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Proof of the impossibility of noncontextual hidden variables in all Hilbert space dimensions,"UMPPT94,hepth/9409149
"... It is shown that the algebraic structure of finite Heisenberg groups associated with the tensor product of two Hilbert spaces leads to a demonstration valid in all Hilbert space dimensions of the impossibility of noncontextual hidden variables. It has been known since the work of Bell and Kochen an ..."
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Cited by 1 (1 self)
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It is shown that the algebraic structure of finite Heisenberg groups associated with the tensor product of two Hilbert spaces leads to a demonstration valid in all Hilbert space dimensions of the impossibility of noncontextual hidden variables. It has been known since the work of Bell and Kochen
Unbounded violations of bipartite Bell inequalities via Operator Space theory
 Communications in Mathematical Physics, 300(3):715–739, 2010. arXiv:0910.4228. Shorter version appeared in PRL 104:170405, arXiv:0912.1941
"... Abstract: In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order Ω n log2 n when observables with n possible outcomes are used. A central tool in the analysis is a close relation between this problem and operator sp ..."
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Cited by 17 (2 self)
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Abstract: In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order Ω n log2 n when observables with n possible outcomes are used. A central tool in the analysis is a close relation between this problem and operator
AVERAGE ENTROPY OF A SUBSYSTEM ∗
, 1993
"... If a quantum system of Hilbert space dimension mn is in a random pure state, the average entropy of a subsystem of dimension m ≤ n is conjectured to be Sm,n = ∑mn k=n+1 1 m−1 k ..."
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If a quantum system of Hilbert space dimension mn is in a random pure state, the average entropy of a subsystem of dimension m ≤ n is conjectured to be Sm,n = ∑mn k=n+1 1 m−1 k
Ktheory for operator algebras
 Mathematical Sciences Research Institute Publications
, 1998
"... p. XII line5: since p. 12: I blew this simple formula: should be α = −〈ξ, η〉/〈η, η〉. p. 2 I.1.1.4: The RieszFischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e int}. If [a, b] is a ..."
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Cited by 559 (0 self)
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is nonseparable. In fact, I. Farah (private communication) has shown that a Hilbert space of dimension 2ℵ0 has a dense subspace which does not contain any uncountable orthonormal set. A similar example was obtained by Dixmier [Dix53]. p. 89 I.2.4.3(i): Some of the statements on p. 9 can be false if the measure
PhysicalResource Demands for Scalable Quantum Computation
, 2008
"... The primary resource for quantum computation is Hilbertspace dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources. Avoiding a demand for an exponential amount of these resources pl ..."
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Cited by 2 (0 self)
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The primary resource for quantum computation is Hilbertspace dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources. Avoiding a demand for an exponential amount of these resources
The large N limit of superconformal field theories and supergravity
, 1998
"... We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of AntideSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and ..."
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Cited by 5673 (21 self)
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We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of AntideSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory
Information Retrieval via Truncated HilbertSpace Expansions
"... Abstract. In addition to the frequency of terms in a document collection, the distribution of terms plays an important role in determining the relevance of documents. In this paper, a new approach for representing term positions in documents is presented. The approach allows an efficient evaluatio ..."
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Abstract. In addition to the frequency of terms in a document collection, the distribution of terms plays an important role in determining the relevance of documents. In this paper, a new approach for representing term positions in documents is presented. The approach allows an efficient evaluation of termpositional information at query evaluation time. Three applications are investigated: a functionbased ranking optimization representing a userdefined document region, a query expansion technique based on overlapping the term distributions in the topranked documents, and cluster analysis of terms in documents. Experimental results demonstrate the effectiveness of the proposed approach. 1
Entanglement Computation in Atoms and Molecules
"... In this paper, a method for computing entanglement of electrons in atoms and molecules is described. The importance of entanglement computation for Quantum Computers and for Biology is highlighted and the existing models ’ pros and cons are illustrated. A description of the algorithms follows, with ..."
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, with some considerations about the execution times and how they scale increasing the system’s Hilbert space dimension.
Shiftable Multiscale Transforms
, 1992
"... Orthogonal wavelet transforms have recently become a popular representation for multiscale signal and image analysis. One of the major drawbacks of these representations is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal. Wavel ..."
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Cited by 557 (36 self)
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. Wavelet transforms are also unstable with respect to dilations of the input signal, and in two dimensions, rotations of the input signal. We formalize these problems by defining a type of translation invariance that we call "shiftability". In the spatial domain, shiftability corresponds to a
Results 1  10
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94,975