1,089 research outputs found
Correlation Energy and Entanglement Gap in Continuous Models
Our goal is to clarify the relation between entanglement and correlation
energy in a bipartite system with infinite dimensional Hilbert space. To this
aim we consider the completely solvable Moshinsky's model of two linearly
coupled harmonic oscillators. Also for small values of the couplings the
entanglement of the ground state is nonlinearly related to the correlation
energy, involving logarithmic or algebraic corrections. Then, looking for
witness observables of the entanglement, we show how to give a physical
interpretation of the correlation energy. In particular, we have proven that
there exists a set of separable states, continuously connected with the
Hartree-Fock state, which may have a larger overlap with the exact ground
state, but also a larger energy expectation value. In this sense, the
correlation energy provides an entanglement gap, i.e. an energy scale, under
which measurements performed on the 1-particle harmonic sub-system can
discriminate the ground state from any other separated state of the system.
However, in order to verify the generality of the procedure, we have compared
the energy distribution cumulants for the 1-particle harmonic sub-system of the
Moshinsky's model with the case of a coupling with a damping Ohmic bath at 0
temperature.Comment: 26 pages, 6 figure
Quantum entanglement
All our former experience with application of quantum theory seems to say:
{\it what is predicted by quantum formalism must occur in laboratory}. But the
essence of quantum formalism - entanglement, recognized by Einstein, Podolsky,
Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a
new resource as real as energy.
This holistic property of compound quantum systems, which involves
nonclassical correlations between subsystems, is a potential for many quantum
processes, including ``canonical'' ones: quantum cryptography, quantum
teleportation and dense coding. However, it appeared that this new resource is
very complex and difficult to detect. Being usually fragile to environment, it
is robust against conceptual and mathematical tools, the task of which is to
decipher its rich structure.
This article reviews basic aspects of entanglement including its
characterization, detection, distillation and quantifying. In particular, the
authors discuss various manifestations of entanglement via Bell inequalities,
entropic inequalities, entanglement witnesses, quantum cryptography and point
out some interrelations. They also discuss a basic role of entanglement in
quantum communication within distant labs paradigm and stress some
peculiarities such as irreversibility of entanglement manipulations including
its extremal form - bound entanglement phenomenon. A basic role of entanglement
witnesses in detection of entanglement is emphasized.Comment: 110 pages, 3 figures, ReVTex4, Improved (slightly extended)
presentation, updated references, minor changes, submitted to Rev. Mod. Phys
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