Correlations in classical ground states

Guangrong Liu, Yang Liu, Xiangrong Li

The characterization of the correlation of quantum States plays a key role in the study of quantum information theory. Classical correlation is a quantum state that remains unchanged under local orthogonal projection, and it is not affected by decoherence. The entangled quantum state must be quantum correlation, and there is also quantum correlation in the separable quantum state. Relevance is a common phenomenon in nature. From the perspective of information theory, classical relevance can be described under Shannon's information theory. Therefore, it is necessary to explore the relationship among classical correlation, quantum correlation and quantum nonlocality. For the two-body quantum system, this paper gives the corresponding definitions of classical correlation state, left classical associated state and right classical associated state from the perspective of probability density, especially the definition of classical independent associated state. Different from the definition of local orthogonal projection measurement, it is easier to construct classical correlation state and quantum correlation state from the perspective of probability distribution, and further analyze the characteristics of eigenvalues and their corresponding eigenvectors. The selection of standard orthogonal basis, the corresponding relationship between separable ground state and classical correlation, entangled ground state and quantum correlation in two-body quantum system are studied. The corresponding characteristics of left classical correlation state and right classical correlation state are explored, and the relationship between separability and correlation, the relationship between convex combination and correlation of quantum States, and the left classical correlation state and right classical correlation state may also be quantum correlation States are illustrated by examples, and the definition of independent classical correlation state and its relationship with edge distribution are further obtained.

Guido Bellomo, A. P. Majtey, Angel Ricardo Plastino +1 more

Nikolai Nikolaevich Bogoliubov, D. N. Zubarev, V. V. Tolmatchev +1 more

Marco Cianciaruso, S. M. Giampaolo, Ferro, L. +4 more

We analyse the nature of spontaneous symmetry breaking in complex quantum systems by investigating the long-standing conjecture that the maximally symmetry-breaking quantum ground states are the most classical ones corresponding to a globally ordered phase. We make this argument quantitatively precise by comparing different local and global indicators of classicality and quantumness, respectively in symmetry-breaking and symmetry-preserving quantum ground states. We first discuss how naively comparing local, pairwise entanglement and discord apparently leads to the opposite conclusion. Indeed, we show that in symmetry-preserving ground states the two-body entanglement captures only a modest portion of the total two-body quantum correlations, while, on the contrary, in maximally symmetry-breaking ground states it contributes the largest amount to the total two-body quantum correlations. We then put to test the conjecture by looking at the global, macroscopic correlation properties of quantum ground states. We prove that the ground states which realize the maximum breaking of the Hamiltonian symmetries, associated to a globally ordered phase, are the only ones that: I) are always locally convertible, i.e. can be obtained from all other ground states by only applying LOCC transformations (local operations and classical communication), while the reverse is never possible; II) minimize the monogamy inequality on the globally shared, macroscopic bipartite entanglement.

E. Heinz, H. Müther, Harry A. Mavromatis

Marco Cianciaruso, Ferro, L., S. M. Giampaolo +2 more

We investigate the nature of spontaneous symmetry breaking in complex quantum systems by conjecturing that the maximally symmetry breaking quantum ground states are the most classical ones corresponding to an ordered phase. We make this argument quantitatively precise by showing that the ground states which realize the maximum breaking of the Hamiltonian symmetries are the only ones that: I) are always locally convertible, i.e. can be obtained from all other ground states by local operations and classical communication, while the reverse is never possible; II) minimize the monogamy inequality for bipartite entanglement; III) minimize quantum correlations, as measured by the quantum discord, for all pairs of dynamical variables and are the only ground states for which the pairwise quantum correlations vanish asymptotically with the intra-pair distance.