4,762 research outputs found
Dynamical symmetries of the Klein-Gordon equation
The dynamical symmetries of the two-dimensional Klein-Gordon equations with
equal scalar and vector potentials (ESVP) are studied. The dynamical symmetries
are considered in the plane and the sphere respectively. The generators of the
SO(3) group corresponding to the Coulomb potential, and the SU(2) group
corresponding to the harmonic oscillator potential are derived. Moreover, the
generators in the sphere construct the Higgs algebra. With the help of the
Casimir operators, the energy levels of the Klein-Gordon systems are yielded
naturally.Comment: 4
Assisted optimal state discrimination without entanglement
A fundamental problem in quantum information is to explore the roles of
different quantum correlations in a quantum information procedure. Recent work
[Phys. Rev. Lett., 107 (2011) 080401] shows that the protocol for assisted
optimal state discrimination (AOSD) may be implemented successfully without
entanglement, but with another correlation, quantum dissonance. However, both
the original work and the extension to discrimination of states [Phys. Rev.
A, 85 (2012) 022328] have only proved that entanglement can be absent in the
case with equal a \emph{priori} probabilities. By improving the protocol in
[Sci. Rep., 3 (2013) 2134], we investigate this topic in a simple case to
discriminate three nonorthogonal states of a qutrit, with positive real
overlaps. In our procedure, the entanglement between the qutrit and an
auxiliary qubit is found to be completely unnecessary. This result shows that
the quantum dissonance may play as a key role in optimal state discrimination
assisted by a qubit for more general cases.Comment: 6 pages, 3 figures. Accepted by EPL. We extended the protocol for
assisted optimal state discrimination to the case with positive real
overlaps, and presented a proof for the absence of entanglemen
Most robust and fragile two-qubit entangled states under depolarizing channels
For a two-qubit system under local depolarizing channels, the most robust and
most fragile states are derived for a given concurrence or negativity. For the
one-sided channel, the pure states are proved to be the most robust ones, with
the aid of the evolution equation for entanglement given by Konrad et al. [Nat.
Phys. 4, 99 (2008)]. Based on a generalization of the evolution equation for
entanglement, we classify the ansatz states in our investigation by the amount
of robustness, and consequently derive the most fragile states. For the
two-sided channel, the pure states are the most robust for a fixed concurrence.
Under the uniform channel, the most fragile states have the minimal negativity
when the concurrence is given in the region [1/2,1]. For a given negativity,
the most robust states are the ones with the maximal concurrence, and the most
fragile ones are the pure states with minimum of concurrence. When the
entanglement approaches zero, the most fragile states under general nonuniform
channels tend to the ones in the uniform channel. Influences on robustness by
entanglement, degree of mixture, and asymmetry between the two qubits are
discussed through numerical calculations. It turns out that the concurrence and
negativity are major factors for the robustness. When they are fixed, the
impact of the mixedness becomes obvious. In the nonuniform channels, the most
fragile states are closely correlated with the asymmetry, while the most robust
ones with the degree of mixture.Comment: 10 pages, 9 figs. to appear in Quantum Information & Computation
(QIC
Irreducible MultiQutrit Correlations in Greenberger-Horne-Zeilinger Type States
Following the idea of the continuity approach in [D. L. Zhou, Phys. Rev.
Lett. 101, 180505 (2008)], we obtain the degrees of irreducible multi-party
correlations in two families of -qutrit Greenberger-Horne-Zeilinger type
states. For the pure states in one of the families, the irreducible 2-party,
-party and -party () correlations are nonzero, which is
different from the -qubit case. We also derive the correlation distributions
in the -qutrit maximal slice state, which can be uniquely determined by its
-qutrit reduced density matrices among pure states. It is proved that
there is no irreducible -qutrit correlation in the maximal slice state. This
enlightens us to give a discussion about how to characterize the pure states
with irreducible -party correlation in arbitrarily high-dimensional systems
by the way of the continuity approach.Comment: 5p, no fi
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