Effect of a large number of parties on the monogamy of quantum correlations

Kumar, Asutosh; Prabhu, R.; SenDe, Aditi; Sen, Ujjwal

doi:10.1103/physreva.91.012341

Cited by 31 publications

(32 citation statements)

References 93 publications

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“…In Ref. [63], it was shown numerically that entanglement measures become monogamous for pure states with increasing number of qubits. It was also figured out that "good" entanglement measures [87] like relative entropy of entanglement, regularized relative entropy of entanglement [88], entanglement cost [89,90], distillable entanglement, all of which are not generally computable, are monogamous for almost all pure states of four or more qubits.…”

Section: Proof Convexity Of Q Implies That Ifmentioning

confidence: 99%

“…Thus, we observe that the convexity plays a key role in establishing monogamy of quantum correlations. In another case, non-monogamous quantum correlation measures become monogamous, for moderately large number of parties [63].…”

Section: Introductionmentioning

confidence: 99%

“…Entanglement measures such as concurrence [58,59], entanglement of formation [60], negativity [61], etc., apart from information-theoretic measures such as quantum discord [4,5] are known to be, in general, non-monogamous. In recent developments on monogamy, we have seen that exponent of a quantum correlation measure and multipartite quantum states play a remarkable role in characterization of monogamy [62,63]. A non-monogamous quantum correlation measure can become monogamous, for three or more parties, when its power is increased [62].…”

Section: Introductionmentioning

confidence: 99%

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Conditions for monogamy of quantum correlations in multipartite systems

Kumar

2016

Physics Letters A

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Monogamy of quantum correlations is a vibrant area of research because of its potential applications in several areas in quantum information ranging from quantum cryptography to co-operative phenomena in many-body physics. In this paper, we investigate conditions under which monogamy is preserved for functions of quantum correlation measures. We prove that a monogamous measure remains monogamous on raising its power, and a non-monogamous measure remains non-monogamous on lowering its power. We also prove that monogamy of a convex quantum correlation measure for arbitrary multipartite pure quantum state leads to its monogamy for mixed states in the same Hilbert space. Monogamy of squared negativity for mixed states and that of entanglement of formation follow as corollaries of our results.

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Section: Proof Convexity Of Q Implies That Ifmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Conditions for monogamy of quantum correlations in multipartite systems

Kumar

2016

Physics Letters A

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“…For the symmetric Dicke states, analytical forms for C 2 , N 2 and D, for any two-qubit density matrices, are known and can be written as [27] …”

Section: Dicke Statesmentioning

confidence: 99%

“…Further, information-theoretic measures of quantum correlation, such as quantum discord and quantum work-deficit, are also known to violate the monogamy inequality for three-qubits [24,25]. Recent results on monogamy of quantum correlation have shown that the monogamy inequality is always satisfied for increasing powers of any quantum correlation measure [26] or when large number of parties are considered [27].…”

Section: Introductionmentioning

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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Lectures on General Quantum Correlations and their Applications

Fanchini¹,

Pinto²,

Adesso³

2017

Quantum Science and Technology

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Monogamy is an intrinsic feature of quantum correlations that gives rise to several interesting quantum characteristics which are not amenable to classical explanations. The monogamy property imposes physical restrictions on unconditional sharability of quantum correlations between the different parts of a multipartite quantum system, and thus has a direct bearing on the cooperative properties of states of multiparty systems, including large many-body systems. On the contrary, a certain party can be maximally classical correlated with an arbitrary number of parties in a multiparty system. In recent years, the monogamy property of quantum correlations has been applied to understand several key aspects of quantum physics, including distribution of quantum resources, security in quantum communication, critical phenomena, and quantum biology. In this chapter, we look at some of the salient developments and applications in quantum physics that have been closely associated with the monogamy of quantum discord, and "discord-like" quantum correlation measures.

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Effect of a large number of parties on the monogamy of quantum correlations

Cited by 31 publications

References 93 publications

Conditions for monogamy of quantum correlations in multipartite systems

Conditions for monogamy of quantum correlations in multipartite systems

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

Lectures on General Quantum Correlations and their Applications

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