54 research outputs found
Concurrence-based Entanglement Measure For True -way Entanglement
An entanglement monotone, which is invariant under the determinant 1 SLOCC
operations and measures the true quadripartite entanglement, is explicitly
constructed.Comment: This paper has been withdrawn by the author due to a crucial
calculational error in (AD)-(BC) partitio
Entanglement of Four-Qubit Rank- Mixed States
It is known that there are three maximally entangled states , , and
in
four-qubit system. It is also known that there are three independent measures
for true four-way quantum
entanglement in the same system. In this paper we compute
and their corresponding linear monotones for three rank-two
mixed states \rho_j = p \ket{\Phi_j}\bra{\Phi_j} + (1 - p) \ket{\mbox{W}_4}
\bra{\mbox{W}_4}, where \ket{\mbox{W}_4} = (\ket{0111} + \ket{1011} +
\ket{1101} + \ket{1110}) / 2. We discuss the possible applications of our
results briefly.Comment: 20 pages, 5 eps figures, will appear in Quantum Information
Processin
REE From EOF
It is well-known that entanglement of formation (EOF) and relative entropy of
entanglement (REE) are exactly identical for all two-qubit pure states even
though their definitions are completely different. We think this fact implies
that there is a veiled connection between EOF and REE. In this context, we
suggest a procedure, which enables us to compute REE from EOF without relying
on the converse procedure. It is shown that the procedure yields correct REE
for many symmetric mixed states such as Bell-diagonal, generalized
Vedral-Plenino, and generalized Horodecki states. It also gives a correct REE
for less symmetric Vedral-Plenio-type state. However, it is shown that the
procedure does not provide correct REE for arbitrary mixed states.Comment: 17 pages, 1 figure, several typos corrected, final version to appear
in Quantum Information Processin
Mixedness and Entanglement in the presence of Localized Closed Timelike Curves
We examine mixedness and entanglement of the chronology-respecting (CR)
system with assuming that quantum mechanical closed timelike curves (CTCs)
exist in nature and by introducing the qubit system and applying the general
controlled operations between CR and CTC systems. We use the magnitude of Bloch
vector as a measure of mixedness. While Deutschian-CTC (D-CTC) either preserves
or decreases the magnitude, postselected-CTC (P-CTC) can increases it.
Nonintuitively, even the completely mixed CR-qubit can be converted into a pure
state after CTC-qubit travels around the P-CTC. It is also shown that while
D-CTC cannot increase the entanglement of CR system, P-CTC can increase it.
Surprisingly, any partially entangled state can be maximally entangled pure
state if P-CTC exists. Thus, distillation of P-CTC-assisted entanglement can be
easily achieved without preparing the multiple copies of the partially
entangled state.Comment: 10 pages, 1 figure; V2 12 pages, references added, will appear in QI
Entanglement Classification of extended Greenberger-Horne-Zeilinger-Symmetric States
In this paper we analyze entanglement classification of extended
Greenberger-Horne-Zeilinger-symmetric states , which is parametrized
by four real parameters , , and . The condition for
separable states of is analytically derived. The higher classes
such as bi-separable, W, and Greenberger-Horne-Zeilinger classes are roughly
classified by making use of the class-specific optimal witnesses or map from
the extended Greenberger-Horne-Zeilinger symmetry to the
Greenberger-Horne-Zeilinger symmetry. From this analysis we guess that the
entanglement classes of are not dependent on individually, but dependent on collectively. The
difficulty arising in extension of analysis with Greenberger-Horne-Zeilinger
symmetry to the higher-qubit system is discussed.Comment: 16 pages, 6 figure
Uncertainties in Gapped Graphene
Motivated by graphene-based quantum computer we examine the time-dependence
of the position-momentum and position-velocity uncertainties in the monolayer
gapped graphene. The effect of the energy gap to the uncertainties is shown to
appear via the Compton-like wavelength . The uncertainties in the
graphene are mainly contributed by two phenomena, spreading and zitterbewegung.
While the former determines the uncertainties in the long-range of time, the
latter gives the highly oscillation to the uncertainties in the short-range of
time. The uncertainties in the graphene are compared with the corresponding
values for the usual free Hamiltonian .
It is shown that the uncertainties can be under control within the quantum
mechanical law if one can choose the gap parameter freely.Comment: 12 pages, 11 figures V2: 21 pages, one more author is added. will
appear in PR
GUP and Point Interaction
The non-relativistic quantum mechanics with the generalized uncertainty
principle (GUP) is examined when the potential is one-dimensional
function. It is shown that unlike usual quantum mechanics, the
Schr\"{o}dinger and Feynman's path-integral approaches are inequivalent at the
first order of GUP parameter.Comment: 9 pages, no figure V2: will appear in PR
Sum Rule of Quantum Uncertainties: Coupled Harmonic Oscillator System with Time-Dependent Parameters
Uncertainties and are analytically derived in
an -coupled harmonic oscillator system when spring and coupling constants
are arbitrarily time-dependent and each oscillator is in an arbitrary excited
state. When , those uncertainties are shown as just arithmetic average
of uncertainties of two single harmonic oscillators. We call this property as
"sum rule of quantum uncertainty". However, this arithmetic average property is
not generally maintained when , but it is recovered in -coupled
oscillator systems if and only if quantum numbers are equal. The
generalization of our results to a more general quantum system is briefly
discussed.Comment: 15 pages, 2 figures v2: 17 pages, will appear in QI
Comment on "Path integral action of a particle with the generalized uncertainty principle and correspondence with noncommutativity"
Recently in [Phys. Rev. D 104010] the non-relativistic Feynman
propagator for harmonic oscillator system is presented when the generalized
uncertainty principle is employed. In this short comment it is shown that the
expression is incorrect. We also derive the correct expression of it.Comment: 5 pages, will appear in PRD (comment
Quantum Discord and Quantum Entanglement in the Background of an Asymptotically Flat Static Black Holes
The quantum discord and tripartite entanglement are discussed in the presence
of an asymptotically flat static black holes. The total correlation, quantum
discord and classical correlation exhibit decreasing behavior with increasing
Hawking temperature. It is shown that the classical correlation is less than
the quantum discord in the full range of Hawking temperature. The tripartite
entanglements for Greenberger-Horne-Zeilinger and W-states also exhibit
decreasing behavior with increasing Hawking temperature. At the infinite limit
of Hawking temperature the tripartite entanglements for
Greenberger-Horne-Zeilinger and W-states reduce to 52% and 33% of the
corresponding values in the flat space limit, respectively.Comment: 13pages,5figure
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