1,167 research outputs found
Comment on "Quantitative wave-particle duality in multibeam interferometers"
In a recent paper [Phys. Rev. {\bf A64}, 042113 (2001)] S. D\"urr proposed an
interesting multibeam generalization of the quantitative formulation of
interferometric wave-particle duality, discovered by Englert for two-beam
interferometers. The proposed generalization is an inequality that relates a
generalized measure of the fringe visibility, to certain measures of the
maximum amount of which-way knowledge that can be stored in a which-way
detector. We construct an explicit example where, with three beams in a pure
state, the scheme proposed by D\"{u}rr leads to the possibility of an ideal
which-way detector, that can achieve a better path-discrimination, at the same
time as a better fringe visibility. In our opinion, this seems to be in
contrast with the intuitive idea of complementarity, as it is implemented in
the two-beams case, where an increase in path discrimination always implies a
decrease of fringe visibility, if the beams and the detector are in pure
states.Comment: 4 pages, 1 encapsulated figure. In press on Phys. Rev.
Characterization of multiqubit pure-state entanglement
A necessary and sufficient entanglement criterion based on variances of
Mermin-Klyshko's Bell operators is proved for multiqubit pure states. Contrary
to Bell's inequalities, entangled pure states strictly satisfy a quadratic
inequality but product ones can attain the equality under some local unitary
transformations, which can be obtained by solving a quadratic maximum problem.
This presents a characterization of multiqubit pure-state entanglement.Comment: 3 page
Physical Logic
In R.D. Sorkin's framework for logic in physics a clear separation is made
between the collection of unasserted propositions about the physical world and
the affirmation or denial of these propositions by the physical world. The
unasserted propositions form a Boolean algebra because they correspond to
subsets of an underlying set of spacetime histories. Physical rules of
inference, apply not to the propositions in themselves but to the affirmation
and denial of these propositions by the actual world. This physical logic may
or may not respect the propositions' underlying Boolean structure. We prove
that this logic is Boolean if and only if the following three axioms hold: (i)
The world is affirmed, (ii) Modus Ponens and (iii) If a proposition is denied
then its negation, or complement, is affirmed. When a physical system is
governed by a dynamical law in the form of a quantum measure with the rule that
events of zero measure are denied, the axioms (i) - (iii) prove to be too rigid
and need to be modified. One promising scheme for quantum mechanics as quantum
measure theory corresponds to replacing axiom (iii) with axiom (iv) Nature is
as fine grained as the dynamics allows.Comment: 14 pages, v2 published version with a change in the title and other
minor change
Localizable Entanglement
We consider systems of interacting spins and study the entanglement that can
be localized, on average, between two separated spins by performing local
measurements on the remaining spins. This concept of Localizable Entanglement
(LE) leads naturally to notions like entanglement length and entanglement
fluctuations. For both spin-1/2 and spin-1 systems we prove that the LE of a
pure quantum state can be lower bounded by connected correlation functions. We
further propose a scheme, based on matrix-product states and the Monte Carlo
method, to efficiently calculate the LE for quantum states of a large number of
spins. The virtues of LE are illustrated for various spin models. In
particular, characteristic features of a quantum phase transition such as a
diverging entanglement length can be observed. We also give examples for pure
quantum states exhibiting a diverging entanglement length but finite
correlation length. We have numerical evidence that the ground state of the
antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum
channel. Furthermore, we apply the numerical method to mixed states and study
the entanglement as a function of temperature.Comment: 19 pages, modified definition of connected string order parameter,
updated reference
Non-local correlations as an information theoretic resource
It is well known that measurements performed on spatially separated entangled
quantum systems can give rise to correlations that are non-local, in the sense
that a Bell inequality is violated. They cannot, however, be used for
super-luminal signalling. It is also known that it is possible to write down
sets of ``super-quantum'' correlations that are more non-local than is allowed
by quantum mechanics, yet are still non-signalling. Viewed as an information
theoretic resource, super-quantum correlations are very powerful at reducing
the amount of communication needed for distributed computational tasks. An
intriguing question is why quantum mechanics does not allow these more powerful
correlations. We aim to shed light on the range of quantum possibilities by
placing them within a wider context. With this in mind, we investigate the set
of correlations that are constrained only by the no-signalling principle. These
correlations form a polytope, which contains the quantum correlations as a
(proper) subset. We determine the vertices of the no-signalling polytope in the
case that two observers each choose from two possible measurements with d
outcomes. We then consider how interconversions between different sorts of
correlations may be achieved. Finally, we consider some multipartite examples.Comment: Revtex. 12 pages, 6 figure
Multipartite quantum nonlocality under local decoherence
We study the nonlocal properties of two-qubit maximally-entangled and N-qubit
Greenberger-Horne-Zeilinger states under local decoherence. We show that the
(non)resilience of entanglement under local depolarization or dephasing is not
necessarily equivalent to the (non)resilience of Bell-inequality violations.
