arXiv subjects

C. Adami

Publications and source records attributed to C. Adami.

228 records · Page 13Linked to original sources

arXiv1997

Negative entropy and information in quantum mechanics

A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon) information theory, quantum (von Neumann) conditional entropies can be negative when considering quantum entangled systems, a fact related to quantum non-separability. The possibility that negative (virtual) information can be carried by entangled particles suggests a consistent interpretation of quantum informational processes.

quant-ph↗

arXiv1997

Quantum conditional operator and a criterion for separability

We analyze the properties of the conditional amplitude operator, the quantum analog of the conditional probability which has been introduced in [quant-ph/9512022]. The spectrum of the conditional operator characterizing a quantum bipartite system is invariant under local unitary transformations and reflects its inseparability. More specifically, it is shown that the conditional amplitude operator of a separable state cannot have an eigenvalue exceeding 1, which results in a necessary condition for separability. This leads us to consider a related separability criterion based on the positive map $Γ:ρ\to (Tr ρ) - ρ$, where $ρ$ is an Hermitian operator. Any separable state is mapped by the tensor product of this map and the identity into a non-negative operator, which provides a simple necessary condition for separability. 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 $2\times 2$ and $2\times 3$ systems. Finally, a simple connection between this map and complex conjugation in the "magic" basis is displayed.

quant-ph↗

arXiv1997

Segregations in clusters of galaxies

We analyse a sample of about 2000 galaxies in 40 regular clusters, to look for evidence of segregation with respect to galaxy luminosities and morphological types. We find evidence of luminosity segregation for galaxies brighter than $M_R < -21.5$, i.e. typically the four brightest members of each cluster. We also find evidence of morphological segregation: both the core-radius and the velocity dispersion increase along the Hubble sequence (ellipticals - S0 - early spirals - late spirals). Galaxies of different types have different velocity dispersion profiles, being steeper for later type galaxies. Simple modelling allows us to show that elliptical (and, to a lesser extent, S0) orbits are mostly tangential in the cluster core, and nearly isotropic outside, while spiral (in particular late-spiral) orbits are predominantly radial. A viable interpretation of our results is that (1) late spirals, at variance with other type galaxies, are a non-virialized cluster population, still on partially radial infalling orbits, (2) the elliptical phase-space distribution is evolving towards energy equipartition through the process of dynamical friction, (3) S0 and early-spirals have intermediate distributions between these two extremes.

astro-ph↗

arXiv1997

The Fundamental Plane of clusters of galaxies

We have used the ESO Nearby Abell Cluster Survey (ENACS) in combination with the Cosmos Galaxy Catalogue, to investigate the existence of a Fundamental Plane (FP) for rich clusters of galaxies. The 20 clusters with the most regular projected galaxy distributions appear to define a quite narrow FP, which is similar to the FP found by Schaeffer et al., who used other clusters. Our cluster FP appears to be different from that of ellipticals, as well as from the virial prediction. The latter fact may have several physical explanations, or a combination thereof. If M/L varies with L this will change the FP slope away from the virial slope. Differences in dynamical structure between clusters will also produce deviations from the virial FP. In view of the long virialization time-scales in all but the very central parts of galaxy clusters, the deviation of the cluster FP from the virial expectation may also result from clusters not being totally virialized. The scatter of the observations around the cluster FP is fairly small. An important part of the observed scatter is likely to be intrinsic. If this intrinsic spread were due exclusively to deviations from the Hubble flow it would imply cluster peculiar velocities of at most about 1000 km.s-1.

astro-ph↗

arXiv1997

A Deep Probing of the Coma cluster

We present here results from a deep spectroscopic survey of the Coma cluster of galaxies (29 galaxies between 18.98<m_R<21.5). Only 1 of these galaxies is within Coma compared to an expected 6.7 galaxies computed from nearby control fields. This discrepancy potentially indicates that Coma's faint end luminosity function has been grossly overestimated and raises concerns about the validity of using 2D statistical subtraction to correct for the background galaxy population when constructing cluster luminosity functions.

astro-ph↗

arXiv1997

Optical Simulation of Quantum Logic

A systematic 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 is reasonable given the present technology in quantum optics, and could be a useful technique for testing simple quantum algorithms or error-correction schemes. The optical circuit for quantum teleportation is presented as an illustration.

quant-ph↗

arXiv1997

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.

quant-ph↗

arXiv1997

Quantum Mechanics of Measurement

An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement outcomes can be negative, implying that measurement can be described via unitary, entropy-conserving, interactions, while still producing randomness in a measurement device. In such a framework, quantum measurement is not accompanied by a wave-function collapse, or a quantum jump. The theory is applied to the measurement of incompatible variables, giving rise to a stronger entropic uncertainty relation than heretofore known. It is also applied to standard quantum measurement situations such as the Stern-Gerlach and double-slit experiments to illustrate how randomness, inherent in the conventional quantum probabilities, arises in a unitary framework. Finally, the present view clarifies the relationship between classical and quantum concepts.

quant-ph↗

arXiv1997

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.

quant-ph↗

arXiv1996

Accessible information in quantum measurement

The amount of information that can be accessed via measurement of a quantum system prepared in different states is limited by the Kholevo bound. We present a simple proof of this theorem and its extension to sequential measurements based on the properties of quantum conditional and mutual entropies. The proof relies on a minimal physical model of the measurement which does not assume environmental decoherence, and has an intuitive diagrammatic representation.

quant-ph↗

arXiv1995

Abundance Distributions in Artificial Life and Stochastic Models: "Age and Area" revisited

Using an artificial system of self-replicating strings, we show a correlation between the age of a genotype and its abundance that reflects a punctuated rather than gradual picture of evolution, as suggested long ago by Willis. In support of this correlation, we measure genotype abundance distributions and find universal coefficients. Finally, we propose a simple stochastic model which describes the dynamics of equilibrium periods and which correctly predicts most of the observed distributions.

adap-org↗

arXiv1994

Self-organized Criticality in Living Systems

We suggest that ensembles of self-replicating entities such as biological systems naturally evolve into a self-organized critical state in which fluctuations, as well as waiting-times between phase transitions are distributed according to a 1/f power law. We demonstrate these concepts by analyzing a population of self-replicating strings (segments of computer-code) subject to mutation and survival of the fittest.

adap-org↗