We introduce a version of the chained Bell inequality for an arbitrary number of measurement outcomes, and use it to give a simple proof that the maximally entangled state of two d dimensional quantum systems has no local component. That is, if we write its quantum correlations as a mixture of local correlations and general (not necessarily quantum) correlations, the coefficient of the local correlations must be zero. This suggests an experimental programme to obtain as good an upper bound as possible on the fraction of local states, and provides a lower bound on the amount of classical communication needed to simulate a maximally entangled state in dxd dimensions. We also prove that the quantum correlations violating the inequality are monogamous among non-signalling correlations, and hence can be used for quantum key distribution secure against post-quantum (but non-signalling) eavesdroppers.
In this paper we focus on the underlying quantum structure of temporal correlations and show their peculiar nature which differentiate them from spatial quantum correlations. We show rigorously that a particular entangled history, which can be associated with a quantum propagator, is monogamous to conserve its consistency throughout time. Yet evolving systems violate monogamous Bell-like multi-time inequalities. This dichotomy, being a novel feature of temporal correlations, has its roots in the measurement process itself which is discussed by means of the bundles of entangled histories. We in…
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 quan…
The distribution of quantum correlations in multipartite systems play a significant role in several aspects of the quantum information theory. While it is well known that these quantum correlations can not be freely distributed, the way that it is shared in multipartite system is an open problem even for small set of qubits. Based on new monogamylike relations between entanglement and discord for $n$-partite systems, we show how these correlations are distributed in general, determining distinct equalities and inequalities to the quantum discord and the entanglement of formation for arbitrary …
In this paper, a computable multipartite multimode Gaussian quantum correlation measure ${\mathcal M}^{(k)}$ is proposed for any $k$-partite continuous-variable (CV) systems with $k\geq 2$. ${\mathcal M}^{(k)}$ depends only on the covariance matrix of CV states, is invariant under any permutation of subsystems, is a quantification without ancilla problem, nonincreasing under $k$-partite local Gaussian channels (particularly, invariant under $k$-partite local Gaussian unitary operations), vanishes on $k$-partite product states. For a $k$-partite Gaussian state $ρ$, ${\mathcal M}^{(k)}(ρ)=0$ if …
One of the fundamental differences between classical and quantum mechanics is in the ways correlations can be distributed among the many parties that compose a system. While classical correlations can be shared among many subsystems, in general quantum correlations cannot be freely shared. This unique property is known as monogamy of quantum correlations. In this work, we study the monogamy properties of the correlated coherence for the l 1 -norm and relative entropy measures of coherence. For the l 1 -norm the correlated coherence is monogamous for a particular class of quantum states. For th…
Adopting the graph-theoretic approach to the correlation experiments, we analyze the origin of monogamy and prove that it can be recognized as a consequence of the exclusivity principle(EP). We provide an operational criterion for monogamy: if the fractional packing number of the graph corresponding to the union of event sets of several physical experiments does not exceed the sum of independence numbers of each individual experiment graph, then these experiments are monogamous. As applications of this observation, several examples are provided, including the monogamy for experiments of Clause…
The maximally entangled state can be in a mixed state as well as the well-known pure state. Taking the negativity as a measure of entanglement, we study the entanglement dynamics of bipartite, mixed maximally entangled states (MMESs) in multipartite cavity-reservoir systems. It is found that the MMES can exhibit the phenomenon of entanglement sudden death, which is quite different from the asymptotic decay of the pure-Bell-state case. We also find that maximal entanglement cannot guarantee maximal nonlocality and the MMES does not correspond to the state with maximal measurement-induced nonloc…
Why the Entanglement of Formation is not generally monogamic
与经典系统的相关性不同，量子系统的纠缠不能随意分配-如果一个系统A与另一个系统B最大纠缠，则它根本不能纠缠到第三个系统C。这个概念被称为纠缠的一夫一妻制，当A与一对BC的纠缠可以被划分为A和B以及A和C之间的纠缠的贡献，加上一个涉及真正的三方纠缠的项τ_{ABC}，因此期望总是正的。量子信息理论中的一个非常重要的测量，形成纠缠（Entanglement of Formation，简称纠缠），不能满足最后一个要求。在这里我们提出了原因，并显示了一组条件，一个任意的纯三分态必须满足的条件，使λ成为一夫一妻制的措施，即τ_{ABC} \ge 0。该关系式与量子关联和经典关联的不一致有关，当量子关联优于经典关联时，τ_{ABC}为负。这一结果被用来解释纠缠在动力学演化过程中的分布特征。它也有助于将所有一夫一妻制的纠缠与压扁的纠缠联系起来，这是一种总是一夫一妻制的纠缠度量。
The celebrated Bell-Kochen-Specker no-go theorem asserts that quantum mechanics does not present the property of realism, the essence of the theorem is the lack of a joint probability distributions for some experiment settings. In this work, we exploit the information theoretic form of the theorem using information measure instead of probabilistic measure and indicate that quantum mechanics does not present such entropic realism neither. The entropic form of Gleason's no-disturbance principle is developed and it turns out to be characterized by the intersection of several entropic cones. Entro…
The monogamy relations of quantum correlation restrict the sharability of quantum correlations in multipartite quantum states. We show that all measures of quantum correlations satisfy some kind of monogamy relations for arbitrary multipartite quantum states. Moreover, by introducing residual quantum correlations, we present tighter monogamy inequalities that are better than all the existing ones. In particular, for multi-qubit pure states, we also establish new monogamous relations based on the concurrence and concurrence of assistance under the partition of the first two qubits and the remai…
We investigate the delocalization of quantum information in the nonequilibrium dynamics of the $XY$ spin chain with asymptotically decaying interactions $\sim 1/r^α$. As a figure of merit, we employ the tripartite mutual information (TMI), whose sign indicates if quantum information is predominantly shared globally. Interestingly, the sign of the TMI distinguishes regimes of the exponent $α$ that are known for different behaviour of information propagation. While an effective causal region bounds the propagation of information, if interactions decay sufficiently fast, this information is mainl…
In the quantum world correlations can take form of entanglement which is known to be monogamous. In this work we show that another type of correlations, indistinguishability, is also restricted by some form of monogamy. Namely, if particles A and B simulate bosons, then A and C cannot perfectly imitate fermions. Our main result consists in demonstrating to what extent it is possible.
