3,952 research outputs found
Microscopic Origin of Quantum Chaos in Rotational Damping
The rotational spectrum of Yb is calculated diagonalizing different
effective interactions within the basis of unperturbed rotational bands
provided by the cranked shell model. A transition between order and chaos
taking place in the energy region between 1 and 2 MeV above the yrast line is
observed, associated with the onset of rotational damping. It can be related to
the higher multipole components of the force acting among the unperturbed
rotational bands.Comment: 7 pages, plain TEX, YITP/K-99
Entanglement requirements for implementing bipartite unitary operations
We prove, using a new method based on map-state duality, lower bounds on
entanglement resources needed to deterministically implement a bipartite
unitary using separable (SEP) operations, which include LOCC (local operations
and classical communication) as a particular case. It is known that the Schmidt
rank of an entangled pure state resource cannot be less than the Schmidt rank
of the unitary. We prove that if these ranks are equal the resource must be
uniformly (maximally) entangled: equal nonzero Schmidt coefficients. Higher
rank resources can have less entanglement: we have found numerical examples of
Schmidt rank 2 unitaries which can be deterministically implemented, by either
SEP or LOCC, using an entangled resource of two qutrits with less than one ebit
of entanglement.Comment: 7 pages Revte
Efficient generation of random multipartite entangled states using time optimal unitary operations
We review the generation of random pure states using a protocol of repeated
two qubit gates. We study the dependence of the convergence to states with Haar
multipartite entanglement distribution. We investigate the optimal generation
of such states in terms of the physical (real) time needed to apply the
protocol, instead of the gate complexity point of view used in other works.
This physical time can be obtained, for a given Hamiltonian, within the
theoretical framework offered by the quantum brachistochrone formalism. Using
an anisotropic Heisenberg Hamiltonian as an example, we find that different
optimal quantum gates arise according to the optimality point of view used in
each case. We also study how the convergence to random entangled states depends
on different entanglement measures.Comment: 5 pages, 2 figures. New title, improved explanation of the algorithm.
To appear in Phys. Rev.
Lower and upper bounds on the fidelity susceptibility
We derive upper and lower bounds on the fidelity susceptibility in terms of
macroscopic thermodynamical quantities, like susceptibilities and thermal
average values. The quality of the bounds is checked by the exact expressions
for a single spin in an external magnetic field. Their usefulness is
illustrated by two examples of many-particle models which are exactly solved in
the thermodynamic limit: the Dicke superradiance model and the single impurity
Kondo model. It is shown that as far as divergent behavior is considered, the
fidelity susceptibility and the thermodynamic susceptibility are equivalent for
a large class of models exhibiting critical behavior.Comment: 19 page
Dynamics of Atom-Field Entanglement from Exact Solutions: Towards Strong Coupling and Non-Markovian Regimes
We examine the dynamics of bipartite entanglement between a two-level atom
and the electromagnetic field. We treat the Jaynes-Cummings model with a single
field mode and examine in detail the exact time evolution of entanglement,
including cases where the atomic state is initially mixed and the atomic
transition is detuned from resonance. We then explore the effects of other
nearby modes by calculating the exact time evolution of entanglement in more
complex systems with two, three, and five field modes. For these cases we can
obtain exact solutions which include the strong coupling regimes. Finally, we
consider the entanglement of a two-level atom with the infinite collection of
modes present in the intracavity field of a Fabre-Perot cavity. In contrast to
the usual treatment of atom-field interactions with a continuum of modes using
the Born-Markov approximation, our treatment in all cases describes the full
non-Markovian dynamics of the atomic subsystem. Only when an analytic
expression for the infinite mode case is desired do we need to make a weak
coupling assumption which at long times approximates Markovian dynamics.Comment: 12 pages, 5 figures; minor changes in grammar, wording, and
formatting. One unnecessary figure removed. Figure number revised (no longer
counts subfigures separately
Does export dependency hurt economic development? Empirical evidence from Singapore
A rapid export growth in East Asia was once identified as a source of the sustainable economic development that the region enjoyed. However, the current global recession has turned exports from an economic virtue to a vice. There is a growing awareness that a heavy reliance on exports has caused a serious economic downturn in the region. The present paper chooses Singapore as a case study to examine the relationship between the origin of the East Asian Miracle (i.e. export dependency) and the economic growth. For this purpose, the study employs a causality test developed by Toda and Yamamoto. The empirical findings indicate that despite a negative long-run relationship between export dependency and economic growth, Singapore's heavy reliance on exports does not seem to have produced negative effects on the nation's economic growth. This is because the increase in export dependency was an effect, and not a cause, of the country's output expansion.
