Physica A: Statistical Mechanics and its Applications, 2016
Systems of identical particles with equal charge are studied under a special type of confinement.... more Systems of identical particles with equal charge are studied under a special type of confinement. These classical particles are free to move inside some convex region S and on the boundary of it Ω (the S d−1 −sphere, in our case). We shall show how particles arrange themselves under the sole action of the Coulomb repulsion in many dimensions in the usual Euclidean space, therefore generalizing the so called Thomson problem to many dimensions. Also, we explore how the problem varies when non-Euclidean geometries are considered. We shall see that optimal configurations in all cases possess a high degree of symmetry, regardless of the concomitant dimension or geometry.
Cooper pair (CP) binding with both zero and nonzero center-of-mass momenta (CMM) is studied with ... more Cooper pair (CP) binding with both zero and nonzero center-of-mass momenta (CMM) is studied with a set of renormalized equations assuming a short-ranged (attractive) pairwise interfermion interaction. Expanding the associated dispersion relation in 2D in powers of the CMM, in weak-to-moderate coupling a term linear in the CMM dominates the pair excitation energy, while the quadratic behavior usually assumed in Bose-Einstein (BE)-condensation studies prevails for any coupling only in the limit of zero Fermi velocity when the Fermi sea disappears, i.e., in vacuum. In 3D this same behavior is observed numerically. The linear term, moreover, exhibits CP breakup beyond a threshold CMM value which vanishes with coupling. This makes all the excited (nonzero-CMM) BE levels with preformed CPs collapse into a single ground level so that a BCS condensate (where only zero CMM CPs are usually allowed) appears in zero coupling to be a special case in either 2D or 3D of the BE condensate of linear-dispersion-relation CPs.
A new boson–fermion statistical model with two-hole (h) as well as two-electron (e) Cooper pairs ... more A new boson–fermion statistical model with two-hole (h) as well as two-electron (e) Cooper pairs (CP) exhibiting Bose–Einstein condensation (BEC)—which simultaneously reduces to BCS theory in weak coupling for perfect eh symmetry and to BEC when no hole CPs are present—yields reasonable transition temperatures for exotic superconductors, whether quasi-2D cuprate or 3D ones, for moderate departures from perfect eh symmetry.
The inference of entangled states on the basis of incomplete prior information is usually affecte... more The inference of entangled states on the basis of incomplete prior information is usually affected by the problem of fake inferred entanglement. We show that different inferences schemes overestimate the amount of entanglement. However, the Maximum-Entropy Minimum-Norm method yields all the accessible states compatible with the prior information of the system. For bipartite systems the entanglement boundaries are explicitly determined
We consider the change of entanglement of formation $\Delta E$ produced by the Hadamard-CNOT circ... more We consider the change of entanglement of formation $\Delta E$ produced by the Hadamard-CNOT circuit on a general (pure or mixed) state $\rho$ describing a system of two qubits. We study numerically the probabilities of obtaining different values of $\Delta E$, 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]. Comment: 12 pages, 2 figures
We investigate quantum states that posses both maximum entanglement and maximum discord between t... more We investigate quantum states that posses both maximum entanglement and maximum discord between the pertinent parties. Since entanglement (discord) is defined only for bipartite (two qubit) systems, we shall introduce an appropriate sum over of all bi-partitions as the associated measure. The ensuing definition --not new for entanglement-- is thus extended here to quantum discord. Also, additional dimensions within the parties are considered ({\it qudits}). We also discuss nonlocality (in the form of maximum violation of a Bell inequality) for all multiqubit systems. The emergence of more nonlocal states than local ones, all of them possessing maximum entanglement, will be linked, surprisingly enough, to whether quantum mechanics is defined over the fields of real or complex numbers.
We discuss some properties of the quantum discord based on the geometric distance advanced by Dak... more We discuss some properties of the quantum discord based on the geometric distance advanced by Dakic, Vedral, and Brukner [Phys. Rev. Lett. {\bf 105}, 190502 (2010)], with emphasis on Werner- and MEM-states. We ascertain just how good the measure is in representing quantum discord. We explore the dependence of quantum discord on the degree of mixedness of the bipartite states,
Physica A: Statistical Mechanics and its Applications, 2003
We consider the change of entanglement of formation ΔE produced by the Hadamard-CNOT circuit on a... more 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 introduced by
ABSTRACT A recent unification of the BCS theory with that of the Bose Einstein condensation (BEC)... more ABSTRACT A recent unification of the BCS theory with that of the Bose Einstein condensation (BEC) through a "complete" boson-fermion model is discussed as a generalization of the "BCS-Bose crossover" picture of superconductivity. Good first-principles Tc predictions in 2D are calculated with no adjustable parameters for the so-called "exotic" cuprate superconductors of the "Uemura plot", without abandoning the phonon interaction mechanism. The only condition is that one depart moderately from the perfect electron-/hole-Cooper-pair symmetry to which BCS (as well as the "crossover") theory are restricted by construction.
