1,569 research outputs found
Largest separable balls around the maximally mixed bipartite quantum state
For finite-dimensional bipartite quantum systems, we find the exact size of
the largest balls, in spectral norms for , of
separable (unentangled) matrices around the identity matrix. This implies a
simple and intutively meaningful geometrical sufficient condition for
separability of bipartite density matrices: that their purity \tr \rho^2 not
be too large. Theoretical and experimental applications of these results
include algorithmic problems such as computing whether or not a state is
entangled, and practical ones such as obtaining information about the existence
or nature of entanglement in states reached by NMR quantum computation
implementations or other experimental situations.Comment: 7 pages, LaTeX. Motivation and verbal description of results and
their implications expanded and improved; one more proof included. This
version differs from the PRA version by the omission of some erroneous
sentences outside the theorems and proofs, which will be noted in an erratum
notice in PRA (and by minor notational differences
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
Positive reduction from spectra
We study the problem of whether all bipartite quantum states having a
prescribed spectrum remain positive under the reduction map applied to one
subsystem. We provide necessary and sufficient conditions, in the form of a
family of linear inequalities, which the spectrum has to verify. Our conditions
become explicit when one of the two subsystems is a qubit, as well as for
further sets of states. Finally, we introduce a family of simple entanglement
criteria for spectra, closely related to the reduction and positive partial
transpose criteria, which also provide new insight into the set of spectra that
guarantee separability or positivity of the partial transpose.Comment: Linear Algebra and its Applications (2015
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