133 research outputs found
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
Description of Quantum Entanglement with Nilpotent Polynomials
We propose a general method for introducing extensive characteristics of
quantum entanglement. The method relies on polynomials of nilpotent raising
operators that create entangled states acting on a reference vacuum state. By
introducing the notion of tanglemeter, the logarithm of the state vector
represented in a special canonical form and expressed via polynomials of
nilpotent variables, we show how this description provides a simple criterion
for entanglement as well as a universal method for constructing the invariants
characterizing entanglement. We compare the existing measures and classes of
entanglement with those emerging from our approach. We derive the equation of
motion for the tanglemeter and, in representative examples of up to four-qubit
systems, show how the known classes appear in a natural way within our
framework. We extend our approach to qutrits and higher-dimensional systems,
and make contact with the recently introduced idea of generalized entanglement.
Possible future developments and applications of the method are discussed.Comment: 40 pages, 7 figures, 1 table, submitted for publication. v2: section
II.E has been changed and the Appendix on "Four qubit sl-entanglement
measure" has been removed. There are changes in the notation of section IV.
Typos and language mistakes has been corrected. A figure has been added and a
figure has been replaced. The references have been update
Three qubits can be entangled in two inequivalent ways
Invertible local transformations of a multipartite system are used to define
equivalence classes in the set of entangled states. This classification
concerns the entanglement properties of a single copy of the state.
Accordingly, we say that two states have the same kind of entanglement if both
of them can be obtained from the other by means of local operations and
classical communcication (LOCC) with nonzero probability. When applied to pure
states of a three-qubit system, this approach reveals the existence of two
inequivalent kinds of genuine tripartite entanglement, for which the GHZ state
and a W state appear as remarkable representatives. In particular, we show that
the W state retains maximally bipartite entanglement when any one of the three
qubits is traced out. We generalize our results both to the case of higher
dimensional subsystems and also to more than three subsystems, for all of which
we show that, typically, two randomly chosen pure states cannot be converted
into each other by means of LOCC, not even with a small probability of success.Comment: 12 pages, 1 figure; replaced with revised version; terminology
adapted to earlier work; reference added; results unchange
Local unitary equivalence and entanglement of multipartite pure states
The necessary and sufficient conditions for the equivalence of arbitrary
n-qubit pure quantum states under Local Unitary (LU) operations derived in [B.
Kraus Phys. Rev. Lett. 104, 020504 (2010)] are used to determine the different
LU-equivalence classes of up to five-qubit states. Due to this classification
new parameters characterizing multipartite entanglement are found and their
physical interpretation is given. Moreover, the method is used to derive
examples of two n-qubit states (with n>2 arbitrary) which have the properties
that all the entropies of any subsystem coincide, however, the states are
neither LU-equivalent nor can be mapped into each other by general local
operations and classical communication
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