Entanglement robustness against particle loss in multiqubit systems

Neven, Antoine; Martin, John P.; Bastin, Thierry

doi:10.1103/physreva.98.062335

Cited by 26 publications

(17 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first example are states that possess a Schmidt decomposition [ 28 ], i.e.,

with

. For qubits, these are exactly the states that become separable as soon as one particle is ignored [ 29 ]. A famous example is the m -partite Greenberger–Horne–Zeilinger (GHZ) state

for which the local projective measurements on

and

are optimal, since the conditional state of all systems is a pure product state independently of the outcome and its energy can thus be minimised using local unitaries.…”

Section: Multipartite Daemonic Ergotropymentioning

confidence: 99%

Daemonic Ergotropy: Generalised Measurements and Multipartite Settings

Bernards

Kleinmann

Gühne

et al. 2019

Entropy

View full text Add to dashboard Cite

Recently, the concept of daemonic ergotropy has been introduced to quantify the maximum energy that can be obtained from a quantum system through an ancilla-assisted work extraction protocol based on information gain via projective measurements [G. Francica et al., npj Quant. Inf. 3, 12 (2018)]. We prove that quantum correlations are not advantageous over classical correlations if projective measurements are considered. We go beyond the limitations of the original definition to include generalised measurements and provide an example in which this allows for a higher daemonic ergotropy. Moreover, we propose a see-saw algorithm to find a measurement that attains the maximum work extraction. Finally, we provide a multipartite generalisation of daemonic ergotropy that pinpoints the influence of multipartite quantum correlations, and study it for multipartite entangled and classical states.

show abstract

“…The first example are states that possess a Schmidt decomposition [ 28 ], i.e.,

with

. For qubits, these are exactly the states that become separable as soon as one particle is ignored [ 29 ]. A famous example is the m -partite Greenberger–Horne–Zeilinger (GHZ) state

for which the local projective measurements on

and

are optimal, since the conditional state of all systems is a pure product state independently of the outcome and its energy can thus be minimised using local unitaries.…”

Section: Multipartite Daemonic Ergotropymentioning

confidence: 99%

Daemonic Ergotropy: Generalised Measurements and Multipartite Settings

Bernards

Kleinmann

Gühne

et al. 2019

Entropy

View full text Add to dashboard Cite

show abstract

“…Let us consider a possibility of non-invertible intermediate transformations of Lqubit states, i.e., non-invertible gates, which are described by the 2 L × 2 L matrices U(r) of (possibly) less than full rank 1 ≤ r ≤ 2 L . This can be related to the production of "degenerate" states (see, e.g., [43]), "particle loss" [53][54][55], and the role of ranks in multiparticle entanglement [56,57].…”

Section: Invertible and Noninvertible Quantum Gatesmentioning

confidence: 99%

Polyadic Braid Operators and Higher Braiding Gates

Duplij

Vogl

2021

Universe

View full text Add to dashboard Cite

A new kind of quantum gates, higher braiding gates, as matrix solutions of the polyadic braid equations (different from the generalized Yang--Baxter equations) is introduced. Such gates lead to another special multiqubit entanglement that can speed up key distribution and accelerate algorithms. Ternary braiding gates acting on three qubit states are studied in detail. We also consider exotic non-invertible gates, which can be related with qubit loss, and define partial identities (which can be orthogonal), partial unitarity, and partially bounded operators (which can be non-invertible). We define two classes of matrices, star and circle ones, such that the magic matrices (connected with the Cartan decomposition) belong to the star class. The general algebraic structure of the introduced classes is described in terms of semigroups, ternary and $5$-ary groups and modules. The higher braid group and its representation by the higher braid operators are given. Finally, we show, that for each multiqubit state, there exist higher braiding gates that are not entangling, and the concrete conditions to be non-entangling are given for the obtained binary and ternary gates.Yang--Baxter equation; braid group; qubit; ternary; polyadic; braiding quantum gate.

show abstract

“…Permutation symmetric N -qubit states draw attention due to their experimental feasibility and for the mathematical simplicity offered by them [49][50][51][52][53][54][55][56][57][58][59][60]. This class of states belong to the d = 2j + 1 = N + 1 dimensional subspace of the 2 N dimensional Hilbert space, which corresponds to the maximum value j = N/2 of angular momentum of N -qubit system.…”

Section: Violation Of Lsur By Permutation Symmetric N -Qubit Statesmentioning

confidence: 99%

Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems

Reena,

Karthik,

Tej

et al. 2021

Preprint

View full text Add to dashboard Cite

We show that violation of variance based local sum uncertainty relation (LSUR) for angular momentum operators of a bipartite system, proposed by Hofmann and Takeuchi [Phys. Rev. A 68, 032103 (2003)], is necessary and sufficient for entanglement in two-qubit permutation symmetric state. Moreover, we also establish its one-to-one connection with negativity of covariance matrix [Phys. Lett. A 364, 203 (2007)] of the two-qubit reduced system of a permutation symmetric Nqubit state. Consequently, it is seen that the violation of the angular momentum LSUR serves as a necessary condition for pairwise entanglement in N -qubit system, obeying exchange symmetry. We illustrate physical examples of entangled permutation symmetric N -qubit systems, where violation of the local sum uncertainty relation manifests itself as a signature of pairwise entanglement.

show abstract

Entanglement robustness against particle loss in multiqubit systems

Cited by 26 publications

References 37 publications

Daemonic Ergotropy: Generalised Measurements and Multipartite Settings

Daemonic Ergotropy: Generalised Measurements and Multipartite Settings

Polyadic Braid Operators and Higher Braiding Gates

Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems

Contact Info

Product

Resources

About