Multi-partite entanglement

Walter, Michael; Gross, David J.; Eisert, Jens

doi:10.48550/arxiv.1612.02437

Cited by 40 publications

(64 citation statements)

References 163 publications

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“…In physics literature one uses the term rank of a composite pure state, which is equal to the rank of the corresponding tensor T . Furthermore, to quantify entanglement of a multipartite state one uses the Schmidt measure [44,101], equal to the log of the rank of the corresponding tensor, E S (|ψ ) = log r(T ). More precise description of multipartite entanglement can be obtained by studying the spectral norm ||T || ∞ of a tensor, under the assumption that the Frobenius norm is fixed to unity, ||T ||…”

Section: Composite Systems and Quantum Entanglementmentioning

confidence: 99%

“…In a similar way any pure state of a larger system consisting of d > 2 parties can be represented by a tensor T with d indices. However, description of entanglement in such a multipartite case is more difficult than for bipartite systems, as algebraic transformations on tensors are much more involved than the operations on matrices [101,9]. For instance, the notion of SVD was generalized for the space of tensors [64,36,75], but in general these decompositions do not bring T to the diagonal form.…”

Section: Introductionmentioning

confidence: 99%

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Tensor rank and entanglement of pure quantum states

Bruzda¹,

Friedland²,

Życzkowski³

2019

Preprint

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The rank of a tensor is analyzed in context of description of entanglement of pure states of multipartite quantum systems. We discuss the notions of the generic rank of a tensor with d indices and n levels in each mode and the maximal rank of a tensor of these dimensions. Other variant of this notion, called border rank of a tensor, is shown to be relevant for characterization of orbits of quantum states generated by the group of special linear transformations. As entanglement of a given quantum state depends on the way the total system is divided into subsystems, we introduce a notion of 'partitioning rank' of a tensor, which depends on a way how the entries forming the tensor are treated. In particular, we analyze the tensor product of several copies of the n-qubit state |Wn and analyze its partitioning rank for various splittings of the entire space. Some results concerning the generic rank of a tensor are also provided.

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Section: Composite Systems and Quantum Entanglementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tensor rank and entanglement of pure quantum states

Bruzda¹,

Friedland²,

Życzkowski³

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Our investigation focuses on establishing a protocol that uses quantum control operations combined with measurement and post-selection to produce highly entangled metrologically relevant states. We will refer to these states as Projected Squeezed states (see [10][11][12][13] for relevant discussions on measures of multipartite entanglement). We further study optimization of the control parameters that produce maximal overlap of the projected squeezed state with the well-known Greenberger-Horne-Zeilinger state (commonly referred to as the maximally entangled state or GHZ state, see [10,14]).…”

Section: Introductionmentioning

confidence: 99%

“…We will refer to these states as Projected Squeezed states (see [10][11][12][13] for relevant discussions on measures of multipartite entanglement). We further study optimization of the control parameters that produce maximal overlap of the projected squeezed state with the well-known Greenberger-Horne-Zeilinger state (commonly referred to as the maximally entangled state or GHZ state, see [10,14]). For a multipartite system consisting of N -qubits, the GHZ state reads as follows…”

Section: Introductionmentioning

confidence: 99%

Generating GHZ states with squeezing and post-selection

Alexander,

Uys,

Bollinger

2019

Preprint

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Many quantum state preparation methods rely on a combination of dissipative quantum state initialization, followed by unitary evolution to a desired target state. Here we demonstrate the usefulness of quantum measurement as an additional tool for quantum state preparation. Starting from a pure separable multipartite state, a control sequence, which includes rotation, spin squeezing via one-axis twisting, quantum measurement and post-selection, generates a highly entangled multipartite state, which we refer to as Projected Squeezed states (or P S states). Through an optimization method, we then identify parameters required to maximize the overlap fidelity of the P S states with the maximally entangled Greenberger-Horne-Zeilinger states (or GHZ states). The method leads to an appreciable decrease in state preparation time of GHZ states when compared to preparation through unitary evolution with one-axis twisting only.

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“…In a nutshell and by oversimplifying, a multi-qubit state is said separable if it can be someway written as a tensor product of some subsystem states, and, hence, if it is not entangled. However, the concepts of separability and entanglement are quite complex, and we refer the reader to[47] for a proper formal definition.…”

mentioning

confidence: 99%

How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation

Koudia,

Cacciapuoti,

Simonov

et al. 2021

Preprint

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In the theory of quantum communications, a deeper structure has been recently unveiled -mainly within the physics community -showing that the capacity does not completely characterize the channel ability to transmit information due to phenomena -namely, superadditivity, superactivation and causal activation -with no counterpart in the classical world. Although how deep goes this structure is yet to be fully uncovered, it is crucial for the communication engineering community to own the implications of these phenomena for understanding and deriving the fundamental limits of communications. Hence, the aim of this paper is to shed light on these phenomena by providing the reader with an easy access and guide towards the relevant literature and the prominent results, by adopting a communication engineering perspective.

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Multi-partite entanglement

Cited by 40 publications

References 163 publications

Tensor rank and entanglement of pure quantum states

Tensor rank and entanglement of pure quantum states

Generating GHZ states with squeezing and post-selection

How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation

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