67 research outputs found
Entanglement sharing among qudits
Consider a system consisting of n d-dimensional quantum particles (qudits),
and suppose that we want to optimize the entanglement between each pair. One
can ask the following basic question regarding the sharing of entanglement:
what is the largest possible value Emax(n,d) of the minimum entanglement
between any two particles in the system? (Here we take the entanglement of
formation as our measure of entanglement.) For n=3 and d=2, that is, for a
system of three qubits, the answer is known: Emax(3,2) = 0.550. In this paper
we consider first a system of d qudits and show that Emax(d,d) is greater than
or equal to 1. We then consider a system of three particles, with three
different values of d. Our results for the three-particle case suggest that as
the dimension d increases, the particles can share a greater fraction of their
entanglement capacity.Comment: 4 pages; v2 contains a new result for 3 qudits with d=
Fluctuations of Quantum Entanglement
It is emphasized that quantum entanglement determined in terms of the von
Neumann entropy operator is a stochastic quantity and, therefore, can
fluctuate. The rms fluctuations of the entanglement entropy of two-qubit
systems in both pure and mixed states have been obtained. It has been found
that entanglement fluctuations in the maximally entangled states are absent.
Regions where the entanglement fluctuations are larger than the entanglement
itself (strong fluctuation regions) have been revealed. It has been found that
the magnitude of the relative entanglement fluctuations is divergent at the
points of the transition of systems from an entangled state to a separable
state. It has been shown that entanglement fluctuations vanish in the separable
states.Comment: 5 pages, 4 figure
Distributed Entanglement
Consider three qubits A, B, and C which may be entangled with each other. We
show that there is a trade-off between A's entanglement with B and its
entanglement with C. This relation is expressed in terms of a measure of
entanglement called the "tangle," which is related to the entanglement of
formation. Specifically, we show that the tangle between A and B, plus the
tangle between A and C, cannot be greater than the tangle between A and the
pair BC. This inequality is as strong as it could be, in the sense that for any
values of the tangles satisfying the corresponding equality, one can find a
quantum state consistent with those values. Further exploration of this result
leads to a definition of the "three-way tangle" of the system, which is
invariant under permutations of the qubits.Comment: 13 pages LaTeX; references added, derivation of Eq. (11) simplifie
Moments of generalized Husimi distributions and complexity of many-body quantum states
We consider generalized Husimi distributions for many-body systems, and show
that their moments are good measures of complexity of many-body quantum states.
Our construction of the Husimi distribution is based on the coherent state of
the single-particle transformation group. Then the coherent states are
independent-particle states, and, at the same time, the most localized states
in the Husimi representation. Therefore delocalization of the Husimi
distribution, which can be measured by the moments, is a sign of many-body
correlation (entanglement). Since the delocalization of the Husimi distribution
is also related to chaoticity of the dynamics, it suggests a relation between
entanglement and chaos. Our definition of the Husimi distribution can be
applied not only to the systems of distinguishable particles, but also to those
of identical particles, i.e., fermions and bosons. We derive an algebraic
formula to evaluate the moments of the Husimi distribution.Comment: published version, 33 pages, 7 figre
Teleportation via thermally entangled state of a two-qubit Heisenberg XX chain
We find that quantum teleportation, using the thermally entangled state of
two-qubit Heisenberg XX chain as a resource, with fidelity better than any
classical communication protocol is possible. However, a thermal state with a
greater amount of thermal entanglement does not necessarily yield better
fidelity. It depends on the amount of mixing between the separable state and
maximally entangled state in the spectra of the two-qubit Heisenberg XX model.Comment: 5 pages, 1 tabl
Necessary And Sufficient Condition of Separability of Any System
The necessary and sufficient condition of separability of a mixed state of
any systems is presented, which is practical in judging the separability of a
mixed state. This paper also presents a method of finding the disentangled
decomposition of a separable mixed state.Comment: RevTeX, 5 pages including 1 figure, to appear in Phys. Rev.
Entangled Rings
Consider a ring of N qubits in a translationally invariant quantum state. We
ask to what extent each pair of nearest neighbors can be entangled. Under
certain assumptions about the form of the state, we find a formula for the
maximum possible nearest-neighbor entanglement. We then compare this maximum
with the entanglement achieved by the ground state of an antiferromagnetic ring
consisting of an even number of spin-1/2 particles. We find that, though the
antiferromagnetic ground state does not maximize the nearest-neighbor
entanglement relative to all other states, it does so relative to other states
having zero z-component of spin.Comment: 19 pages, no figures; v2 includes new results; v3 corrects a
numerical error for the case N=
Entanglement and spin squeezing in the two-atom Dicke model
We analyze the relation between the entanglement and spin-squeezing parameter
in the two-atom Dicke model and identify the source of the discrepancy recently
reported by Banerjee and Zhou et al that one can observe entanglement without
spin squeezing. Our calculations demonstrate that there are two criteria for
entanglement, one associated with the two-photon coherences that create
two-photon entangled states, and the other associated with populations of the
collective states. We find that the spin-squeezing parameter correctly predicts
entanglement in the two-atom Dicke system only if it is associated with
two-photon entangled states, but fails to predict entanglement when it is
associated with the entangled symmetric state. This explicitly identifies the
source of the discrepancy and explains why the system can be entangled without
spin-squeezing. We illustrate these findings in three examples of the
interaction of the system with thermal, classical squeezed vacuum and quantum
squeezed vacuum fields.Comment: 7 pages, 1 figur
Relational interpretation of the wave function and a possible way around Bell's theorem
The famous ``spooky action at a distance'' in the EPR-szenario is shown to be
a local interaction, once entanglement is interpreted as a kind of ``nearest
neighbor'' relation among quantum systems. Furthermore, the wave function
itself is interpreted as encoding the ``nearest neighbor'' relations between a
quantum system and spatial points. This interpretation becomes natural, if we
view space and distance in terms of relations among spatial points. Therefore,
``position'' becomes a purely relational concept. This relational picture leads
to a new perspective onto the quantum mechanical formalism, where many of the
``weird'' aspects, like the particle-wave duality, the non-locality of
entanglement, or the ``mystery'' of the double-slit experiment, disappear.
Furthermore, this picture cirumvents the restrictions set by Bell's
inequalities, i.e., a possible (realistic) hidden variable theory based on
these concepts can be local and at the same time reproduce the results of
quantum mechanics.Comment: Accepted for publication in "International Journal of Theoretical
Physics
Entanglement in a simple quantum phase transition
What entanglement is present in naturally occurring physical systems at
thermal equilibrium? Most such systems are intractable and it is desirable to
study simple but realistic systems which can be solved. An example of such a
system is the 1D infinite-lattice anisotropic XY model. This model is exactly
solvable using the Jordan-Wigner transform, and it is possible to calculate the
two-site reduced density matrix for all pairs of sites. Using the two-site
density matrix, the entanglement of formation between any two sites is
calculated for all parameter values and temperatures. We also study the
entanglement in the transverse Ising model, a special case of the XY model,
which exhibits a quantum phase transition. It is found that the next-nearest
neighbour entanglement (though not the nearest-neighbour entanglement) is a
maximum at the critical point. Furthermore, we show that the critical point in
the transverse Ising model corresponds to a transition in the behaviour of the
entanglement between a single site and the remainder of the lattice.Comment: 14 pages, 7 eps figure
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