We investigate the general monogamy and polygamy relations satisfied by quantum correlation measures. We show that there exist two real numbers $α$ and $β$ such that for any quantum correlation measure $Q$, $Q^x$ is monogamous if $x\geq α$ and polygamous if $0\leq x\leq β$ for a given multipartite state $ρ$. For $β<x<α$, we show that the monogamy relation can be superactivated by finite $m$ copies $ρ^{\otimes m}$ of $ρ$ for nonadditive correlation measures. As a detailed example, we use the negativity as the quantum correlation measure to illustrate such superactivation of monogamy properties.…
Analyzing shareability of correlations arising in any physical theory may be considered as a fruitful technique of studying the theory. Our present topic of discussion involves an analogous approach of studying quantum theory. For our purpose, we have deviated from the usual procedure of assessing monogamous nature of quantum correlations in standard Bell-CHSH scenario. We have considered correlations arising in a quantum network involving independent sources. Precisely speaking, we have analyzed monogamy of nonbilocal correlations by deriving a relation restricting marginals. Interestingly, r…
We propose a condition for a measure of quantum correlation to be polygamous without the traditional polygamy inequality. It is shown to be equivalent to the standard polygamy inequalities for any continuous measure of quantum correlation with the polygamy power. We then show that any entanglement of assistance is polygamous but not monogamous and any faithful entanglement measure is not polygamous.
We show that for any prime odd integer $d$, there exists a correlation of size $Θ(r)$ that can robustly self-test a maximally entangled state of dimension $4d-4$, where $r$ is the smallest multiplicative generator of $\mathbb{Z}_d^\ast$. The construction of the correlation uses the embedding procedure proposed by Slofstra (Forum of Mathematics, Pi. Vol. $7$, ($2019$)). Since there are infinitely many prime numbers whose smallest multiplicative generator is at most $5$ (M. Murty The Mathematical Intelligencer $10.4$ ($1988$)), our result implies that constant-sized correlations are sufficient f…
The purpose of the paper is mainly to investigate the quantum critical behavior of two-dimensional XY spin system by calculating quantum correlation and monogamy relation through implementation of quantum renormalization group theory. Numerical analysis indicates that quantum correlation as well as quantum nonlocality can be used to efficiently detect the quantum critical property in two-dimensional XY spin system. The nonanalytic behavior of the first derivative of quantum correlation approaches infinity and the critical point is reached as the size of the model increases. Furthermore, we dis…
We study the set of quantum correlations generated by actions on maximally entangled states. We show that such correlations are dense in their own convex hull. As a consequence, we show that these correlations are dense in the set of synchronous quantum correlations. We introduce the concept of corners of correlation sets and show that every local or nonsignalling correlation can be realized as the corner of a synchronous local or nonsignalling correlation. We provide partial results for other correlation sets.
We derive the analytical expression of local quantum uncertainty for three-qubit X-states. We give also the expressions of quantum discord and the negativity. A comparison of these three quantum correlations quantifiers is discussed in the special cases of mixed GHZ states and Bell-type states. We find that local quantum uncertainty gives the same amount of non-classical correlations as are measured by entropic quantum discord and goes beyond negativity. We also discuss the dynamics of non-classical correlations under the effect of phase damping, depolarizing and phase reversal channels. We fi…
We introduce a proposal to prepare spin-obit maximally discordant mixed states by a linear optical circuit, with quantum bits (qubits) encoded in the polarization and transverse mode degrees of freedom of photons. In particular, we discuss how to prepare non-balanced spin-orbit entangled states, applying this technique to obtain maximally discordant mixed states. We present a simulation of the optical circuit by using the Jones matrix formalism. We performed a study of entanglement, classical and quantum correlations. The results show excellent agreement with the underlying theory and open a n…
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 su…
Device-independent certification, also known as self-testing, aims at guaranteeing the proper functioning of untrusted and uncharacterized devices. For example, the quality of an unknown source expected to produce two-qubit maximally entangled states can be evaluated in a bi-partite scenario, each party using two binary measurements. The most robust approach consists in deducing the fidelity of produced states with respect to a two-qubit maximally entangled state from the violation of the CHSH inequality. In this paper, we show how the self-testing of two-qubit maximally entangled states is im…
It is well known that certain quantum correlations like quantum steering exhibit a monogamous relationship. In this paper, we exploit the asymmetric nature of quantum steering and show that there exist states which exhibit a polygamous correlation, known as collective correlation [He and Reid, Phys. Rev. Lett. 111, 250403 (2013)], where the state of one party, Alice, can be steered only by the joint effort of the other two parties, Bob and Charlie. As an example, we explicitly single out a particular set of $3$ qubit states which exhibit this polygamous relationship, known as collective steera…
A measure of total correlations cannot increase under deterministic local operations. We show that, for any number of systems, this condition alone does not guarantee the existence of maximally correlated states. Namely, there is no state that simultaneously maximizes all the measures satisfying it. If, in addition, the measures do not increase with probability unity under local measurements, then such states exist for two systems. They are the maximally entangled states. For a larger number of systems, it depends on their Hilbert space dimensions.
