310 research outputs found
Interference Visibility as a Witness of Entanglement and Quantum Correlation
In quantum information and communication one looks for the non-classical
features like interference and quantum correlations to harness the true power
of composite systems. We show how the concept akin to interference is, in fact,
intertwined in a quantitative manner to entanglement and quantum correlation.
In particular, we prove that the difference in the squared visibility for a
density operator before and after a complete measurement, averaged over all
unitary evolutions, is directly related to the quantum correlation measure
based on the measurement disturbance. For pure and mixed bipartite states the
unitary average of the squared visibility is related to entanglement measure.
This may constitute direct detection of entanglement and quantum correlations
with quantum interference setups. Furthermore, we prove that for a fixed purity
of the subsystem state, there is a complementarity relation between the linear
entanglement of formation and the measurement disturbance. This brings out a
quantitative difference between two kinds of quantum correlations.Comment: 6 pages, Revtex4-1, no figure. Any comments or remarks are welcome
Distinguishability of generic quantum states
Properties of random mixed states of order distributed uniformly with
respect to the Hilbert-Schmidt measure are investigated. We show that for large
, due to the concentration of measure, the trace distance between two random
states tends to a fixed number , which yields the
Helstrom bound on their distinguishability. To arrive at this result we apply
free random calculus and derive the symmetrized Marchenko--Pastur distribution,
which is shown to describe numerical data for the model of two coupled quantum
kicked tops. Asymptotic values for the fidelity, Bures and transmission
distances between two random states are obtained. Analogous results for quantum
relative entropy and Chernoff quantity provide other bounds on the
distinguishablity of both states in a multiple measurement setup due to the
quantum Sanov theorem.Comment: 13 pages including supplementary information, 6 figure
Infinitesimal local operations and differential conditions for entanglement monotones
Much of the theory of entanglement concerns the transformations that are
possible to a state under local operations with classical communication (LOCC);
however, this set of operations is complicated and difficult to describe
mathematically. An idea which has proven very useful is that of the {\it
entanglement monotone}: a function of the state which is invariant under local
unitary transformations and always decreases (or increases) on average after
any local operation. In this paper we look on LOCC as the set of operations
generated by {\it infinitesimal local operations}, operations which can be
performed locally and which leave the state little changed. We show that a
necessary and sufficient condition for a function of the state to be an
entanglement monotone under local operations that do not involve information
loss is that the function be a monotone under infinitesimal local operations.
We then derive necessary and sufficient differential conditions for a function
of the state to be an entanglement monotone. We first derive two conditions for
local operations without information loss, and then show that they can be
extended to more general operations by adding the requirement of {\it
convexity}. We then demonstrate that a number of known entanglement monotones
satisfy these differential criteria. Finally, as an application, we use the
differential conditions to construct a new polynomial entanglement monotone for
three-qubit pure states. It is our hope that this approach will avoid some of
the difficulties in the theory of multipartite and mixed-state entanglement.Comment: 21 pages, RevTeX format, no figures, three minor corrections,
including a factor of two in the differential conditions, the tracelessness
of the matrix in the convexity condition, and the proof that the local purity
is a monotone under local measurements. The conclusions of the paper are
unaffecte
Thermodynamic cost of creating correlations
We investigate the fundamental limitations imposed by thermodynamics for
creating correlations. Considering a collection of initially uncorrelated
thermal quantum systems, we ask how much classical and quantum correlations can
be obtained via a cyclic Hamiltonian process. We derive bounds on both the
mutual information and entanglement of formation, as a function of the
temperature of the systems and the available energy. While for a finite number
of systems there is a maximal temperature allowing for the creation of
entanglement, we show that genuine multipartite entanglement---the strongest
form of entanglement in multipartite systems---can be created at any
temperature when sufficiently many systems are considered. This approach may
find applications, e.g. in quantum information processing, for physical
platforms in which thermodynamic considerations cannot be ignored.Comment: 17 pages, 3 figures, substantially rewritten with some new result
The role of quantum information in thermodynamics --- a topical review
This topical review article gives an overview of the interplay between
quantum information theory and thermodynamics of quantum systems. We focus on
several trending topics including the foundations of statistical mechanics,
resource theories, entanglement in thermodynamic settings, fluctuation theorems
and thermal machines. This is not a comprehensive review of the diverse field
of quantum thermodynamics; rather, it is a convenient entry point for the
thermo-curious information theorist. Furthermore this review should facilitate
the unification and understanding of different interdisciplinary approaches
emerging in research groups around the world.Comment: published version. 34 pages, 6 figure
Bipartite quantum states and random complex networks
We introduce a mapping between graphs and pure quantum bipartite states and
show that the associated entanglement entropy conveys non-trivial information
about the structure of the graph. Our primary goal is to investigate the family
of random graphs known as complex networks. In the case of classical random
graphs we derive an analytic expression for the averaged entanglement entropy
while for general complex networks we rely on numerics. For large
number of nodes we find a scaling where both
the prefactor and the sub-leading O(1) term are a characteristic of
the different classes of complex networks. In particular, encodes
topological features of the graphs and is named network topological entropy.
Our results suggest that quantum entanglement may provide a powerful tool in
the analysis of large complex networks with non-trivial topological properties.Comment: 4 pages, 3 figure
Entangling power of quantized chaotic systems
We study the quantum entanglement caused by unitary operators that have
classical limits that can range from the near integrable to the completely
chaotic. Entanglement in the eigenstates and time-evolving arbitrary states is
studied through the von Neumann entropy of the reduced density matrices. We
demonstrate that classical chaos can lead to substantially enhanced
entanglement. Conversely, entanglement provides a novel and useful
characterization of quantum states in higher dimensional chaotic or complex
systems. Information about eigenfunction localization is stored in a graded
manner in the Schmidt vectors, and the principal Schmidt vectors can be scarred
by the projections of classical periodic orbits onto subspaces. The eigenvalues
of the reduced density matrices are sensitive to the degree of wavefunction
localization, and are roughly exponentially arranged. We also point out the
analogy with decoherence, as reduced density matrices corresponding to
subsystems of fully chaotic systems are diagonally dominant.Comment: 21 pages including 9 figs. (revtex
Entanglement, quantum randomness, and complexity beyond scrambling
Scrambling is a process by which the state of a quantum system is effectively
randomized due to the global entanglement that "hides" initially localized
quantum information. In this work, we lay the mathematical foundations of
studying randomness complexities beyond scrambling by entanglement properties.
We do so by analyzing the generalized (in particular R\'enyi) entanglement
entropies of designs, i.e. ensembles of unitary channels or pure states that
mimic the uniformly random distribution (given by the Haar measure) up to
certain moments. A main collective conclusion is that the R\'enyi entanglement
entropies averaged over designs of the same order are almost maximal. This
links the orders of entropy and design, and therefore suggests R\'enyi
entanglement entropies as diagnostics of the randomness complexity of
corresponding designs. Such complexities form a hierarchy between information
scrambling and Haar randomness. As a strong separation result, we prove the
existence of (state) 2-designs such that the R\'enyi entanglement entropies of
higher orders can be bounded away from the maximum. However, we also show that
the min entanglement entropy is maximized by designs of order only logarithmic
in the dimension of the system. In other words, logarithmic-designs already
achieve the complexity of Haar in terms of entanglement, which we also call
max-scrambling. This result leads to a generalization of the fast scrambling
conjecture, that max-scrambling can be achieved by physical dynamics in time
roughly linear in the number of degrees of freedom.Comment: 72 pages, 4 figures. Rewritten version with new title. v3: published
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