384 research outputs found
Entanglement in thermal equilibrium states
We revisist the issue of entanglement of thermal equilibrium states in
composite quantum systems. The possible scenarios are exemplified in bipartite
qubit/qubit and qubit/qutrit systems.Comment: 4 figure
Entropy reduction of quantum measurements
It is observed that the entropy reduction (the information gain in the
initial terminology) of an efficient (ideal or pure) quantum measurement
coincides with the generalized quantum mutual information of a q-c channel
mapping an a priori state to the corresponding posteriori probability
distribution of the outcomes of the measurement. This observation makes it
possible to define the entropy reduction for arbitrary a priori states (not
only for states with finite von Neumann entropy) and to study its analytical
properties by using general properties of the quantum mutual information.
By using this approach one can show that the entropy reduction of an
efficient quantum measurement is a nonnegative lower semicontinuous concave
function on the set of all a priori states having continuous restrictions to
subsets on which the von Neumann entropy is continuous. Monotonicity and
subadditivity of the entropy reduction are also easily proved by this method.
A simple continuity condition for the entropy reduction and for the mean
posteriori entropy considered as functions of a pair (a priori state,
measurement) is obtained.
A characterization of an irreducible measurement (in the Ozawa sense) which
is not efficient is considered in the Appendix.Comment: 21 pages, minor corrections have been mad
Entropy inequalities from reflection positivity
We investigate the question of whether the entropy and the Renyi entropies of
the vacuum state reduced to a region of the space can be represented in terms
of correlators in quantum field theory. In this case, the positivity relations
for the correlators are mapped into inequalities for the entropies. We write
them using a real time version of reflection positivity, which can be
generalized to general quantum systems. Using this generalization we can prove
an infinite sequence of inequalities which are obeyed by the Renyi entropies of
integer index. There is one independent inequality involving any number of
different subsystems. In quantum field theory the inequalities acquire a simple
geometrical form and are consistent with the integer index Renyi entropies
being given by vacuum expectation values of twisting operators in the Euclidean
formulation. Several possible generalizations and specific examples are
analyzed.Comment: Significantly enlarged and corrected version. Counterexamples found
for the most general form of the inequalities. V3: minor change
Partial separability revisited: Necessary and sufficient criteria
We extend the classification of mixed states of quantum systems composed of
arbitrary number of subsystems of arbitrary dimensions. This extended
classification is complete in the sense of partial separability and gives
1+18+1 partial separability classes in the tripartite case contrary to a former
1+8+1. Then we give necessary and sufficient criteria for these classes, which
make it possible to determine to which class a mixed state belongs. These
criteria are given by convex roof extensions of functions defined on pure
states. In the special case of three-qubit systems, we define a different set
of such functions with the help of the Freudenthal triple system approach of
three-qubit entanglement.Comment: v3: 22 pages, 5 tables, 1 figure, minor corrections (typos),
clarification in the Introduction. Accepted in Phys. Rev. A. Comments are
welcom
Free energy density for mean field perturbation of states of a one-dimensional spin chain
Motivated by recent developments on large deviations in states of the spin
chain, we reconsider the work of Petz, Raggio and Verbeure in 1989 on the
variational expression of free energy density in the presence of a mean field
type perturbation. We extend their results from the product state case to the
Gibbs state case in the setting of translation-invariant interactions of finite
range. In the special case of a locally faithful quantum Markov state, we
clarify the relation between two different kinds of free energy densities (or
pressure functions).Comment: 29 pages, Section 5 added, to appear in Rev. Math. Phy
Local asymptotic normality for qubit states
We consider n identically prepared qubits and study the asymptotic properties
of the joint state \rho^{\otimes n}. We show that for all individual states
\rho situated in a local neighborhood of size 1/\sqrt{n} of a fixed state
\rho^0, the joint state converges to a displaced thermal equilibrium state of a
quantum harmonic oscillator. The precise meaning of the convergence is that
there exist physical transformations T_{n} (trace preserving quantum channels)
which map the qubits states asymptotically close to their corresponding
oscillator state, uniformly over all states in the local neighborhood.
A few consequences of the main result are derived. We show that the optimal
joint measurement in the Bayesian set-up is also optimal within the pointwise
approach. Moreover, this measurement converges to the heterodyne measurement
which is the optimal joint measurement of position and momentum for the quantum
oscillator. A problem of local state discrimination is solved using local
asymptotic normality.Comment: 16 pages, 3 figures, published versio
Quantum measurements without macroscopic superpositions
We study a class of quantum measurement models. A microscopic object is
entangled with a macroscopic pointer such that each eigenvalue of the measured
object observable is tied up with a specific pointer deflection. Different
pointer positions mutually decohere under the influence of a bath.
Object-pointer entanglement and decoherence of distinct pointer readouts
proceed simultaneously. Mixtures of macroscopically distinct object-pointer
states may then arise without intervening macroscopic superpositions.
Initially, object and apparatus are statistically independent while the latter
has pointer and bath correlated according to a metastable local thermal
equilibrium. We obtain explicit results for the object-pointer dynamics with
temporal coherence decay in general neither exponential nor Gaussian. The
decoherence time does not depend on details of the pointer-bath coupling if it
is smaller than the bath correlation time, whereas in the opposite Markov
regime the decay depends strongly on whether that coupling is Ohmic or
super-Ohmic.Comment: 50 pages, 5 figures, changed conten
How to detect a possible correlation from the information of a sub-system in quantum mechanical systems
A possibility to detect correlations between two quantum mechanical systems
only from the information of a subsystem is investigated. For generic cases, we
prove that there exist correlations between two quantum systems if the
time-derivative of the reduced purity is not zero. Therefore, an
experimentalist can conclude non-zero correlations between his/her system and
some environment if he/she finds the time-derivative of the reduced purity is
not zero. A quantitative estimation of a time-derivative of the reduced purity
with respect to correlations is also given. This clarifies the role of
correlations in the mechanism of decoherence in open quantum systems.Comment: 7 pages, 1 figur
A Quantum Broadcasting Problem in Classical Low Power Signal Processing
We pose a problem called ``broadcasting Holevo-information'': given an
unknown state taken from an ensemble, the task is to generate a bipartite state
transfering as much Holevo-information to each copy as possible.
We argue that upper bounds on the average information over both copies imply
lower bounds on the quantum capacity required to send the ensemble without
information loss. This is because a channel with zero quantum capacity has a
unitary extension transfering at least as much information to its environment
as it transfers to the output.
For an ensemble being the time orbit of a pure state under a Hamiltonian
evolution, we derive such a bound on the required quantum capacity in terms of
properties of the input and output energy distribution. Moreover, we discuss
relations between the broadcasting problem and entropy power inequalities.
The broadcasting problem arises when a signal should be transmitted by a
time-invariant device such that the outgoing signal has the same timing
information as the incoming signal had. Based on previous results we argue that
this establishes a link between quantum information theory and the theory of
low power computing because the loss of timing information implies loss of free
energy.Comment: 28 pages, late
Conditional Intensity and Gibbsianness of Determinantal Point Processes
The Papangelou intensities of determinantal (or fermion) point processes are
investigated. These exhibit a monotonicity property expressing the repulsive
nature of the interaction, and satisfy a bound implying stochastic domination
by a Poisson point process. We also show that determinantal point processes
satisfy the so-called condition which is a general form of
Gibbsianness. Under a continuity assumption, the Gibbsian conditional
probabilities can be identified explicitly.Comment: revised and extende
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