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Quantum interactive proofs and the complexity of entanglement detection
, 2013
"... This paper identifies a formal connection between physical problems related to entanglement detection and complexity classes in theoretical computer science. In particular, we show that to nearly every quantum interactive proof complexity class (including BQP, QMA, QMA(2), QSZK, and QIP), there corr ..."
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This paper identifies a formal connection between physical problems related to entanglement detection and complexity classes in theoretical computer science. In particular, we show that to nearly every quantum interactive proof complexity class (including BQP, QMA, QMA(2), QSZK, and QIP), there corresponds a natural entanglement or correlation detection problem that is complete for that class. In this sense, we can say that an entanglement or correlation detection problem captures the expressive power of each quantum interactive proof complexity class. The only promise problem of this flavor that is not known to be complete for a quantum interactive proof complexity class is a variation of the original quantum separability problem in which the goal is to decide if a quantum state output by a quantum circuit is separable or entangled. We also show that the difficulty of entanglement detection depends on whether the distance measure used is the trace distance or the oneway LOCC distance. 1
C Pineda1,2,3, T Gorin3,4, and T H Seligman1,3 1Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México,
, 2007
"... Decoherence of two qubit systems: ..."
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AlbertLudwigsUniversität Freiburg im Breisgau
"... Multitieranwendungen werden herkömmlicherweise im Stile der ClientServerArchitektur entworfen. Bei solch einem Entwurf muss das System typischerweise passend zur anvisierten Zielplattform in Module aufgeteilt werden. Obwohl das modulare Entwerfen unbestritten viele Vorteile besitzt, ist es fraglic ..."
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Multitieranwendungen werden herkömmlicherweise im Stile der ClientServerArchitektur entworfen. Bei solch einem Entwurf muss das System typischerweise passend zur anvisierten Zielplattform in Module aufgeteilt werden. Obwohl das modulare Entwerfen unbestritten viele Vorteile besitzt, ist es fraglich, ob die Auswahl einer bestimmten Architektur für den physikalischen Systementwurf Einfluss auf den logischen Systementwurf haben sollte. Des Weiteren geht das manuelle Entwickeln von verteilten Anwendungen in der Regel mit einer erhöhten Systemkomplexität einher, was das Auftreten von Laufzeitfehlern begünstigt. In der vorliegenden Arbeit präsentieren wir die Grundbausteine zur Realisierung einer sequentiellen Multitierprogrammiersprache. Statt wie üblicherweise manuell verteilt zu programmieren, erlaubt es eine solche Programmiersprache Multitieranwendungen sequentiell zu schreiben. Die Modularisierung des Programmcodes in zu den vorgesehenen Schichten passende Programmkomponenten kann somit automatischen — oder zumindest halbautomatisch — mit Hilfe eines Programmierwerkzeugs erfolgen. Der mit dieser Dissertation präsentierte Ansatz zur Umsetzung dieser Idee fußt auf
2Instituto de Fı́sica, Universidade Federal do Rio de Janeiro, Caixa Postal
"... Just as a coherent state may be considered as a quantum point, its restriction to a factor space of the full Hilbert space can be interpreted as a quantum plane. The overlap of such a factor coherent state with a full pure state is akin to a quantum section. It defines a reduced pure state in the co ..."
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Just as a coherent state may be considered as a quantum point, its restriction to a factor space of the full Hilbert space can be interpreted as a quantum plane. The overlap of such a factor coherent state with a full pure state is akin to a quantum section. It defines a reduced pure state in the cofactor Hilbert space. Physically, this factorization corresponds to the description of interacting components of a quantum system with many degrees of freedom and the sections could be generated by conceivable partial measurements. The collection of all the Wigner functions corresponding to a full set of parallel quantum sections defines the Husimi–Wigner representation. It occupies an intermediate ground between the drastic suppression of nonclassical features, characteristic of Husimi functions, and the daunting complexity of higher dimensional Wigner functions. After analysing these features for simpler states, we exploit this new representation as a probe of numerically computed eigenstates of a chaotic Hamiltonian. Though less regular, the individual twodimensional Wigner functions resemble those of semiclassically quantized states.
Multipartite entanglement dynamics in a cavity
"... Abstract. We study the dynamics of two kinds of entanglement, and there interplay. On one hand, the intrinsic entanglement within a central system composed by three two level atoms, and measured by multipartite concurrence; on the other, the entanglement between the central system and a cavity, acti ..."
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Abstract. We study the dynamics of two kinds of entanglement, and there interplay. On one hand, the intrinsic entanglement within a central system composed by three two level atoms, and measured by multipartite concurrence; on the other, the entanglement between the central system and a cavity, acting as an environment, and measured with purity. Using dipoledipole and Ising interactions between atoms we propose two Hamiltonians, a homogeneous and a quasihomogeneous one. We find an upper bound for concurrence as a function of purity, associated to the evolution of the W state. A lower bound is also observed for the homogeneous case. In both situations, we show the existence of critical values of the interaction, for which the dynamics of entanglement seem complex. PACS numbers: 03.65.Yz,03.67.a 1.