50 research outputs found
Monogamy equalities for qubit entanglement from Lorentz invariance
A striking result from nonrelativistic quantum mechanics is the monogamy of
entanglement, which states that a particle can be maximally entangled only with
one other party, not with several ones. While there is the exact quantitative
relation for three qubits and also several inequalities describing monogamy
properties it is not clear to what extent exact monogamy relations are a
general feature of quantum mechanics. We prove that in all many-qubit systems
there exist strict monogamy laws for quantum correlations. They come about
through the curious relation between the nonrelativistic quantum mechanics of
qubits and Minkowski space. We elucidate the origin of entanglement monogamy
from this symmetry perspective and provide recipes to construct new families of
such equalities.Comment: 4 pages, 3 figure
Entanglement of three-qubit Greenberger-Horne-Zeilinger-symmetric states
The first characterization of mixed-state entanglement was achieved for
two-qubit states in Werner's seminal work [Phys. Rev. A 40, 4277 (1989)]. A
physically important extension of this result concerns mixtures of a pure
entangled state (such as the Greenberger-Horne-Zeilinger [GHZ] state) and the
completely unpolarized state. These mixed states serve as benchmark for the
robustness of entanglement. They share the same symmetries as the GHZ state. We
call such states GHZ-symmetric. Despite significant progress their multipartite
entanglement properties have remained an open problem. Here we give a complete
description of the entanglement in the family of three-qubit GHZ-symmetric
states and, in particular, of the three-qubit generalized Werner states. Our
method relies on the appropriate parameterization of the states and on the
invariance of entanglement properties under general local operations. An
immediate application of our results is the definition of a symmetrization
witness for the entanglement class of arbitrary three-qubit states.Comment: 4 pages, 2 figure
Partial transpose as a direct link between concurrence and negativity
Detection of entanglement in bipartite states is a fundamental task in
quantum information. The first method to verify entanglement in mixed states
was the partial-transpose criterion. Subsequently, numerous quantifiers for
bipartite entanglement were introduced, among them concurrence and negativity.
Surprisingly, these quantities are often treated as distinct or independent of
each other. The aim of this contribution is to highlight the close relations
between these concepts, to show the connections between seemingly independent
results, and to present various estimates for the mixed-state concurrence
within the same framework.Comment: 10 pages, 3 figure
Maximum N-body correlations do not in general imply genuine multipartite entanglement
The existence of correlations between the parts of a quantum system on the one hand, and entanglement between them on the other, are different properties. Yet, one intuitively would identify strong N-party correlations with N-party entanglement in an N-partite quantum state. If the local systems are qubits, this intuition is confirmed: The state with the strongest N-party correlations is the Greenberger-Horne-Zeilinger (GHZ) state, which does have genuine multipartite entanglement. However, for high-dimensional local systems the state with strongest N-party correlations may be a tensor product of Bell states, that is, partially separable. We show this by introducing several novel tools for handling the Bloch representation
Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems
We present evidence that nonlinear resonances govern the tunneling process
between symmetry-related islands of regular motion in mixed regular-chaotic
systems.In a similar way as for near-integrable tunneling, such resonances
induce couplings between regular states within the islands and states that are
supported by the chaotic sea. On the basis of this mechanism, we derive a
semiclassical expression for the average tunneling rate, which yields good
agreement in comparison with the exact quantum tunneling rates calculated for
the kicked rotor and the kicked Harper.Comment: 4 pages, 2 figure
The shape of higher-dimensional state space: Bloch-ball analog for a qutrit
Geometric intuition is a crucial tool to obtain deeper insight into many
concepts of physics. A paradigmatic example of its power is the Bloch ball, the
geometrical representation for the state space of the simplest possible quantum
system, a two-level system (or qubit). However, already for a three-level
system (qutrit) the state space has eight dimensions, so that its complexity
exceeds the grasp of our three-dimensional space of experience. This is
unfortunate, given that the geometric object describing the state space of a
qutrit has a much richer structure and is in many ways more representative for
a general quantum system than a qubit. In this work we demonstrate that, based
on the Bloch representation of quantum states, it is possible to construct a
three dimensional model for the qutrit state space that captures most of the
essential geometric features of the latter. Besides being of indisputable
theoretical value, this opens the door to a new type of representation, thus
extending our geometric intuition beyond the simplest quantum systems.Comment: 10 pages, 5 figures; discussion of results improved, one new figur
Distribution of entanglement and correlations in all finite dimensions
The physics of a many-particle system is determined by the correlations in its quantum state. Therefore, analyzing these correlations is the foremost task of many-body physics. Any 'a priori' constraint for the properties of the global vs. the local states-the so-called marginals-would help in order to narrow down the wealth of possible solutions for a given many-body problem, however, little is known about such constraints. We derive an equality for correlation-related quantities of any multipartite quantum system composed of finite-dimensional local parties. This relation defines a necessary condition for the compatibility of the marginal properties with those of the joint state. While the equality holds both for pure and mixed states, the pure-state version containing only entanglement measures represents a fully general monogamy relation for entanglement. These findings have interesting implications in terms of conservation laws for correlations, and also with respect to topology