Apart from entanglement and Bell-inequality violations, we consider also
nonlocality as quantified by the nonlocal content of correlations, and provide
several examples of anomalous behaviors, both in the bipartite and multipartite
cases. In addition, we study the practical implications of these anomalies on
the usefulness of noisy Greenberger-Horne-Zeilinger states as resources for
nonlocality-based physical protocols given by communication complexity
problems. There, we provide examples of quantum gains improving with the number
of particles that coexist with exponentially-decaying entanglement and
non-local contents.Comment: 6 pages, 4 figure
Realisation of Hardy's Thought Experiment
We present an experimental realisation of Hardy's thought experiment [Phys.
Rev. Lett. {\bf 68}, 2981 (1992)], using photons. The experiment consists of a
pair of Mach-Zehnder interferometers that interact through photon bunching at a
beam splitter. A striking contradiction is created between the predictions of
quantum mechanics and local hidden variable based theories. The contradiction
relies on non-maximally entangled position states of two particles.Comment: 5 page
Minimal instances for toric code ground states
A decade ago Kitaev's toric code model established the new paradigm of
topological quantum computation. Due to remarkable theoretical and experimental
progress, the quantum simulation of such complex many-body systems is now
within the realms of possibility. Here we consider the question, to which
extent the ground states of small toric code systems differ from LU-equivalent
graph states. We argue that simplistic (though experimentally attractive)
setups obliterate the differences between the toric code and equivalent graph
states; hence we search for the smallest setups on the square- and triangular
lattice, such that the quasi-locality of the toric code hamiltonian becomes a
distinctive feature. To this end, a purely geometric procedure to transform a
given toric code setup into an LC-equivalent graph state is derived. In
combination with an algorithmic computation of LC-equivalent graph states, we
find the smallest non-trivial setup on the square lattice to contain 5
plaquettes and 16 qubits; on the triangular lattice the number of plaquettes
and qubits is reduced to 4 and 9, respectively.Comment: 14 pages, 11 figure
Two-Setting Bell Inequalities for Many Qubits
We present a family of Bell inequalities involving only two measurement
settings of each party for N>2 qubits. Our inequalities include all the
standard ones with fewer than N qubits and thus gives a natural generalization.
It is shown that all the Greenberger-Horne-Zeilinger states violate the
inequalities maximally, with an amount that grows exponentially as
2^{{(N-2)}/2}. The inequalities are also violated by some states that do
satisfy all the standard Bell inequalities. Remarkably, our results yield in an
efficient and simple way an implementation of nonlocality tests of many qubits
favorably within reach of the well-established technology of linear optics.Comment: 4 pages, no figur
Decoherence-based exploration of d-dimensional one-way quantum computation
We study the effects of amplitude and phase damping decoherence in
d-dimensional one-way quantum computation (QC). Our investigation shows how
information transfer and entangling gate simulations are affected for d>=2. To
understand motivations for extending the one-way model to higher dimensions, we
describe how d-dimensional qudit cluster states deteriorate under environmental
noise. In order to protect quantum information from the environment we consider
the encoding of logical qubits into physical qudits and compare entangled pairs
of linear qubit-cluster states with single qudit clusters of equal length and
total dimension. Our study shows a significant reduction in the performance of
one-way QC for d>2 in the presence of Markovian type decoherence models.Comment: 8 pages, 11 figures, RevTeX
- …