405 research outputs found
Quantum analog of the original Bell inequality for two-qudit states with perfect correlations/anticorrelations
For an even qudit dimension we introduce a class of two-qudit
states exhibiting perfect correlations/anticorrelations and prove via the
generalized Gell-Mann representation that, for each two-qudit state from this
class, the maximal violation of the original Bell inequality is bounded from
above by the value - the upper bound attained on some two-qubit states.
We show that the two-qudit Greenberger-Horne-Zeilinger (GHZ) state with an
arbitrary even exhibits perfect correlations/anticorrelations and
belongs to the introduced two-qudit state class. These new results are
important steps towards proving in general the upper bound on
quantum violation of the original Bell inequality. The latter would imply that
similarly as the Tsirelson upper bound specifies the quantum analog
of the CHSH inequality for all bipartite quantum states, the upper bound
specifies the quantum analog of the original Bell inequality for
all bipartite quantum states with perfect correlations/ anticorrelations.
Possible consequences for the experimental tests on violation of the original
Bell inequality are briefly discussed.Comment: 16 page
Entanglement in continuous variable systems: Recent advances and current perspectives
We review the theory of continuous-variable entanglement with special
emphasis on foundational aspects, conceptual structures, and mathematical
methods. Much attention is devoted to the discussion of separability criteria
and entanglement properties of Gaussian states, for their great practical
relevance in applications to quantum optics and quantum information, as well as
for the very clean framework that they allow for the study of the structure of
nonlocal correlations. We give a self-contained introduction to phase-space and
symplectic methods in the study of Gaussian states of infinite-dimensional
bosonic systems. We review the most important results on the separability and
distillability of Gaussian states and discuss the main properties of bipartite
entanglement. These include the extremal entanglement, minimal and maximal, of
two-mode mixed Gaussian states, the ordering of two-mode Gaussian states
according to different measures of entanglement, the unitary (reversible)
localization, and the scaling of bipartite entanglement in multimode Gaussian
states. We then discuss recent advances in the understanding of entanglement
sharing in multimode Gaussian states, including the proof of the monogamy
inequality of distributed entanglement for all Gaussian states, and its
consequences for the characterization of multipartite entanglement. We finally
review recent advances and discuss possible perspectives on the qualification
and quantification of entanglement in non Gaussian states, a field of research
that is to a large extent yet to be explored.Comment: 61 pages, 7 figures, 3 tables; Published as Topical Review in J.
Phys. A, Special Issue on Quantum Information, Communication, Computation and
Cryptography (v3: few typos corrected
Spin phase diagram of the nu_e=4/11 composite fermion liquid
Spin polarization of the "second generation" nu_e=4/11 fractional quantum
Hall state (corresponding to an incompressible liquid in a one-third-filled
composite fermion Landau level) is studied by exact diagonalization. Spin phase
diagram is determined for GaAs structures of different width and electron
concentration. Transition between the polarized and partially unpolarized
states with distinct composite fermion correlations is predicted for realistic
parameters.Comment: 5 pages, 3 figure
On the quantum origin of the seeds of cosmic structure
The current understanding of the quantum origin of cosmic structure is
discussed critically. We point out that in the existing treatments a transition
from a symmetric quantum state to an (essentially classical) non-symmetric
state is implicitly assumed, but not specified or analyzed in any detail. In
facing the issue we are led to conclude that new physics is required to explain
the apparent predictive power of the usual schemes. Furthermore we show that
the novel way of looking at the relevant issues opens new windows from where
relevant information might be extracted regarding cosmological issues and
perhaps even clues about aspects of quantum gravity.Comment: replacement with final version to appear in Classical and Quantum
Gravit
Spectral densities of Wishart-Levy free stable random matrices: Analytical results and Monte Carlo validation
Random matrix theory is used to assess the significance of weak correlations
and is well established for Gaussian statistics. However, many complex systems,
with stock markets as a prominent example, exhibit statistics with power-law
tails, that can be modelled with Levy stable distributions. We review
comprehensively the derivation of an analytical expression for the spectra of
covariance matrices approximated by free Levy stable random variables and
validate it by Monte Carlo simulation.Comment: 10 pages, 1 figure, submitted to Eur. Phys. J.
Correlation evolution and monogamy of two geometric quantum discords in multipartite systems
We explore two different geometric quantum discords defined respectively via
the trace norm (GQD-1) and Hilbert-Schmidt norm (GQD-2) in multipartite
systems. A rigorous hierarchy relation is revealed for the two GQDs in a class
of symmetric two-qubit -shape states. For multiqubit pure states, it is
found that both GQDs are related to the entanglement concurrence, with the
hierarchy relation being saturated. Furthermore, we look into a four-partite
dynamical system consisting of two cavities interacting with independent
reservoirs. It is found that the GQD-2 can exhibit various sudden change
behaviours, while the GQD-1 only evolves asymptotically, with the two GQDs
exhibiting different monogamous properties.Comment: 5 pages, 3 figure
- …