than 2.3 Gyrs for 90% of the sample) non-starburst objects. The later their type, the younger fLSBs are. A significant part of the fLSBs are quite dusty objects. fLSBs are low stellar mass objects (the later their type the less massive they are), with stellar masses comparable to globular clusters for the faintest ones. Their characteristics are correlated with infall directions, confirming the disruptive origin for part of them.Comment: Accepted for publication in A&A, 10 pages, 10 figure

Reduction criterion for separability

We introduce a separability criterion based on the positive map Γ:ρ→(Tr ρ)-ρ, where ρ is a trace-class Hermitian operator. Any separable state is mapped by the tensor product of Γ and the identity into a non-negative operator, which provides a simple necessary condition for separability. This condition is generally not sufficient because it is vulnerable to the dilution of entanglement. In the special case where one subsystem is a quantum bit, Γ reduces to time reversal, so that this separability condition is equivalent to partial transposition. It is therefore also sufficient for 2×2 and 2×3 systems. Finally, a simple connection between this map for two qubits and complex conjugation in the “magic” basis [Phys. Rev. Lett. 78, 5022 (1997)] is displayed

Optical simulation of quantum logic

A constructive method for simulating small-scale quantum circuits by use of linear optical devices is presented. It relies on the representation of several quantum bits by a single photon, and on the implementation of universal quantum gates using simple optical components (beam splitters, phase shifters, etc.). This suggests that the optical realization of small quantum networks with present-day quantum optics technology is a reasonable goal. This technique could be useful for demonstrating basic concepts of simple quantum algorithms or error-correction schemes. The optical analog of a nontrivial three-bit quantum circuit is presented as an illustration