864 research outputs found
Entanglement for rank-2 mixed states
In a recent paper, Rungta et. al. [Phys. Rev. A, 64, 042315, 2001] introduced
a measure of mixed-state entanglement called the I-concurrence for arbitrary
pairs of qudits. We find an exact formula for an entanglement measure closely
related to the I-concurrence, the I-tangle, for all mixed states of two qudits
having no more than two nonzero eigenvalues. We use this formula to provide a
tight upper bound for the entanglement of formation for rank-2 mixed states of
a qubit and a qudit.Comment: 5 pages, uses amsthm and mathrsf
Lower Bound on Entanglement of Formation for the Qubit-Qudit System
Wootters [PRL 80, 2245 (1998)] has derived a closed formula for the
entanglement of formation (EOF) of an arbitrary mixed state in a system of two
qubits. There is no known closed form expression for the EOF of an arbitrary
mixed state in any system more complicated than two qubits. This paper, via a
relatively straightforward generalization of Wootters' original derivation,
obtains a closed form lower bound on the EOF of an arbitary mixed state of a
system composed of a qubit and a qudit (a d-level quantum system, with d
greater than or equal to 3). The derivation of the lower bound is detailed for
a system composed of a qubit and a qutrit (d = 3); the generalization to d
greater than 3 then follows readily.Comment: 14 pages, 0 Figures, 0 Table
Perfect Test of Entanglement for Two-level Systems
A 3-setting Bell-type inequality enforced by the indeterminacy relation of
complementary local observables is proposed as an experimental test of the
2-qubit entanglement. The proposed inequality has an advantage of being a
sufficient and necessary criterion of the separability. Therefore any entangled
2-qubit state cannot escape the detection by this kind of tests. It turns out
that the orientation of the local testing observables plays a crucial role in
our perfect detection of the entanglement.Comment: 4 pages, RevTe
Local cloning of two product states
Local quantum operations and classical communication (LOCC) put considerable
constraints on many quantum information processing tasks such as cloning and
discrimination. Surprisingly however, discrimination of any two pure states
survives such constraints in some sense. In this paper, we show that cloning is
not that lucky; namely, conclusive LOCC cloning of two product states is
strictly less efficient than global cloning.Comment: Totally rewritten with improved result
Separability for lattice systems at high temperature
Equilibrium states of infinite extended lattice systems at high temperature
are studied with respect to their entanglement. Two notions of separability are
offered. They coincide for finite systems but differ for infinitely extended
ones. It is shown that for lattice systems with localized interaction for high
enough temperature there exists no local entanglement. Even more quasifree
states at high temperature are also not distillably entangled for all local
regions of arbitrary size. For continuous systems entanglement survives for all
temperatures. In mean field theories it is possible, that local regions are not
entangled but the entanglement is hidden in the fluctuation algebra
Entanglement fidelity and measurement of entanglement preserving in quantum processes
The entanglement fidelity provides a measure of how well the entanglement
between two subsystems is preserved in a quantum process. By using a simple
model we show that in some cases this quantity in its original definition fails
in the measurement of the entanglement preserving. On the contrary, the
modified entanglement fidelity, obtained by using a proper local unitary
transformation on a subsystem, is shown to exhibit the behavior similar to that
of the concurrence in the quantum evolution.Comment: 4 pages, 2 figures. v2: repaired a severe oversight, removed an
incorrect claim, added references; v3: version accepted for publication in
Phys. Rev.
Universality in the entanglement structure of ferromagnets
Systems of exchange-coupled spins are commonly used to model ferromagnets.
The quantum correlations in such magnets are studied using tools from quantum
information theory. Isotropic ferromagnets are shown to possess a universal
low-temperature density matrix which precludes entanglement between spins, and
the mechanism of entanglement cancellation is investigated, revealing a core of
states resistant to pairwise entanglement cancellation. Numerical studies of
one-, two-, and three-dimensional lattices as well as irregular geometries
showed no entanglement in ferromagnets at any temperature or magnetic field
strength.Comment: 4 pages, 2 figure
Local and global statistical distances are equivalent on pure states
The statistical distance between pure quantum states is obtained by finding a
measurement that is optimal in a sense defined by Wootters. As such, one may
expect that the statistical distance will turn out to be different if the set
of possible measurements is restricted in some way. It nonetheless turns out
that if the restriction is to local operations and classical communication
(LOCC) on any multipartite system, then the statistical distance is the same as
it is without restriction, being equal to the angle between the states in
Hilbert space.Comment: 5 pages, comments welcom
- …