18 research outputs found
Generalized entropy optimized by an arbitrary distribution
We construct the generalized entropy optimized by a given arbitrary
statistical distribution with a finite linear expectation value of a random
quantity of interest. This offers, via the maximum entropy principle, a unified
basis for a great variety of distributions observed in nature, which can hardly
be described by the conventional methods. As a simple example, we explicitly
derive the entropy associated with the stretched exponential distribution. To
include the distributions with the divergent moments (e.g., the Levy stable
distributions), it is necessary to modify the definition of the expectation
value.Comment: 10 pages, no figure
Conditional q-Entropies and Quantum Separability: A Numerical Exploration
We revisit the relationship between quantum separability and the sign of the
relative q-entropies of composite quantum systems. The q-entropies depend on
the density matrix eigenvalues p_i through the quantity omega_q = sum_i p_i^q.
Renyi's and Tsallis' measures constitute particular instances of these
entropies. We perform a systematic numerical survey of the space of mixed
states of two-qubit systems in order to determine, as a function of the degree
of mixture, and for different values of the entropic parameter q, the volume in
state space occupied by those states characterized by positive values of the
relative entropy. Similar calculations are performed for qubit-qutrit systems
and for composite systems described by Hilbert spaces of larger dimensionality.
We pay particular attention to the limit case q --> infinity. Our numerical
results indicate that, as the dimensionalities of both subsystems increase,
composite quantum systems tend, as far as their relative q-entropies are
concerned, to behave in a classical way