L. N. Tolstoi i S. A. Tolstaia, Perepiska s N. N. Strakhovym: The Tolstoys' Correspondence with N. N. Strakhov

Jones, W. G.; Donskov, Andrew; Gromova, L. D.; Nikiforova, T. G.

doi:10.2307/3735700

Cited by 4 publications

(10 citation statements)

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“…The complete list of all no-signaling vertices is also known in the case of two inputs (m = 2) and an arbitrary number of outputs (Barrett et al, 2005b) and in the case of two outputs (∆ = 2) and an arbitrary number of inputs (Barrett and Pironio, 2005;Jones and Masanes, 2005). In both cases, the corresponding non-local vertices can be seen as as straightforward generalizations of the PR-box.…”

Section: No-signaling Boundsmentioning

confidence: 99%

Bell nonlocality

et al. 2014

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Bell’s 1964 theorem, which states that the predictions of quantum theory cannot be accounted for by any local theory, represents one of the most profound developments in the foundations of physics. In the last two decades, Bell’s theorem has been a central theme of research from a variety of perspectives, mainly motivated by quantum information science, where the nonlocality of quantum theory underpins many of the advantages afforded by a quantum processing of information. The focus of this review is to a large extent oriented by these later developments. The main concepts and tools which have been developed to describe and study the nonlocality of quantum theory and which have raised this topic to the status of a full subfield of quantum information science are reviewed

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Section: No-signaling Boundsmentioning

confidence: 99%

Bell nonlocality

et al. 2014

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“…It was first proved in [17] that a generic three-qubit pure state is UDA by its two-body RDMs. [20] provided a more general result, showing that a generic N-qudit pure quantum state is UDA by its ⌈ N 2 ⌉ + 1 -body RDMs. [20] also proved that ⌊ N 2 ⌋-body RDMs are not sufficient for uniquely determining a generic N-qudit pure state.…”

Section: Introductionmentioning

confidence: 99%

“…[20] provided a more general result, showing that a generic N-qudit pure quantum state is UDA by its ⌈ N 2 ⌉ + 1 -body RDMs. [20] also proved that ⌊ N 2 ⌋-body RDMs are not sufficient for uniquely determining a generic N-qudit pure state. However, a gap appears when N is odd: whether N+1 2 -qudit RDMs are sufficient to uniquely determine a generic pure state or not remains open.…”

Section: Introductionmentioning

confidence: 99%

“…Naive full tomography, as literally, need D 2 measurements, where D = d N is the dimension of the N-qudit system (d is the dimension of the qudit). For pure states or density operators with low rank, reduced density matrices (RDMs) may contain information to characterize the global system [15,16], thus a more promising approach for QST can be implemented as follows: acquiring a set of RDMs by local measurements, then applying post-processing algorithm to reconstruct the state [17][18][19][20][21][22][23]. Usually, we have no knowledge about the system before measurements.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, when the original state is pure, i.e., r = 1, O(D log 2 D) Pauli measurements are needed. [20] provided an approach using ⌊ N 2 ⌋ ⌈ N 2 ⌉ + 1 -qudit RDMs and hence O(D log D) (D = d N ) local measurements to uniquely determine a generic Nqudit pure state. However, a simple parameter counting argument suggests that O(D) measurements could be possibly sufficient for uniquely determining an N-qudit pure state.…”

Section: Introductionmentioning

confidence: 99%

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Quantum state tomography for generic pure states

Huang

Chen²,

et al. 2018

Sci. China Phys. Mech. Astron.

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We examine the problem of whether a multipartite pure quantum state can be uniquely determined by its reduced density matrices. We show that a generic pure state in three party Hilbert space, can be uniquely determined by its reduced states on subsystems H A ⊗ H B and H A ⊗ H C . Then we generalize the conclusion to the case that dim(H 1 ) > 2. As a corollary, we show that a generic N-qudit pure quantum state is uniquely determined by only 2 of its ⌈ N+1 2 ⌉-particle reduced density matrices. Furthermore, our results do indicate a method to uniquely determine a generic N-qudit pure state of dimension D = d N with only O(D) local measurements, which is an improvement comparing to the previous known approach using O(D log 2 D) or O(D log D) local measurements.

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Detecting multipartite entanglement

2005

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We discuss the problem of determining whether the state of several quantum mechanical subsystems is entangled. As in previous work on two subsystems we introduce a procedure for checking separability that is based on finding state extensions with appropriate properties and may be implemented as a semidefinite program. The main result of this work is to show that there is a series of tests of this kind such that if a multiparty state is entangled this will eventually be detected by one of the tests. The procedure also provides a means of constructing entanglement witnesses that could in principle be measured in order to demonstrate that the state is entangled.

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L. N. Tolstoi i S. A. Tolstaia, Perepiska s N. N. Strakhovym: The Tolstoys' Correspondence with N. N. Strakhov

Cited by 4 publications

References 0 publications

Bell nonlocality

Bell nonlocality

Quantum state tomography for generic pure states

Detecting multipartite entanglement

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