The use of the so-called entropic inequalities is revisited in the light of new quantum correlati... more The use of the so-called entropic inequalities is revisited in the light of new quantum correlation measures, specially nonlocality. We introduce the concept of classicality as the non-violation of these classical inequalities by quantum states of several multiqubit systems and compare it with the non-violation of Bell inequalities, that is, locality. We explore -numerically and analyticallythe relationship between several other quantum measures and discover the deep connection existing between them. The results are surprising due to the fact that these measures are very different in their nature and application. The cases for n = 2, 3, 4 qubits and a generalization to systems with arbitrary number of qubits are studied here when discriminated according to their degree of mixture.
Physica A: Statistical Mechanics and its Applications, 2002
We introduce trial functions of a form that maximizes Tsallis' information measure with the goal ... more We introduce trial functions of a form that maximizes Tsallis' information measure with the goal of using them together with the supersymmetric variational approach of Cooper, Dawson, and Shepard.
Any set of pure states living in an given Hilbert space possesses a natural and unique metric -th... more Any set of pure states living in an given Hilbert space possesses a natural and unique metric -the Haar measure-on the group U (N ) of unitary matrices. However, there is no specific measure induced on the set of eigenvalues ∆ of any density matrix ρ. Therefore, a general approach to the global properties of mixed states depends on the specific metric defined on ∆. In the present work we shall employ a simple measure on ∆ that has the advantage of possessing a clear geometric visualization whenever discussing how arbitrary states are distributed according to some measure of mixedness. The degree of mixture will be that of the participation ratio R = 1/T r(ρ 2 ) and the concomitant maximum eigenvalue λ m . The cases studied will be the qubit-qubit system and the qubit-qutrit system, whereas some discussion will be made on higher-dimensional bipartite cases in both the R-domain and the λ m -domain.
We ascertain, following ideas of Arnesen, Bose, and Vedral concerning thermal entanglement [Phys.... more We ascertain, following ideas of Arnesen, Bose, and Vedral concerning thermal entanglement [Phys. Rev. Lett. 87 (2001) 017901] and using the statistical tool called entropic non-triviality [Lamberti, Martin, Plastino, and Rosso, Physica A 334 , that there is a one to one correspondence between (i) the mixing coefficient x of a Werner state, on the one hand, and (ii) the temperature T of the one-dimensional Heisenberg two-spin chain with a magnetic field B along the z−axis, on the other one. This is true for each value of B below a certain critical value Bc. The pertinent mapping depends on the particular B−value one selects within such a range. 89.70.+c;
Physica A: Statistical Mechanics and its Applications, 2016
Systems of identical particles with equal charge are studied under a special type of confinement.... more Systems of identical particles with equal charge are studied under a special type of confinement. These classical particles are free to move inside some convex region S and on the boundary of it Ω (the S d−1 −sphere, in our case). We shall show how particles arrange themselves under the sole action of the Coulomb repulsion in many dimensions in the usual Euclidean space, therefore generalizing the so called Thomson problem to many dimensions. Also, we explore how the problem varies when non-Euclidean geometries are considered. We shall see that optimal configurations in all cases possess a high degree of symmetry, regardless of the concomitant dimension or geometry.
Cooper pair (CP) binding with both zero and nonzero center-of-mass momenta (CMM) is studied with ... more Cooper pair (CP) binding with both zero and nonzero center-of-mass momenta (CMM) is studied with a set of renormalized equations assuming a short-ranged (attractive) pairwise interfermion interaction. Expanding the associated dispersion relation in 2D in powers of the CMM, in weak-to-moderate coupling a term linear in the CMM dominates the pair excitation energy, while the quadratic behavior usually assumed in Bose-Einstein (BE)-condensation studies prevails for any coupling only in the limit of zero Fermi velocity when the Fermi sea disappears, i.e., in vacuum. In 3D this same behavior is observed numerically. The linear term, moreover, exhibits CP breakup beyond a threshold CMM value which vanishes with coupling. This makes all the excited (nonzero-CMM) BE levels with preformed CPs collapse into a single ground level so that a BCS condensate (where only zero CMM CPs are usually allowed) appears in zero coupling to be a special case in either 2D or 3D of the BE condensate of linear-dispersion-relation CPs.
A new boson–fermion statistical model with two-hole (h) as well as two-electron (e) Cooper pairs ... more A new boson–fermion statistical model with two-hole (h) as well as two-electron (e) Cooper pairs (CP) exhibiting Bose–Einstein condensation (BEC)—which simultaneously reduces to BCS theory in weak coupling for perfect eh symmetry and to BEC when no hole CPs are present—yields reasonable transition temperatures for exotic superconductors, whether quasi-2D cuprate or 3D ones, for moderate departures from perfect eh symmetry.
