A Family of Multipartite Entanglement Measures

Vrana, Péter

doi:10.1007/s00220-023-04731-8

Commun. Math. Phys.

2023

DOI: 10.1007/s00220-023-04731-8

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A Family of Multipartite Entanglement Measures

Péter Vrana

Abstract: We construct a family of additive entanglement measures for pure multipartite states. The family is parametrised by a simplex and interpolates between the Rényi entropies of the one-particle reduced states and the recently found universal spectral points (Christandl, Vrana, and Zuiddam, J of the AMS 2023) that serve as monotones for tensor degeneration.

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2024

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Cited by 3 publications

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Interpolating Between Rényi Entanglement Entropies for Arbitrary Bipartitions via Operator Geometric Means

Bugár,

Vrana

2024

Ann. Henri Poincaré

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The asymptotic restriction problem for tensors can be reduced to finding all parameters that are normalized, monotone under restrictions, additive under direct sums and multiplicative under tensor products, the simplest of which are the flattening ranks. Over the complex numbers, a refinement of this problem, originating in the theory of quantum entanglement, is to find the optimal rate of entanglement transformations as a function of the error exponent. This trade-off can also be characterized in terms of the set of normalized, additive, multiplicative functionals that are monotone in a suitable sense, which includes the restriction-monotones as well. For example, the flattening ranks generalize to the (exponentiated) Rényi entanglement entropies of order $$\alpha \in [0,1]$$ α ∈ [ 0 , 1 ] . More complicated parameters of this type are known, which interpolate between the flattening ranks or Rényi entropies for special bipartitions, with one of the parts being a single tensor factor. We introduce a new construction of subadditive and submultiplicative monotones in terms of a regularized Rényi divergence between many copies of the pure state represented by the tensor and a suitable sequence of positive operators. We give explicit families of operators that correspond to the flattening-based functionals, and show that they can be combined in a nontrivial way using weighted operator geometric means. This leads to a new characterization of the previously known additive and multiplicative monotones, and gives new submultiplicative and subadditive monotones that interpolate between the Rényi entropies for all bipartitions. We show that for each such monotone there exist pointwise smaller multiplicative and additive ones as well. In addition, we find lower bounds on the new functionals that are superadditive and supermultiplicative.

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Interpolating Between Rényi Entanglement Entropies for Arbitrary Bipartitions via Operator Geometric Means

Bugár,

Vrana

2024

Ann. Henri Poincaré

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Explicit Error Bounds for Entanglement Transformations Between Sparse Multipartite States

Bugár,

Vrana

2024

IEEE Trans. Inform. Theory

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Fractional squashed entanglement and its efficiency

El-Hadidy,

El Anouz,

Metwally

2024

J. Opt. Soc. Am. B

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In this paper we investigate the fractional quantum correlations via squashed entanglement and negativity, where an analytical solution of a fractional Schrödinger equation under an XXX model of a spin-spin Hamiltonian has been introduced. It has shown that, by starting with an initially large entangled state, both quantifiers decrease during the interaction. This decay increases as one increases the degree of the fractional order and the coupling constant between the two spins. However, the squashed entanglement and the negativity increase gradually if the initial state contains a small amount of quantum correlations. The sudden/gradual changes of these phenomena have been observed at small/large values of the fractional order, respectively. The constant behavior of these measures is observed at small values of fractional orders. Our results show that the fractional state can be used as a quantum channel with high efficiency to perform quantum teleportation. The long-lived constant behavior of the teleportation inequality indicates that the efficiency of this channel will be constant during the teleportation process.

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A Family of Multipartite Entanglement Measures

Cited by 3 publications

References 34 publications

Interpolating Between Rényi Entanglement Entropies for Arbitrary Bipartitions via Operator Geometric Means

Interpolating Between Rényi Entanglement Entropies for Arbitrary Bipartitions via Operator Geometric Means

Explicit Error Bounds for Entanglement Transformations Between Sparse Multipartite States

Fractional squashed entanglement and its efficiency

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