12,551 research outputs found
Closed formula for the relative entropy of entanglement in all dimensions
The relative entropy of entanglement is defined in terms of the relative
entropy between an entangled state and its closest separable state (CSS). Given
a multipartite-state on the boundary of the set of separable states, we find a
closed formula for all the entangled state for which this state is a CSS. Quite
amazing, our formula holds for multipartite states in all dimensions. In
addition we show that if an entangled state is full rank, then its CSS is
unique. For the bipartite case of two qubits our formula reduce to the one
given in Phys. Rev. A 78, 032310 (2008).Comment: 8 pages, 1 figure, significantly revised; theorem 1 is now providing
necessary and sufficient conditions to determine if a state is CS
Atemporal diagrams for quantum circuits
A system of diagrams is introduced that allows the representation of various
elements of a quantum circuit, including measurements, in a form which makes no
reference to time (hence ``atemporal''). It can be used to relate quantum
dynamical properties to those of entangled states (map-state duality), and
suggests useful analogies, such as the inverse of an entangled ket. Diagrams
clarify the role of channel kets, transition operators, dynamical operators
(matrices), and Kraus rank for noisy quantum channels. Positive (semidefinite)
operators are represented by diagrams with a symmetry that aids in
understanding their connection with completely positive maps. The diagrams are
used to analyze standard teleportation and dense coding, and for a careful
study of unambiguous (conclusive) teleportation. A simple diagrammatic argument
shows that a Kraus rank of 3 is impossible for a one-qubit channel modeled
using a one-qubit environment in a mixed state.Comment: Minor changes in references. Latex 32 pages, 13 figures in text using
PSTrick
Rate-dependent morphology of Li2O2 growth in Li-O2 batteries
Compact solid discharge products enable energy storage devices with high
gravimetric and volumetric energy densities, but solid deposits on active
surfaces can disturb charge transport and induce mechanical stress. In this
Letter we develop a nanoscale continuum model for the growth of Li2O2 crystals
in lithium-oxygen batteries with organic electrolytes, based on a theory of
electrochemical non-equilibrium thermodynamics originally applied to Li-ion
batteries. As in the case of lithium insertion in phase-separating LiFePO4
nanoparticles, the theory predicts a transition from complex to uniform
morphologies of Li2O2 with increasing current. Discrete particle growth at low
discharge rates becomes suppressed at high rates, resulting in a film of
electronically insulating Li2O2 that limits cell performance. We predict that
the transition between these surface growth modes occurs at current densities
close to the exchange current density of the cathode reaction, consistent with
experimental observations.Comment: 8 pages, 6 fig
Interplay between computable measures of entanglement and other quantum correlations
Composite quantum systems can be in generic states characterized not only by
entanglement, but also by more general quantum correlations. The interplay
between these two signatures of nonclassicality is still not completely
understood. In this work we investigate this issue focusing on computable and
observable measures of such correlations: entanglement is quantified by the
negativity N, while general quantum correlations are measured by the
(normalized) geometric quantum discord D_G. For two-qubit systems, we find that
the geometric discord reduces to the squared negativity on pure states, while
the relationship holds for arbitrary mixed states. The latter
result is rigorously extended to pure, Werner and isotropic states of two-qudit
systems for arbitrary d, and numerical evidence of its validity for arbitrary
states of a qubit and a qutrit is provided as well. Our results establish an
interesting hierarchy, that we conjecture to be universal, between two relevant
and experimentally friendly nonclassicality indicators. This ties in with the
intuition that general quantum correlations should at least contain and in
general exceed entanglement on mixed states of composite quantum systems.Comment: 10 pages, 4 figure
Dynamic quantum clustering: a method for visual exploration of structures in data
A given set of data-points in some feature space may be associated with a
Schrodinger equation whose potential is determined by the data. This is known
to lead to good clustering solutions. Here we extend this approach into a
full-fledged dynamical scheme using a time-dependent Schrodinger equation.
Moreover, we approximate this Hamiltonian formalism by a truncated calculation
within a set of Gaussian wave functions (coherent states) centered around the
original points. This allows for analytic evaluation of the time evolution of
all such states, opening up the possibility of exploration of relationships
among data-points through observation of varying dynamical-distances among
points and convergence of points into clusters. This formalism may be further
supplemented by preprocessing, such as dimensional reduction through singular
value decomposition or feature filtering.Comment: 15 pages, 9 figure
Quantum Nonlocal Boxes Exhibit Stronger Distillability
The hypothetical nonlocal box (\textsf{NLB}) proposed by Popescu and Rohrlich
allows two spatially separated parties, Alice and Bob, to exhibit stronger than
quantum correlations. If the generated correlations are weak, they can
sometimes be distilled into a stronger correlation by repeated applications of
the \textsf{NLB}. Motivated by the limited distillability of \textsf{NLB}s, we
initiate here a study of the distillation of correlations for nonlocal boxes
that output quantum states rather than classical bits (\textsf{qNLB}s). We
propose a new protocol for distillation and show that it asymptotically
distills a class of correlated quantum nonlocal boxes to the value , whereas in contrast, the optimal non-adaptive
parity protocol for classical nonlocal boxes asymptotically distills only to
the value 3.0. We show that our protocol is an optimal non-adaptive protocol
for 1, 2 and 3 \textsf{qNLB} copies by constructing a matching dual solution
for the associated primal semidefinite program (SDP). We conclude that
\textsf{qNLB}s are a stronger resource for nonlocality than \textsf{NLB}s. The
main premise that develops from this conclusion is that the \textsf{NLB} model
is not the strongest resource to investigate the fundamental principles that
limit quantum nonlocality. As such, our work provides strong motivation to
reconsider the status quo of the principles that are known to limit nonlocal
correlations under the framework of \textsf{qNLB}s rather than \textsf{NLB}s.Comment: 25 pages, 7 figure
Properties of contact matrices induced by pairwise interactions in proteins
The total conformational energy is assumed to consist of pairwise interaction
energies between atoms or residues, each of which is expressed as a product of
a conformation-dependent function (an element of a contact matrix, C-matrix)
and a sequence-dependent energy parameter (an element of a contact energy
matrix, E-matrix). Such pairwise interactions in proteins force native
C-matrices to be in a relationship as if the interactions are a Go-like
potential [N. Go, Annu. Rev. Biophys. Bioeng. 12. 183 (1983)] for the native
C-matrix, because the lowest bound of the total energy function is equal to the
total energy of the native conformation interacting in a Go-like pairwise
potential. This relationship between C- and E-matrices corresponds to (a) a
parallel relationship between the eigenvectors of the C- and E-matrices and a
linear relationship between their eigenvalues, and (b) a parallel relationship
between a contact number vector and the principal eigenvectors of the C- and
E-matrices; the E-matrix is expanded in a series of eigenspaces with an
additional constant term, which corresponds to a threshold of contact energy
that approximately separates native contacts from non-native ones. These
relationships are confirmed in 182 representatives from each family of the SCOP
database by examining inner products between the principal eigenvector of the
C-matrix, that of the E-matrix evaluated with a statistical contact potential,
and a contact number vector. In addition, the spectral representation of C- and
E-matrices reveals that pairwise residue-residue interactions, which depends
only on the types of interacting amino acids but not on other residues in a
protein, are insufficient and other interactions including residue
connectivities and steric hindrance are needed to make native structures the
unique lowest energy conformations.Comment: Errata in DOI:10.1103/PhysRevE.77.051910 has been corrected in the
present versio
- …