The inference of entangled states on the basis of incomplete prior information is usually affecte... more The inference of entangled states on the basis of incomplete prior information is usually affected by the problem of fake inferred entanglement. We show that different inferences schemes overestimate the amount of entanglement. However, the Maximum-Entropy Minimum-Norm method yields all the accessible states compatible with the prior information of the system. For bipartite systems the entanglement boundaries are explicitly determined
We consider the change of entanglement of formation $\Delta E$ produced by the Hadamard-CNOT circ... more We consider the change of entanglement of formation $\Delta E$ produced by the Hadamard-CNOT circuit on a general (pure or mixed) state $\rho$ describing a system of two qubits. We study numerically the probabilities of obtaining different values of $\Delta E$, 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]. Comment: 12 pages, 2 figures
We investigate quantum states that posses both maximum entanglement and maximum discord between t... more We investigate quantum states that posses both maximum entanglement and maximum discord between the pertinent parties. Since entanglement (discord) is defined only for bipartite (two qubit) systems, we shall introduce an appropriate sum over of all bi-partitions as the associated measure. The ensuing definition --not new for entanglement-- is thus extended here to quantum discord. Also, additional dimensions within the parties are considered ({\it qudits}). We also discuss nonlocality (in the form of maximum violation of a Bell inequality) for all multiqubit systems. The emergence of more nonlocal states than local ones, all of them possessing maximum entanglement, will be linked, surprisingly enough, to whether quantum mechanics is defined over the fields of real or complex numbers.
We discuss some properties of the quantum discord based on the geometric distance advanced by Dak... more We discuss some properties of the quantum discord based on the geometric distance advanced by Dakic, Vedral, and Brukner [Phys. Rev. Lett. {\bf 105}, 190502 (2010)], with emphasis on Werner- and MEM-states. We ascertain just how good the measure is in representing quantum discord. We explore the dependence of quantum discord on the degree of mixedness of the bipartite states,
Physica A: Statistical Mechanics and its Applications, 2003
We consider the change of entanglement of formation ΔE produced by the Hadamard-CNOT circuit on a... more 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 introduced by
ABSTRACT A recent unification of the BCS theory with that of the Bose Einstein condensation (BEC)... more ABSTRACT A recent unification of the BCS theory with that of the Bose Einstein condensation (BEC) through a "complete" boson-fermion model is discussed as a generalization of the "BCS-Bose crossover" picture of superconductivity. Good first-principles Tc predictions in 2D are calculated with no adjustable parameters for the so-called "exotic" cuprate superconductors of the "Uemura plot", without abandoning the phonon interaction mechanism. The only condition is that one depart moderately from the perfect electron-/hole-Cooper-pair symmetry to which BCS (as well as the "crossover") theory are restricted by construction.
The use of the so-called entropic inequalities is revisited in the light of new quantum correlati... more The use of the so-called entropic inequalities is revisited in the light of new quantum correlation measures, specially nonlocality. We introduce the concept of classicality as the non-violation of these classical inequalities by quantum states of several multiqubit systems and compare it with the non-violation of Bell inequalities, that is, locality. We explore -numerically and analyticallythe relationship between several other quantum measures and discover the deep connection existing between them. The results are surprising due to the fact that these measures are very different in their nature and application. The cases for n = 2, 3, 4 qubits and a generalization to systems with arbitrary number of qubits are studied here when discriminated according to their degree of mixture.
Physica A: Statistical Mechanics and its Applications, 2002
We introduce trial functions of a form that maximizes Tsallis' information measure with the goal ... more We introduce trial functions of a form that maximizes Tsallis' information measure with the goal of using them together with the supersymmetric variational approach of Cooper, Dawson, and Shepard.
Any set of pure states living in an given Hilbert space possesses a natural and unique metric -th... more Any set of pure states living in an given Hilbert space possesses a natural and unique metric -the Haar measure-on the group U (N ) of unitary matrices. However, there is no specific measure induced on the set of eigenvalues ∆ of any density matrix ρ. Therefore, a general approach to the global properties of mixed states depends on the specific metric defined on ∆. In the present work we shall employ a simple measure on ∆ that has the advantage of possessing a clear geometric visualization whenever discussing how arbitrary states are distributed according to some measure of mixedness. The degree of mixture will be that of the participation ratio R = 1/T r(ρ 2 ) and the concomitant maximum eigenvalue λ m . The cases studied will be the qubit-qubit system and the qubit-qutrit system, whereas some discussion will be made on higher-dimensional bipartite cases in both the R-domain and the λ m -domain.
We ascertain, following ideas of Arnesen, Bose, and Vedral concerning thermal entanglement [Phys.... more We ascertain, following ideas of Arnesen, Bose, and Vedral concerning thermal entanglement [Phys. Rev. Lett. 87 (2001) 017901] and using the statistical tool called entropic non-triviality [Lamberti, Martin, Plastino, and Rosso, Physica A 334 , that there is a one to one correspondence between (i) the mixing coefficient x of a Werner state, on the one hand, and (ii) the temperature T of the one-dimensional Heisenberg two-spin chain with a magnetic field B along the z−axis, on the other one. This is true for each value of B below a certain critical value Bc. The pertinent mapping depends on the particular B−value one selects within such a range. 89.70.+c;
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Papers by J. Batle