3,234 research outputs found
Quantum state-independent contextuality requires 13 rays
We show that, regardless of the dimension of the Hilbert space, there exists
no set of rays revealing state-independent contextuality with less than 13
rays. This implies that the set proposed by Yu and Oh in dimension three [Phys.
Rev. Lett. 108, 030402 (2012)] is actually the minimal set in quantum theory.
This contrasts with the case of Kochen-Specker sets, where the smallest set
occurs in dimension four.Comment: 8 pages, 2 tables, 1 figure, v2: minor change
Minimal true-implies-false and true-implies-true sets of propositions in noncontextual hidden variable theories
An essential ingredient in many examples of the conflict between quantum
theory and noncontextual hidden variables (e.g., the proof of the
Kochen-Specker theorem and Hardy's proof of Bell's theorem) is a set of atomic
propositions about the outcomes of ideal measurements such that, when outcome
noncontextuality is assumed, if proposition is true, then, due to
exclusiveness and completeness, a nonexclusive proposition () must be
false (true). We call such a set a {\em true-implies-false set} (TIFS) [{\em
true-implies-true set} (TITS)]. Here we identify all the minimal TIFSs and
TITSs in every dimension , i.e., the sets of each type having the
smallest number of propositions. These sets are important because each of them
leads to a proof of impossibility of noncontextual hidden variables and
corresponds to a simple situation with quantum vs classical advantage.
Moreover, the methods developed to identify them may be helpful to solve some
open problems regarding minimal Kochen-Specker sets.Comment: 9 pages, 7 figure
Memory cost of quantum contextuality
The simulation of quantum effects requires certain classical resources, and
quantifying them is an important step in order to characterize the difference
between quantum and classical physics. For a simulation of the phenomenon of
state-independent quantum contextuality, we show that the minimal amount of
memory used by the simulation is the critical resource. We derive optimal
simulation strategies for important cases and prove that reproducing the
results of sequential measurements on a two-qubit system requires more memory
than the information carrying capacity of the system.Comment: 18 pages, no figures, v2: revised for clarit
Kochen-Specker set with seven contexts
The Kochen-Specker (KS) theorem is a central result in quantum theory and has
applications in quantum information. Its proof requires several yes-no tests
that can be grouped in contexts or subsets of jointly measurable tests.
Arguably, the best measure of simplicity of a KS set is the number of contexts.
The smaller this number is, the smaller the number of experiments needed to
reveal the conflict between quantum theory and noncontextual theories and to
get a quantum vs classical outperformance. The original KS set had 132
contexts. Here we introduce a KS set with seven contexts and prove that this is
the simplest KS set that admits a symmetric parity proof.Comment: REVTeX4, 7 pages, 1 figur
Quantum social networks
We introduce a physical approach to social networks (SNs) in which each actor
is characterized by a yes-no test on a physical system. This allows us to
consider SNs beyond those originated by interactions based on pre-existing
properties, as in a classical SN (CSN). As an example of SNs beyond CSNs, we
introduce quantum SNs (QSNs) in which actor is characterized by a test of
whether or not the system is in a quantum state. We show that QSNs outperform
CSNs for a certain task and some graphs. We identify the simplest of these
graphs and show that graphs in which QSNs outperform CSNs are increasingly
frequent as the number of vertices increases. We also discuss more general SNs
and identify the simplest graphs in which QSNs cannot be outperformed.Comment: REVTeX4, 6 pages, 3 figure
Basic exclusivity graphs in quantum correlations
A fundamental problem is to understand why quantum theory only violates some
noncontextuality (NC) inequalities and identify the physical principles that
prevent higher-than-quantum violations. We prove that quantum theory only
violates those NC inequalities whose exclusivity graphs contain, as induced
subgraphs, odd cycles of length five or more, and/or their complements. In
addition, we show that odd cycles are the exclusivity graphs of a well-known
family of NC inequalities and that there is also a family of NC inequalities
whose exclusivity graphs are the complements of odd cycles. We characterize the
maximum noncontextual and quantum values of these inequalities, and provide
evidence supporting the conjecture that the maximum quantum violation of these
inequalities is exactly singled out by the exclusivity principle.Comment: REVTeX4, 7 pages, 2 figure
El frijol en El Salvador: implicaciones para la investigacion agricola
Results of a study on bean cultivation in El Salvador are given. Aspects analyzed were as follows: consumption structure (apparent, per capita, and rural-urban; preferences, consumption and cooking ways, and nutritive value); area, production, and yields (at national and regional levels, by cropping system, and by planting time), production constraints (abiotic, biotic, and technological factors), and production perspectives. Recommendations are included on future research activities. (CIAT
Compact set of invariants characterizing graph states of up to eight qubits
The set of entanglement measures proposed by Hein, Eisert, and Briegel for
n-qubit graph states [Phys. Rev. A 69, 062311 (2004)] fails to distinguish
between inequivalent classes under local Clifford operations if n > 6. On the
other hand, the set of invariants proposed by van den Nest, Dehaene, and De
Moor (VDD) [Phys. Rev. A 72, 014307 (2005)] distinguishes between inequivalent
classes, but contains too many invariants (more than 2 10^{36} for n=7) to be
practical. Here we solve the problem of deciding which entanglement class a
graph state of n < 9 qubits belongs to by calculating some of the state's
intrinsic properties. We show that four invariants related to those proposed by
VDD are enough for distinguishing between all inequivalent classes with n < 9
qubits.Comment: REVTeX4, 9 pages, 1 figur
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