259 research outputs found
Generalized conditional entropy optimization for qudit-qubit states
We derive a general approximate solution to the problem of minimizing the
conditional entropy of a qudit-qubit system resulting from a local projective
measurement on the qubit, which is valid for general entropic forms and becomes
exact in the limit of weak correlations. This entropy measures the average
conditional mixedness of the post-measurement state of the qudit, and its
minimum among all local measurements represents a generalized entanglement of
formation. In the case of the von Neumann entropy, it is directly related to
the quantum discord. It is shown that at the lowest non-trivial order, the
problem reduces to the minimization of a quadratic form determined by the
correlation tensor of the system, the Bloch vector of the qubit and the local
concavity of the entropy, requiring just the diagonalization of a
matrix. A simple geometrical picture in terms of an associated correlation
ellipsoid is also derived, which illustrates the link between entropy
optimization and correlation access and which is exact for a quadratic entropy.
The approach enables a simple estimation of the quantum discord. Illustrative
results for two-qubit states are discussed.Comment: 11 pages, 6 figures. Final published versio
Generalized conditional entropy in bipartite quantum systems
We analyze, for a general concave entropic form, the associated conditional
entropy of a quantum system A+B, obtained as a result of a local measurement on
one of the systems (B). This quantity is a measure of the average mixedness of
A after such measurement, and its minimum over all local measurements is shown
to be the associated entanglement of formation between A and a purifying third
system C. In the case of the von Neumann entropy, this minimum determines also
the quantum discord. For classically correlated states and mixtures of a pure
state with the maximally mixed state, we show that the minimizing measurement
can be determined analytically and is universal, i.e., the same for all concave
forms. While these properties no longer hold for general states, we also show
that in the special case of the linear entropy, an explicit expression for the
associated conditional entropy can be obtained, whose minimum among projective
measurements in a general qudit-qubit state can be determined analytically, in
terms of the largest eigenvalue of a simple 3x3 correlation matrix. Such
minimum determines the maximum conditional purity of A, and the associated
minimizing measurement is shown to be also universal in the vicinity of maximal
mixedness. Results for X states, including typical reduced states of spin pairs
in XY chains at weak and strong transverse fields, are also provided and
indicate that the measurements minimizing the von Neumann and linear
conditional entropies are typically coincident in these states, being
determined essentially by the main correlation. They can differ, however,
substantially from that minimizing the geometric discord.Comment: 11 pages, 2 figures; References adde
History state formalism for Dirac's theory
We propose a history state formalism for a Dirac particle. By introducing a
reference quantum clock system it is first shown that Dirac's equation can be
derived by enforcing a timeless Wheeler-DeWitt-like equation for a global
state. The Hilbert space of the whole system constitutes a unitary
representation of the Lorentz group with respect to a properly defined
invariant product, and the proper normalization of global states directly
ensures standard Dirac's norm. Moreover, by introducing a second quantum clock,
the previous invariant product emerges naturally from a generalized continuity
equation. The invariant parameter associated with this second clock
labels history states for different particles, yielding an observable evolution
in the case of an hypothetical superposition of different masses. Analytical
expressions for both space-time density and electron-time entanglement are
provided for two particular families of electron's states, the former including
Pryce localized particles.Comment: 9 pages, 2 figures, final versio
Quantum discord and information deficit in spin chains
We examine the behavior of quantum correlations of spin pairs in a finite
anisotropic spin chain immersed in a transverse magnetic field, through
the analysis of the quantum discord and the conventional and quadratic one
way-information deficits. We first provide a brief review of these measures,
showing that the last ones can be obtained as particular cases of a generalized
information deficit based on general entropic forms. All these measures
coincide with an entanglement entropy in the case of pure states, but can be
non-zero in separable mixed states, vanishing just for classically correlated
states. It is then shown that their behavior in the exact ground state of the
chain exhibits similar features, deviating significantly from that of the pair
entanglement below the critical field. In contrast with entanglement, they
reach full range in this region, becoming independent of the pair separation
and coupling range in the immediate vicinity of the factorizing field. It is
also shown, however, that significant differences between the quantum discord
and the information deficits arise in the local minimizing measurement that
defines them. Both analytical and numerical results are provided.Comment: 14 pages, 5 figure
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