arXiv subjects

M. Casas

Publications and source records attributed to M. Casas.

At least 37 records · Page 2Linked to original sources

arXiv2006

Understanding Quantum Entanglement: Qubits, Rebits and the Quaternionic Approach

It has been recently pointed out by Caves, Fuchs, and Rungta that real quantum mechanics (that is, quantum mechanics defined over real vector spaces provides an interesting foil theory whose study may shed some light on just which particular aspects of quantum entanglement are unique to standard quantum theory, and which ones are more generic over other physical theories endowed with this phenomenon. Following this work, we discuss some entanglement properties of two-rebits systems, making a comparison with the basic properties of two-qubits systems, i.e., the ones described by standard complex quantum mechanics. We also discuss the use of quaternionic quantum mechanics as applied to the phenomenon of entanglement.

quant-ph↗

arXiv2006

Entanglement Distribution and Entangling Power of Quantum Gates

Quantum gates, that play a fundamental role in quantum computation and other quantum information processes, are unitary evolution operators $\hat U$ that act on a composite system changing its entanglement. In the present contribution we study some aspects of these entanglement changes. By recourse of a Monte Carlo procedure, we compute the so called "entangling power" for several paradigmatic quantum gates and discuss results concerning the action of the CNOT gate. We pay special attention to the distribution of entanglement among the several parties involved.

quant-ph↗

arXiv2005

On the Connection Between Entanglement and the Speed of Quantum Evolution

It has been recently pointed out [V. Giovanetti, S. Lloyd, and L. Maccone, Europhys. Lett., {\bf 62} pp. 615-621 (2003)] that, for certain classes of states, quantum entanglement enhances the "speed" of evolution of composite quantum systems, as measured by the time a given initial state requires to evolve to an orthogonal state. We provide here a systematic study of this effect for pure states of bipartite systems of low dimensionality, considering both distinguishable (two-qubits) subsystems, and systems constituted of two indistinguishable particles.

quant-ph↗

arXiv2004

Jensen-Shannon divergence, Fisher information, and Wootters' hypothesis

We discuss different statistical distances in probability space, with emphasis on the Jensen-Shannon divergence, vis-a-vis {\it metrics} in Hilbert space and their relationship with Fisher's information measure. This study provides further reconfirmation of Wootters' hypothesis concerning the possibility that statistical fluctuations in the outcomes of measurements be regarded (at least partly) as responsible for the Hilbert-space structure of quantum mechanics.

quant-ph↗

arXiv2003

Inclusion relations among separability criteria

We revisit the application of different separability criteria by recourse to an exhaustive Monte Carlo exploration involving the pertinent state-space of pure and mixed states. The corresponding chain of implications of different criteria is in such a way numerically elucidated. We also quantify, for a bipartite system of arbitrary dimension, the proportion of states $ρ$ that can be distilled according to a definite criterion. Our work can be regarded as a complement to the recent review paper by B. Terhal [Theor. Comp. Sci. {\bf 287} (2002) 313]. Some questions posed there receive an answer here.

quant-ph↗

arXiv2003

Some Features of the Conditional $q$-Entropies of Composite Quantum Systems

The study of conditional $q$-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The $q$-entropies depend on the density matrix $ρ$ through the quantity $ω_q = Trρ^q$, and admit as a particular instance the standard von Neumann entropy in the limit case $q\to 1$. A comprehensive numerical survey of the space of pure and mixed states of bipartite systems is here performed, in order to determine the volumes in state space occupied by those states exhibiting various special properties related to the signs of their conditional $q$-entropies and to their connections with other separability-related features, including the majorization condition. Different values of the entropic parameter $q$ are considered, as well as different values of the dimensions $N_1$ and $N_2$ of the Hilbert spaces associated with the constituting subsystems. Special emphasis is paid to the analysis of the monotonicity properties, both as a function of $q$ and as a function of $N_1$ and $N_2$, of the various entropic functionals considered.

quant-ph↗

arXiv2003

How fundamental is the character of thermal uncertainty relations?

