Quantifying entanglement resources

Eltschka, Christopher; Siewert, Jens

doi:10.1088/1751-8113/47/42/424005

Cited by 156 publications

(178 citation statements)

References 264 publications

(629 reference statements)

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“…3. Recall that negativity for D × D systems has bounds 0 ≤ N ≤ D − 1 [26]. The condition on d is related to conditions on the marginal eigenvalues: Higuchi found a necessary condi-tion on the univariate marginal eigenvalues for pure Nqudit systems [27]; for three qudits it is,…”

Section: Fig 2: Achievable Qubit Negativitymentioning

confidence: 99%

Polynomial Monogamy Relations for Entanglement Negativity

Allen

Meyer

2017

Phys. Rev. Lett.

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The notion of non-classical correlations is a powerful contrivance for explaining phenomena exhibited in quantum systems. It is well known, however, that quantum systems are not free to explore arbitrary correlations-the church of the smaller Hilbert space only accepts monogamous congregants. We demonstrate how to characterize the limits of what is quantum mechanically possible with a computable measure, entanglement negativity. We show that negativity only saturates the standard linear monogamy inequality in trivial cases implied by its monotonicity under LOCC, and derive a necessary and sufficient inequality which, for the first time, is a non-linear higher degree polynomial. For very large quantum systems, we prove that the negativity can be distributed at least linearly for the tightest constraint and conjecture that it is at most linear.The prototypical quantum correlation, entanglement, accounts for many of the effects seen in quantum theory, and there is a significant effort to enslave it as a resource to be manipulated and exploited by quantum engineers [1]. The most striking property of entanglement is its distributability, or lack there of, exemplified by its compliance with, for example, monogamy laws [2] and area laws [3], laws which constrain the shareability of correlations. The former law states that the closer two parties are to being maximally entangled, the more the pair become separated and hidden from all other parties. The latter law requires that for certain types of many-particle ground states split in twain, the entanglement between the parts scales according to the size of the separation boundary. Both laws set the stage for entanglement to play a central role in physics, and an active research community continues to strengthen this role [4].The secludedness of maximally entangled states has specifically impacted quantum key distribution [5], ground state frustration [6], and even black holes [7]. These perspectives on monogamy have traditionally been understood in terms of multi-qubit networks. In the case of tripartite systems, the monogamy law can be written in terms of concurrence [8], as the following,where C is the concurrence, subscripts label the parties, and the vertical bar denotes the bipartite split across which it is computed. In this way, if C 2 A|BC ≈ C 2 A|B ≈ 1, i.e., A and B are maximally entangled, then C 2 A|C ≈ 0, hence the personification of entanglement.The elegance and simplicity of the monogamy inequality has made it the paragon for entanglement shareability. It has since been shown that other entanglement measures such as entanglement of formation [9], squashed entanglement [10], and entanglement negativity [11], all satisfy the same monogamy relation. This raises two issues: the monogamy inequality may just be a first order approximation to the shareability of correlational resources, so to what extent can we quantify the exact amount possible to share? Second, is the limited shareability a consequence of limited systems, i.e., qubits?The first issue has recent...

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Section: Fig 2: Achievable Qubit Negativitymentioning

confidence: 99%

Polynomial Monogamy Relations for Entanglement Negativity

Allen

Meyer

2017

Phys. Rev. Lett.

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“…However, for four-qubits, there exist infinitely many inequivalent SLOCC classes of states [51]. A useful classification into nine classes for fourqubit was obtained in [42,43].…”

Section: Appendix 1 Four-qubit Slocc Classesmentioning

confidence: 99%

Forbidden regimes in the distribution of bipartite quantum correlations due to multiparty entanglement

et al. 2017

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Monogamy is a nonclassical property that limits the distribution of quantum correlation among subparts of a multiparty system. We show that monogamy scores for different quantum correlation measures are bounded above by functions of genuine multipartite entanglement for a large majority of pure multiqubit states. The bound is universal for all three-qubit pure states. We derive necessary conditions to characterize the states that violate the bound, which can also be observed by numerical simulation for a small set of states, generated Haar uniformly. The results indicate that genuine multipartite entanglement restricts the distribution of bipartite quantum correlations in a multiparty system.

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“…(20) There exists the same form of inequality between the 2-concurrence and the negativity in entanglement theory [35]. Second, combining Theorem 4 with Eq.…”

Section: Comparison Of C (2) Cmentioning

confidence: 87%

Generalized coherence concurrence and path distinguishability

Chin¹

2017

J. Phys. A: Math. Theor.

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We propose a new family of coherence monotones, named the generalized coherence concurrence (or coherence k-concurrence), which is an analogous concept to the generalized entanglement concurrence. The coherence k-concurrence of a state is nonzero if and only if the coherence number (a recently introduced discrete coherence monotone) of the state is not smaller than k, and a state can be converted to a state with nonzero entanglement k-concurrence via incoherent operations if and only if the state has nonzero coherence k-concurrence. We apply the coherence concurrence family to the problem of wave-particle duality in multi-path interference phenomena. We obtain a sharper equation for path distinguishability (which witness the duality) than the known value and show that the amount of each concurrence for the quanton state determines the number of slits which are identified unambiguously.

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Quantifying entanglement resources

Cited by 156 publications

References 264 publications

Polynomial Monogamy Relations for Entanglement Negativity

Polynomial Monogamy Relations for Entanglement Negativity

Forbidden regimes in the distribution of bipartite quantum correlations due to multiparty entanglement

Generalized coherence concurrence and path distinguishability

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