Monogamy Inequality for Any Local Quantum Resource and Entanglement

Camalet, S.

doi:10.1103/physrevlett.119.110503

Cited by 31 publications

(55 citation statements)

References 40 publications

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“…The above Theorem applies to many kinds of external correlations, as discussed below Lemma 1. When C is an entanglement monotone, it generalizes previously obtained results [16]. As mentioned above, C can also be a measure of total correlations, or the HV measure of classical correlations.…”

supporting

confidence: 81%

“…where the supremum is taken over the orthonormal basis sets {|i } of H d1 ⊗ H d2 , for p ∈ E d1d2 , and by s d1,d2 (p) = e d1 otherwise [16]. First note that s d1,d2 depends on d 1 , since its maximum value is e d1 .…”

Section: Proof Of Lemmamentioning

confidence: 99%

“…Other examples are the nonuniformity, which can be quantified by ln d − S(ρ A ) for a system A of Hilbert space dimension d [52], and the coherence, which can be quantified by − i p i ln p i − S(ρ A ), where p i = i|ρ A |i and {|i } i is the basis with respect to which the incoherent states are defined [53]. In both these cases, inequality (3) is satisfied with the above corresponding measure in place of E, ln d − x in place of ξ d1,d2 (x), and any correlation monotone C for which f = h [16]. A relation of the form of eq.…”

mentioning

confidence: 99%

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Internal Entanglement and External Correlations of Any Form Limit Each Other

Camalet

2018

Phys. Rev. Lett.

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We show a relation between entanglement and correlations of any form. The internal entanglement of a bipartite system, and its correlations with another system, limit each other. A measure of correlations, of any nature, cannot increase under local operations. Examples are the entanglement monotones, the mutual information that quantifies total correlations, and the Henderson-Vedral measure of classical correlations. External correlations, evaluated by such a measure, set a tight upper bound on the internal entanglement that decreases as they increase, and so does quantum discord.

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supporting

confidence: 81%

Section: Proof Of Lemmamentioning

confidence: 99%

mentioning

confidence: 99%

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Internal Entanglement and External Correlations of Any Form Limit Each Other

Camalet

2018

Phys. Rev. Lett.

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“…In contrast with the classical world, it is not possible to prepare three qubits A, B, C in a way that any two qubits are maximally entangled [1]. In fact, if qubit A is maximally entangled with qubit B, then it must be uncorrelated (not even classically) with qubit C. This phenomenon of monogamy of entanglement was first quantified in a seminal paper by Coffman, Kundu, and Wootters (CKW) [1] for three qubits, and later on studied intensively in more general settings [2,3,4,5,14,15,6,16,17,18,7,19,20,21,22,23,24,25,8,9,26,27,10,11,28,29,30,12,13,31,32,33,34,35,36,37,38,39,40].…”

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confidence: 99%

Monogamy of entanglement without inequalities

Gour

Guo

2018

Quantum

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We provide a fine-grained definition of monogamous measure of entanglement that does not invoke any particular monogamy relation. Our definition is given in terms of an equality, as opposed to inequality, that we call the "disentangling condition". We relate our definition to the more traditional one, by showing that it generates standard monogamy relations. We then show that all quantum Markov states satisfy the disentangling condition for any entanglement monotone. In addition, we demonstrate that entanglement monotones that are given in terms of a convex roof extension are monogamous if they are monogamous on pure states, and show that for any quantum state that satisfies the disentangling condition, its entanglement of formation equals the entanglement of assistance. We characterize all bipartite mixed states with this property, and use it to show that the G-concurrence is monogamous. In the case of two qubits, we show that the equality between entanglement of formation and assistance holds if and only if the state is a rank 2 bipartite state that can be expressed as the marginal of a pure 3-qubit state in the W class.Monogamy of entanglement is one of the nonintuitive phenomena of quantum physics that distinguish it from classical physics. Classically, three random bits can be maximally correlated. For example, three coins can be prepared in a state in which with 50% chance all three coins show "head", and with the other 50% chance they all show "tail".

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“…Bell nonlocality and quantum entanglement are two distinct notions, whose relation is not straightforward [1][2][3][4]. Entanglement is a quantum resource [5][6][7][8][9][10] which cannot be generated by deterministic state transformations involving only local operations and classical communication (LOCC) [11,12]. In other words, a state is necessarily changed into a less, or equally, entangled state, by such a LOCC transformation.…”

Section: Introductionmentioning

confidence: 99%

Measure-independent anomaly of nonlocality

Camalet

2017

Phys. Rev. A

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We show that any Bell local state, with a hidden nonlocality that can be revealed by local filtering, is more, or equally, entangled than nonlocal states. More precisely, it can be deterministically transformed into a nonlocal state, by local operations and classical communication. For such a state, there is a clear anomaly of nonlocality, for any measures of entanglement and nonlocality. Moreover, we prove that the hidden nonlocality of any bipartite state more, or equally, entangled than nonlocal states, can be revealed by local operations and the sending of two one-bit messages, one in each direction. For some particular states, one bit of communication is even enough.

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Monogamy Inequality for Any Local Quantum Resource and Entanglement

Cited by 31 publications

References 40 publications

Internal Entanglement and External Correlations of Any Form Limit Each Other

Internal Entanglement and External Correlations of Any Form Limit Each Other

Monogamy of entanglement without inequalities

Measure-independent anomaly of nonlocality

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