113 research outputs found
General Monogamy Inequality for Bipartite Qubit Entanglement
We consider multipartite states of qubits and prove that their bipartite
quantum entanglement, as quantified by the concurrence, satisfies a monogamy
inequality conjectured by Coffman, Kundu, and Wootters. We relate this monogamy
inequality to the concept of frustration of correlations in quantum spin
systems.Comment: Fixed spelling mistake. Added references. Fixed error in
transformation law. Shorter and more explicit proof of capacity formula.
Reference added. Rewritten introduction and conclusion
Quantum phase transitions in matrix product systems
We investigate quantum phase transitions (QPTs) in spin chain systems
characterized by local Hamiltonians with matrix product ground states. We show
how to theoretically engineer such QPT points between states with predetermined
properties. While some of the characteristics of these transitions are
familiar, like the appearance of singularities in the thermodynamic limit,
diverging correlation length, and vanishing energy gap, others differ from the
standard paradigm: In particular, the ground state energy remains analytic, and
the entanglement entropy of a half-chain stays finite. Examples demonstrate
that these kinds of transitions can occur at the triple point of `conventional'
QPTs.Comment: 5 pages, 1 figur
PEPS as unique ground states of local Hamiltonians
In this paper we consider projected entangled pair states (PEPS) on arbitrary
lattices. We construct local parent Hamiltonians for each PEPS and isolate a
condition under which the state is the unique ground state of the Hamiltonian.
This condition, verified by generic PEPS and examples like the AKLT model, is
an injective relation between the boundary and the bulk of any local region.
While it implies the existence of an energy gap in the 1D case we will show
that in certain cases (e.g., on a 2D hexagonal lattice) the parent Hamiltonian
can be gapless with a critical ground state. To show this we invoke a mapping
between classical and quantum models and prove that in these cases the
injectivity relation between boundary and bulk solely depends on the lattice
geometry.Comment: 8 page
Quantum entanglement theory in the presence of superselection rules
Superselection rules severly constrain the operations which can be
implemented on a distributed quantum system. While the restriction to local
operations and classical communication gives rise to entanglement as a nonlocal
resource, particle number conservation additionally confines the possible
operations and should give rise to a new resource. In [Phys. Rev. Lett. 92,
087904 (2004), quant-ph/0310124] we showed that this resource can be quantified
by a single additional number, the superselection induced variance (SiV)
without changing the concept of entanglement. In this paper, we give the
results on pure states in greater detail; additionally, we provide a discussion
of mixed state nonlocality with superselection rules where we consider both
formation and distillation. Finally, we demonstrate that SiV is indeed a
resource, i.e., that it captures how well a state can be used to overcome the
restrictions imposed by the superselection rule.Comment: 16 pages, 5 figure
Sequentially generated states for the study of two dimensional systems
Matrix Product States can be defined as the family of quantum states that can
be sequentially generated in a one-dimensional system. We introduce a new
family of states which extends this definition to two dimensions. Like in
Matrix Product States, expectation values of few body observables can be
efficiently evaluated and, for the case of translationally invariant systems,
the correlation functions decay exponentially with the distance. We show that
such states are a subclass of Projected Entangled Pair States and investigate
their suitability for approximating the ground states of local Hamiltonians.Comment: 10 pages, 4 figure
Multipartite entanglement in 2 x 2 x n quantum systems
We classify multipartite entangled states in the 2 x 2 x n (n >= 4) quantum
system, for example the 4-qubit system distributed over 3 parties, under local
filtering operations. We show that there exist nine essentially different
classes of states, and they give rise to a five-graded partially ordered
structure, including the celebrated Greenberger-Horne-Zeilinger (GHZ) and W
classes of 3 qubits. In particular, all 2 x 2 x n-states can be
deterministically prepared from one maximally entangled state, and some
applications like entanglement swapping are discussed.Comment: 9 pages, 3 eps figure
Area laws in quantum systems: mutual information and correlations
The holographic principle states that on a fundamental level the information
content of a region should depend on its surface area rather than on its
volume. This counterintuitive idea which has its roots in the nonextensive
nature of black-hole entropy serves as a guiding principle in the search for
the fundamental laws of Planck-scale physics. In this paper we show that a
similar phenomenon emerges from the established laws of classical and quantum
physics: the information contained in part of a system in thermal equilibrium
obeys an area law. While the maximal information per unit area depends
classically only on the number of microscopic degrees of freedom, it may
diverge as the inverse temperature in quantum systems. A rigorous relation
between area laws and correlations is established and their explicit behavior
is revealed for a large class of quantum many-body states beyond equilibrium
systems.Comment: 5 pages, 2 figures, published version with appendi
Strings, Projected Entangled Pair States, and variational Monte Carlo methods
We introduce string-bond states, a class of states obtained by placing
strings of operators on a lattice, which encompasses the relevant states in
Quantum Information. For string-bond states, expectation values of local
observables can be computed efficiently using Monte Carlo sampling, making them
suitable for a variational abgorithm which extends DMRG to higher dimensional
and irregular systems. Numerical results demonstrate the applicability of these
states to the simulation of many-body sytems.Comment: 4 pages. v2: Submitted version, containing more numerical data.
Changed title and renamed "string states" to "string-bond states" to comply
with PRL conventions. v3: Accepted version, Journal-Ref. added (title differs
from journal
Entropy scaling and simulability by matrix product states
We investigate the relation between the scaling of block entropies and the efficient simulability by matrix product states (MPSs) and clarify the connection both for von Neumann and Renyi entropies. Most notably, even states obeying a strict area law for the von Neumann entropy are not necessarily approximable by MPSs. We apply these results to illustrate that quantum computers might outperform classical computers in simulating the time evolution of quantum systems, even for completely translational invariant systems subject to a time-independent Hamiltonian
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