We show that thermodynamic uncertainties do not preserve their form if the underlying probability distribution is transformed into an escort one. Heisenberg's relations, on the other hand, are not affected by such transformation. We conclude therefore that the former uncertainty cannot be as fundamental as the quantum one.

cond-mat.stat-mech↗

arXiv2003

On the Correlations Between Quantum Entanglement and q-Information Measures

In the present study we revisit the application of the $q$-information measures $R_q$ of Rényi's and $S_q$ of Tsallis' to the discussion of special features of two qubits systems. More specifically, we study the correlations between the $q$-information measures and the entanglement of formation of a general (pure or mixed) state $ρ$ describing a system of two qubits. The analysis uses a Monte Carlo procedure involving the 15-dimensional 2-qubits space of pure and mixed states, under the assumption that these states are uniformly distributed according to the product measure recently introduced by Zyczkowski {\it et al} [Phys. Rev. A {\bf 58} (1998) 883].

quant-ph↗

arXiv2002

BCS and BEC Finally Unified: A Brief Review

We review efforts to unify both the Bardeen, Cooper and Schrieffer (BCS) and Bose-Einstein condensation (BEC) pictures of superconductivity. We have finally achieved this in terms of a "\textit{complete} boson-fermion (BF) model" (CBFM) that reduces in special cases to all the main continuum (as opposed to "spin") statistical theories of superconductivity. Our BF model is "complete" in the sense that not only two-electron (2e) but also two-hole (2h) Cooper pairs (CPs) are allowed in arbitrary proportions. In contrast, BCS-Bogoliubov theory--which can also be considered as the theory of a mixture of kinematically independent electrons, 2e- and 2h-CPs--allows only equal, 50%-50%, mixtures of the two kinds of CPs. This is obvious from the perfect symmetry about $μ$, the electron chemical potential, of the well-known Bogoliubov $v^{2}(ε)$ and $u^{2}(ε)$ coefficients, where $ε$ is the electron energy. The CBFM is then applied to see: a) whether the BCS model interaction for the electron-phonon dynamical mechanism is sufficient to predict the unusually high values of $T_{c}$ (in units of the Fermi temperature) of $\simeq 0.01-0.1$ exhibited by the so-called ``exotic'' superconductors \cite{Brandow} in both 2D and 3D--relative to the low values of $\lesssim 10^{-3}$ more or less correctly predicted by BCS theory for conventional, elemental superconductors; and b) whether it can at least suggest, if not explain, why "hole superconductors" have higher $T_{c}$'s.

cond-mat.supr-con↗

arXiv2002

The statistics of the entanglement changes generated by the Hadamard-CNOT quantum circuit

We consider the change of entanglement of formation $ΔE$ produced by the Hadamard-CNOT circuit on a general (pure or mixed) state $ρ$ describing a system of two qubits. We study numerically the probabilities of obtaining different values of $ΔE$, assuming that the initial state is randomly distributed in the space of all states according to the product measure recently introduced by Zyczkowski {\it et al.} [Phys. Rev. A {\bf 58} (1998) 883].

quant-ph↗

arXiv2002

Conditional q-Entropies and Quantum Separability: A Numerical Exploration

We revisit the relationship between quantum separability and the sign of the relative q-entropies of composite quantum systems. The q-entropies depend on the density matrix eigenvalues p_i through the quantity omega_q = sum_i p_i^q. Renyi's and Tsallis' measures constitute particular instances of these entropies. We perform a systematic numerical survey of the space of mixed states of two-qubit systems in order to determine, as a function of the degree of mixture, and for different values of the entropic parameter q, the volume in state space occupied by those states characterized by positive values of the relative entropy. Similar calculations are performed for qubit-qutrit systems and for composite systems described by Hilbert spaces of larger dimensionality. We pay particular attention to the limit case q --> infinity. Our numerical results indicate that, as the dimensionalities of both subsystems increase, composite quantum systems tend, as far as their relative q-entropies are concerned, to behave in a classical way.

quant-ph↗

arXiv2002

On the Entanglement Properties of Two-Rebits Systems

Following the recent work of Caves, Fuchs, and Rungta [Found. of Phys. Lett. {\bf 14} (2001) 199], we discuss some entanglement properties of two-rebits systems. We pay particular attention to the relationship between entanglement and purity. In particular, we determine (i) the probability densities for finding pure and mixed states with a given amount of entanglement, and (ii) the mean entanglement of two-rebits states as a function of the participation ratio.

