295 research outputs found
Operationally Invariant Measure of the Distance between Quantum States by Complementary Measurements
We propose an operational measure of distance of two quantum states, which
conversely tells us their closeness. This is defined as a sum of differences in
partial knowledge over a complete set of mutually complementary measurements
for the two states. It is shown that the measure is operationally invariant and
it is equivalent to the Hilbert-Schmidt distance. The operational measure of
distance provides a remarkable interpretation of the information distance
between quantum states.Comment: 4 page
Partial ferromagnetic ordering and indirect exchange interaction in spatially anisotropic kagome antiferromagnet Cs_2Cu_3CeF_{12}
We report the crystal structure and unconventional magnetic ordering of
Cs_2Cu_3CeF_{12}, which is composed of buckled kagome lattice of Cu^{2+} ions.
The exchange network in the buckled kagome lattice is fairly anisotropic, so
that the present spin system can be divided into two subsystems: alternating
Heisenberg chains with strong antiferromagnetic exchange interactions and
dangling spins. Although the direct exchange interactions between neighboring
spins were found to be all antiferromagnetic, ferromagnetic magnetic ordering
of the dangling spins was observed. Magnetization exhibits a plateau at
one-third of the saturation magnetization. These observations can be understood
in terms of the indirect interaction between dangling spins mediated by the
chain spin.Comment: 4 pages, 3 figure
Fundamental properties of Tsallis relative entropy
Fundamental properties for the Tsallis relative entropy in both classical and
quantum systems are studied. As one of our main results, we give the parametric
extension of the trace inequality between the quantum relative entropy and the
minus of the trace of the relative operator entropy given by Hiai and Petz. The
monotonicity of the quantum Tsallis relative entropy for the trace preserving
completely positive linear map is also shown without the assumption that the
density operators are invertible.
The generalized Tsallis relative entropy is defined and its subadditivity is
shown by its joint convexity. Moreover, the generalized Peierls-Bogoliubov
inequality is also proven
Different Types of Conditional Expectation and the Lueders - von Neumann Quantum Measurement
In operator algebra theory, a conditional expectation is usually assumed to
be a projection map onto a sub-algebra. In the paper, a further type of
conditional expectation and an extension of the Lueders - von Neumann
measurement to observables with continuous spectra are considered; both are
defined for a single operator and become a projection map only if they exist
for all operators. Criteria for the existence of the different types of
conditional expectation and of the extension of the Lueders - von Neumann
measurement are presented, and the question whether they coincide is studied.
All this is done in the general framework of Jordan operator algebras. The
examples considered include the type I and type II operator algebras, the
standard Hilbert space model of quantum mechanics, and a no-go result
concerning the conditional expectation of observables that satisfy the
canonical commutator relation.Comment: 10 pages, the original publication is available at
http://www.springerlink.co
Validity of the second law in nonextensive quantum thermodynamics
The second law of thermodynamics in nonextensive statistical mechanics is
discussed in the quantum regime. Making use of the convexity property of the
generalized relative entropy associated with the Tsallis entropy indexed by q,
Clausius' inequality is shown to hold in the range of q between zero and two.
This restriction on the range of the entropic index, q, is purely quantum
mechanical and there exists no upper bound of q for validity of the second law
in classical theory.Comment: 12 pages, no figure
Strengthened Lindblad inequality: applications in non equilibrium thermodynamics and quantum information theory
A strengthened Lindblad inequality has been proved. We have applied this
result for proving a generalized -theorem in non equilibrium thermodynamics.
Information processing also can be considered as some thermodynamic process.
From this point of view we have proved a strengthened data processing
inequality in quantum information theory.Comment: 7 pages, revte
On non-completely positive quantum dynamical maps on spin chains
The new arguments based on Majorana fermions indicating that non-completely
positive maps can describe open quantum evolution are presented.Comment: published; small change
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