512 research outputs found
Average R\'{e}nyi Entropy of a Subsystem in Random Pure State
In this paper we examine the average R\'{e}nyi entropy of a
subsystem when the whole composite system is a random pure state. We
assume that the Hilbert space dimensions of and are and
respectively. First, we compute the average R\'{e}nyi entropy analytically for
. We compare this analytical result with the approximate
average R\'{e}nyi entropy, which is shown to be very close. For general case we
compute the average of the approximate R\'{e}nyi entropy
analytically. When ,
reduces to , which is in agreement with the asymptotic expression of the average
von Neumann entropy. Based on the analytic result of we plot the -dependence of the quantum information derived from
. It is remarkable to note that the nearly
vanishing region of the information becomes shorten with increasing ,
and eventually disappears in the limit of . The
physical implication of the result is briefly discussed.Comment: 14 pages, 3 figure
Mixed-State Entanglement and Quantum Teleportation through Noisy Channels
The quantum teleportation with noisy EPR state is discussed. Using an optimal
decomposition technique, we compute the concurrence, entanglement of formation
and Groverian measure for various noisy EPR resources. It is shown analytically
that all entanglement measures reduce to zero when , where
is an average fidelity between Alice and Bob. This fact indicates
that the entanglement is a genuine physical resource for the teleportation
process. This fact gives valuable clues on the optimal decomposition for
higher-qubit mixed states. As an example, the optimal decompositions for the
three-qubit mixed states are discussed by adopting a teleportation with W-stateComment: 18 pages, 4 figure
Tripartite Entanglement in Noninertial Frame
The tripartite entanglement is examined when one of the three parties moves
with a uniform acceleration with respect to other parties. As Unruh effect
indicates, the tripartite entanglement exhibits a decreasing behavior with
increasing the acceleration. Unlike the bipartite entanglement, however, the
tripartite entanglement does not completely vanish in the infinite acceleration
limit. If the three parties, for example, share the Greenberger-Horne-Zeilinger
or W-state initially, the corresponding -tangle, one of the measures for
tripartite entanglement, is shown to be or 0.176 in this
limit, respectively. This fact indicates that the tripartite quantum
information processing may be possible even if one of the parties approaches to
the Rindler horizon. The physical implications of this striking result are
discussed in the context of black hole physics.Comment: 19 pages, 5 figure
Aharonov-Bohm-Coulomb Problem in Graphene Ring
We study the Aharonov-Bohm-Coulomb problem in a graphene ring. We
investigate, in particular, the effects of a Coulomb type potential of the form
on the energy spectrum of Dirac electrons in the graphene ring in two
different ways: one for the scalar coupling and the other for the vector
coupling. It is found that, since the potential in the scalar coupling breaks
the time-reversal symmetry between the two valleys as well as the effective
time-reversal symmetry in a single valley, the energy spectrum of one valley is
separated from that of the other valley, demonstrating a valley polarization.
In the vector coupling, however, the potential does not break either of the two
symmetries and its effect appears only as an additive constant to the spectrum
of Aharonov-Bohm potential. The corresponding persistent currents, the
observable quantities of the symmetry-breaking energy spectra, are shown to be
asymmetric about zero magnetic flux in the scalar coupling, while symmetric in
the vector coupling.Comment: 20 pages, 12 figures (V2) 18 pages, accepted in JPHYS
Attack of Many Eavesdroppers via Optimal Strategy in Quantum Cryptography
We examine a situation that eavesdroppers attack the Bennett-Brassard
cryptographic protocol via their own optimal and symmetric strategies.
Information gain and mutual information with sender for each eavesdropper are
explicitly derived. The receiver's error rate for the case of arbitrary
eavesdroppers can be derived using a recursive relation. Although first
eavesdropper can get mutual information without disturbance arising due to
other eavesdroppers, subsequent eavesdropping generally increases the
receiver's error rate. Other eavesdroppers cannot gain information on the input
signal sufficiently. As a result, the information each eavesdropper gains
becomes less than optimal one.Comment: 17 pages, 8 figure
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