arXiv subjects

Antonio J. Lopez-Tarrida

Publications and source records attributed to Antonio J. Lopez-Tarrida.

8 recordsLinked to original sources

arXiv2014

Multigraph approach to quantum non-locality

Non-contextuality (NC) and Bell inequalities can be expressed as bounds $Ω$ for positive linear combinations $S$ of probabilities of events, $S \leq Ω$. Exclusive events in $S$ can be represented as adjacent vertices of a graph called the exclusivity graph of $S$. In the case that events correspond to the outcomes of quantum projective measurements, quantum probabilities are intimately related to the Grötschel-Lovász-Schrijver theta body of the exclusivity graph. Then, one can easily compute an upper bound to the maximum quantum violation of any NC or Bell inequality by optimizing $S$ over the theta body and calculating the Lovász number of the corresponding exclusivity graph. In some cases, this upper bound is tight and gives the exact maximum quantum violation. However, in general, this is not the case. The reason is that the exclusivity graph does not distinguish among the different ways exclusivity can occur in Bell-inequality (and similar) scenarios. An interesting question is whether there is a graph-theoretical concept which accounts for this problem. Here we show that, for any given $N$-partite Bell inequality, an edge-coloured multigraph composed of $N$ single-colour graphs can be used to encode the relationships of exclusivity between each party's parts of the events. Then, the maximum quantum violation of the Bell inequality is exactly given by a refinement of the Lovász number that applies to these edge-coloured multigraphs. We show how to calculate upper bounds for this number using a hierarchy of semi-definite programs and calculate upper bounds for $I_3$, $I_{3322}$ and the three bipartite Bell inequalities whose exclusivity graph is a pentagon. The multigraph-theoretical approach introduced here may remove some obstacles in the program of explaining quantum correlations from first principles.

quant-ph↗

arXiv2013

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.

quant-ph↗

arXiv2012

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.

physics.soc-ph↗

arXiv2012

Experimental fully contextual correlations

Quantum correlations are contextual yet, in general, nothing prevents the existence of even more contextual correlations. We identify and test a noncontextuality inequality in which the quantum violation cannot be improved by any hypothetical postquantum theory, and use it to experimentally obtain correlations in which the fraction of noncontextual correlations is less than 0.06. Our correlations are experimentally generated from the results of sequential compatible tests on a four-state quantum system encoded in the polarization and path of a single photon.

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arXiv2011

Optimal preparation of graph states

We show how to prepare any graph state of up to 12 qubits with: (a) the minimum number of controlled-Z gates, and (b) the minimum preparation depth. We assume only one-qubit and controlled-Z gates. The method exploits the fact that any graph state belongs to an equivalence class under local Clifford operations. We extend up to 12 qubits the classification of graph states according to their entanglement properties, and identify each class using only a reduced set of invariants. For any state, we provide a circuit with both properties (a) and (b), if it does exist, or, if it does not, one circuit with property (a) and one with property (b), including the explicit one-qubit gates needed.

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arXiv2010

Entanglement in eight-qubit graph states

Any 8-qubit graph state belongs to one of the 101 equivalence classes under local unitary operations within the Clifford group. For each of these classes we obtain a representative which requires the minimum number of controlled-Z gates for its preparation, and calculate the Schmidt measure for the 8-partite split, and the Schmidt ranks for all bipartite splits. This results into an extension to 8 qubits of the classification of graph states proposed by Hein, Eisert, and Briegel [Phys. Rev. A 69, 062311 (2004)].

quant-ph↗

arXiv2009

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.

quant-ph↗

arXiv2005

Proposed experiment for the quantum "Guess my number" protocol

An experimental realization of the entanglement-assisted "Guess my number" protocol for the reduction of communication complexity, introduced by Steane and van Dam, would require producing and detecting three-qubit GHZ states with an efficiency eta > 0.70, which would require single photon detectors of efficiency sigma > 0.89. We propose a modification of the protocol which can be translated into a real experiment using present-day technology. In the proposed experiment, the quantum reduction of the multi-party communication complexity would require an efficiency eta > 0.05, achievable with detectors of sigma > 0.47, for four parties, and eta > 0.17 (sigma > 0.55) for three parties.

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