quant-ph↗

arXiv2001

Pre-formed Cooper pairs and Bose-Einstein condensation in cuprate superconductors

A two-dimensional (2D) assembly of noninteracting, temperature-dependent, pre-formed Cooper pairs in chemical/thermal equilibrium with unpaired fermions is examined in a binary boson-fermion statistical model as the Bose-Einstein condensation (BEC) singularity temperature $T_{c}$ is approached from above. Compared with BCS theory (which is {\it not} a BEC theory) substantially higher $T_{c}$'s are obtained without any adjustable parameters, that fall roughly within the range of empirical $T_{c}$'s for quasi-2D cuprate superconductors.

cond-mat.supr-con↗

arXiv2001

Two-dimensional Bose-Einstein Condensation in Cuprate Superconductors

Transition temperatures $T_{c}$ calculated using the BCS model electron-phonon interaction without any adjustable parameters agree with empirical values for quasi-2D cuprate superconductors. They follow from a two-dimensional gas of temperature-dependent Cooper pairs in chemical and thermal equilibrium with unpaired fermions in a boson-fermion (BF) statistical model as the Bose-Einstein condensation (BEC) singularity temperature is approached from above. The {\it linear} (as opposed to quadratic) boson dispersion relation due to the Fermi sea yields substantially higher $T_{c}$'s with the BF model than with BCS or pure-boson BEC theories.

cond-mat.supr-con↗

arXiv2001

On the "Fake" Inferred Entanglement Associated with the Maximum Entropy Inference of Quantum States

The inference of entangled quantum states by recourse to the maximum entropy principle is considered in connection with the recently pointed out problem of fake inferred entanglement [R. Horodecki, {\it et al.}, Phys. Rev. A {\it 59} (1999) 1799]. We show that there are operators $\hat A$, both diagonal and non diagonal in the Bell basis, such that when the expectation value $<\hat A>$ is taken as prior information the problem of fake entanglement is not solved by adding a new constraint associated with the mean value of $\hat A^2$ (unlike what happens when the partial information is given by the expectation value of a Bell operator). The fake entanglement generated by the maximum entropy principle is also studied quantitatively by comparing the entanglement of formation of the inferred state with that of the original one.

quant-ph↗

arXiv2001

Multipole response of doped $^3$He drops

The multipole response of $^3$He$_N$ drops doped with very attractive impurities, such as a Xe atom or an SF$_6$ molecule, has been investigated in the framework of the Finite Range Density Functional Theory and the Random Phase Approximation. We show that volume ($L$ = 0) and surface ($L$ = 1, 2) modes become more fragmented, as compared with the results obtained for pure $^3$He$_N$ drops. In addition, the dipole mean energy goes smoothly to zero when $N$ increases, indicating that for large $N$ values these impurities are delocalized in the bulk of the drop.

physics.atm-clus↗

arXiv2001

Cooper pair dispersion relation in two dimensions

The Cooper pair binding energy {\it vs.} center-of-mass-momentum dispersion relation for Bose-Einstein condensation studies of superconductivity is found in two dimensions for a renormalized attractive delta interaction. It crosses over smoothly from a linear to a quadratic form as coupling varies from weak to strong.

cond-mat.str-el↗

arXiv2000

Statistical Model of Superconductivity in a 2D Binary Boson-Fermion Mixture

A two-dimensional (2D) assembly of noninteracting, temperature-dependent, composite-boson Cooper pairs (CPs) in chemical and thermal equilibrium with unpaired fermions is examined in a binary boson-fermion statistical model as the superconducting singularity temperature is approached from above. The model is derived from {\it first principles} for the BCS model interfermion interaction from three extrema of the system Helmholtz free energy (subject to constant pairable-fermion number) with respect to: a) the pairable-fermion distribution function; b) the number of excited (bosonic) CPs, i.e., with nonzero total momenta--usually ignored in BCS theory--and with the appropriate (linear, as opposed to quadratic) dispersion relation that arises from the Fermi sea; and c) the number of CPs with zero total momenta. Compared with the BCS theory condensate, higher singularity temperatures for the Bose-Einstein condensate are obtained in the binary boson-fermion mixture model which are in rough agreement with empirical critical temperatures for quasi-2D superconductors

cond-mat.supr-con↗