Universal bounds for the Holevo quantity, coherent information \\ and the Jensen-Shannon divergence
The Holevo quantity provides an upper bound for the mutual information
between the sender of a classical message encoded in quantum carriers and the
receiver. Applying the strong sub-additivity of entropy we prove that the
Holevo quantity associated with an initial state and a given quantum operation
represented in its Kraus form is not larger than the exchange entropy. This
implies upper bounds for the coherent information and for the quantum
Jensen--Shannon divergence. Restricting our attention to classical information
we bound the transmission distance between any two probability distributions by
the entropic distance, which is a concave function of the Hellinger distance.Comment: 5 pages, 2 figure
Information theoretic treatment of tripartite systems and quantum channels
A Holevo measure is used to discuss how much information about a given POVM
on system is present in another system , and how this influences the
presence or absence of information about a different POVM on in a third
system . The main goal is to extend information theorems for mutually
unbiased bases or general bases to arbitrary POVMs, and especially to
generalize "all-or-nothing" theorems about information located in tripartite
systems to the case of \emph{partial information}, in the form of quantitative
inequalities. Some of the inequalities can be viewed as entropic uncertainty
relations that apply in the presence of quantum side information, as in recent
work by Berta et al. [Nature Physics 6, 659 (2010)]. All of the results also
apply to quantum channels: e.g., if \EC accurately transmits certain POVMs,
the complementary channel \FC will necessarily be noisy for certain other
POVMs. While the inequalities are valid for mixed states of tripartite systems,
restricting to pure states leads to the basis-invariance of the difference
between the information about contained in and .Comment: 21 pages. An earlier version of this paper attempted to prove our
main uncertainty relation, Theorem 5, using the achievability of the Holevo
quantity in a coding task, an approach that ultimately failed because it did
not account for locking of classical correlations, e.g. see [DiVincenzo et
al. PRL. 92, 067902 (2004)]. In the latest version, we use a very different
approach to prove Theorem
U-duality covariant membranes
We outline a formulation of membrane dynamics in D=8 which is fully covariant
under the U-duality group SL(2,Z) x SL(3,Z), and encodes all interactions to
fields in the eight-dimensional supergravity, which is constructed through
Kaluza-Klein reduction on T^3. Among the membrane degrees of freedom is an
SL(2,R) doublet of world-volume 2-form potentials, whose quantised electric
fluxes determine the membrane charges, and are conjectured to provide an
interpretation of the variables occurring in the minimal representation of
E_{6(6)} which appears in the context of automorphic membranes. We solve the
relevant equations for the action for a restricted class of supergravity
backgrounds. Some comments are made on supersymmetry and lower dimensions.Comment: LaTeX, 21 pages. v2: Minor changes in text, correction of a sign. v3:
some changes in text, a sign convention changed; version to appear in JHE
Summing free unitary random matrices
I use quaternion free probability calculus - an extension of free probability
to non-Hermitian matrices (which is introduced in a succinct but self-contained
way) - to derive in the large-size limit the mean densities of the eigenvalues
and singular values of sums of independent unitary random matrices, weighted by
complex numbers. In the case of CUE summands, I write them in terms of two
"master equations," which I then solve and numerically test in four specific
cases. I conjecture a finite-size extension of these results, exploiting the
complementary error function. I prove a central limit theorem, and its first
sub-leading correction, for independent identically-distributed zero-drift
unitary random matrices.Comment: 17 pages, 15 figure
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