17,399 research outputs found
Closed formula for the relative entropy of entanglement in all dimensions
The relative entropy of entanglement is defined in terms of the relative
entropy between an entangled state and its closest separable state (CSS). Given
a multipartite-state on the boundary of the set of separable states, we find a
closed formula for all the entangled state for which this state is a CSS. Quite
amazing, our formula holds for multipartite states in all dimensions. In
addition we show that if an entangled state is full rank, then its CSS is
unique. For the bipartite case of two qubits our formula reduce to the one
given in Phys. Rev. A 78, 032310 (2008).Comment: 8 pages, 1 figure, significantly revised; theorem 1 is now providing
necessary and sufficient conditions to determine if a state is CS
Entanglement-Saving Channels
The set of Entanglement Saving (ES) quantum channels is introduced and
characterized. These are completely positive, trace preserving transformations
which when acting locally on a bipartite quantum system initially prepared into
a maximally entangled configuration, preserve its entanglement even when
applied an arbitrary number of times. In other words, a quantum channel
is said to be ES if its powers are not entanglement-breaking for all
integers . We also characterize the properties of the Asymptotic
Entanglement Saving (AES) maps. These form a proper subset of the ES channels
that is constituted by those maps which, not only preserve entanglement for all
finite , but which also sustain an explicitly not null level of entanglement
in the asymptotic limit~. Structure theorems are provided
for ES and for AES maps which yield an almost complete characterization of the
former and a full characterization of the latter.Comment: 26 page
Lower Bounds of Concurrence for Tripartite Quantum Systems
We derive an analytical lower bound for the concurrence of tripartite quantum
mixed states. A functional relation is established relating concurrence and the
generalized partial transpositions.Comment: 10 page
Phase boundaries in deterministic dense coding
We consider dense coding with partially entangled states on bipartite systems
of dimension , studying the conditions under which a given number of
messages, , can be deterministically transmitted. It is known that the
largest Schmidt coefficient, , must obey the bound , and considerable empirical evidence points to the conclusion that there
exist states satisfying for every and except the
special cases and . We provide additional conditions under
which this bound cannot be reached -- that is, when it must be that
-- yielding insight into the shapes of boundaries separating
entangled states that allow messages from those that allow only . We
also show that these conclusions hold no matter what operations are used for
the encoding, and in so doing, identify circumstances under which unitary
encoding is strictly better than non-unitary.Comment: 7 pages, 1 figur
Maximization of thermal entanglement of arbitrarily interacting two qubits
We investigate the thermal entanglement of interacting two qubits. We
maximize it by tuning a local Hamiltonian under a given interaction
Hamiltonian. We prove that the optimizing local Hamiltonian takes a simple form
which dose not depend on the temperature and that the corresponding optimized
thermal entanglement decays as at high temperatures. We also find
that at low temperatures the thermal entanglement is maximum without any local
Hamiltonians and that the second derivative of the maximized thermal
entanglement changes discontinuously at the boundary between the high- and
low-temperature phases.Comment: 23 pages, 4 figure
Majorization criterion for distillability of a bipartite quantum state
Bipartite quantum states are classified into three categories: separable
states, bound entangled states, and free entangled states. It is of great
importance to characterize these families of states for the development of
quantum information science. In this paper, I show that the separable states
and the bound entangled states have a common spectral property. More precisely,
I prove that for undistillable -- separable and bound entangled -- states, the
eigenvalue vector of the global system is majorized by that of the local
system. This result constitutes a new sufficient condition for distillability
of bipartite quantum states. This is achieved by proving that if a bipartite
quantum state satisfies the reduction criterion for distillability, then it
satisfies the majorization criterion for separability.Comment: 4 pages, no figures, REVTEX. A new lemma (Lemma 2) added. To appear
in Physical Review Letter
Wave Profile for Anti-force Waves with Maximum Possible Currents
In the theoretical investigation of the electrical breakdown of a gas, we apply a one-dimensional, steady state, constant velocity, three component fluid model and consider the electrons to be the main element in propagation of the wave. The electron gas temperature, and therefore the electron gas partial pressure, is considered to be large enough to provide the driving force. The wave is considered to have a shock front, followed by a thin dynamical transition region. Our set of electron fluid-dynamical equations consists of the equations of conservation of mass, momentum, and energy, plus the Poisson\u27s equation. The set of equations is referred to as the electron fluid dynamical equations; and a successful solution therefor must meet a set of acceptable physical conditions at the trailing edge of the wave. For breakdown waves with a significant current behind the shock front, modifications must be made to the set of electron fluid dynamical equations, as well as the shock condition on electron temperature. Considering existence of current behind the shock front, we have derived the shock condition on electron temperature, and for a set of experimentally measured wave speeds, we have been able to find maximum current values for which solutions to our set of electron velocity, electron temperature, and electron number density within the dynamical transition region of the wave
Interplay between computable measures of entanglement and other quantum correlations
Composite quantum systems can be in generic states characterized not only by
entanglement, but also by more general quantum correlations. The interplay
between these two signatures of nonclassicality is still not completely
understood. In this work we investigate this issue focusing on computable and
observable measures of such correlations: entanglement is quantified by the
negativity N, while general quantum correlations are measured by the
(normalized) geometric quantum discord D_G. For two-qubit systems, we find that
the geometric discord reduces to the squared negativity on pure states, while
the relationship holds for arbitrary mixed states. The latter
result is rigorously extended to pure, Werner and isotropic states of two-qudit
systems for arbitrary d, and numerical evidence of its validity for arbitrary
states of a qubit and a qutrit is provided as well. Our results establish an
interesting hierarchy, that we conjecture to be universal, between two relevant
and experimentally friendly nonclassicality indicators. This ties in with the
intuition that general quantum correlations should at least contain and in
general exceed entanglement on mixed states of composite quantum systems.Comment: 10 pages, 4 figure
Witnessing quantum discord in 2 x N systems
Bipartite states with vanishing quantum discord are necessarily separable and
hence positive partial transpose (PPT). We show that 2 x N states satisfy
additional property: the positivity of their partial transposition is
recognized with respect to the canonical factorization of the original density
operator. We call such states SPPT (for strong PPT). Therefore, we provide a
natural witness for a quantum discord: if a 2 x N state is not SPPT it must
contain nonclassical correlations measured by quantum discord. It is an analog
of the celebrated Peres-Horodecki criterion: if a state is not PPT it must be
entangled.Comment: 5 page
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