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Register a new userNonlocality in many-body quantum systems detected with two-body correlators
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Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems, mostly because the available multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access theoretically, and even harder experimentally. Standard, theorist- and experimentalist-friendly many-body observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have succeeded in constructing multipartite Bell inequalities that involve two- and one-body correlations only, and showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Science 344, 1256 (2014)]. With the present contribution we continue our work on this problem. On the one hand, we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First, we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities which reveal nonlocality of the Dicke states---ground states of physically relevant and experimentally realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures.
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Current understanding of correlations and quantum phase transitions in many-body systems has significantly improved thanks to the recent intensive studies of their entanglement properties. In contrast, much less is known about the role of quantum non-locality in these systems. On the one hand, standard, theorist- and experimentalist-friendly many-body observables involve correlations among only few (one, two, rarely three...) particles. On the other hand, most of the available multipartite Bell inequalities involve correlations among many particles. Such correlations are notoriously hard to access theoretically, and even harder experimentally. Typically, there is no Bell inequality for many-body systems built only from low-order correlation functions. Recently, however, it has been shown in [J. Tura et al., Science 344, 1256 (2014)] that multipartite Bell inequalities constructed only from two-body correlation functions are strong enough to reveal non-locality in some many-body states, in particular those relevant for nuclear and atomic physics. The purpose of this lecture is to provide an overview of the problem of quantum correlations in many-body systems - from entanglement to nonlocality - and the methods for their characterization.
We consider a bipartite scenario where two parties hold ensembles of $1/2$-spins which can only be measured collectively. We give numerical arguments supporting the conjecture that in this scenario no Bell inequality can be violated for arbitrary numbers of spins if only first order moment observables are available. We then give a recipe to achieve a significant Bell violation with a split many-body system when this restriction is lifted. This highlights the strong requirements needed to detect bipartite quantum correlations in many-body systems device-independently.
A hierarchy of equations for equilibrium reduced density matrices obtained earlier is used to consider systems of spinless bosons bound by forces of gravity alone. The systems are assumed to be at absolute zero of temperature under conditions of Bose condensation. In this case, a peculiar interplay of quantum effects and of very weak gravitational interaction between microparticles occurs. As a result, there can form spatially-bounded equilibrium structures macroscopic in size, both immobile and rotating. The size of a structure is inversely related to the number of particles in the structure. When the number of particles is relatively small the size can be enormous, whereas if this numbder equals Avogadros number the radius of the structure is about 30 cm in the case that the structure consists of hydrogen atoms. The rotating objects have the form of rings and exhibit superfluidity. An atmosphere that can be captured by tiny celestial bodies from the ambient medium is considered too. The thickness of the atmosphere decreases as its mass increases. If short-range intermolecular forces are taken into account, the results obtained hold for excited states whose lifetime can however be very long. The results of the paper can be utilized for explaining the first stage of formation of celestial bodies from interstellar and even intergalactic gases.
One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as is the system in state A or state B?. In quantum mechanics, the latter type of measurements can be studied and optimized using the framework of quantum hypothesis testing. In many cases one can explicitly find the optimal measurement in the limit where one has simultaneous access to a large number $n$ of identical copies of the system, and estimate the expected error as $n$ becomes large. Interestingly, error estimates turn out to involve various quantum information theoretic quantities such as relative entropy, thereby giving these quantities operational meaning. In this paper we consider the application of quantum hypothesis testing to quantum many-body systems and quantum field theory. We review some of the necessary background material, and study in some detail the situation where the two states one wants to distinguish are parametrically close. The relevant error estimates involve quantities such as the variance of relative entropy, for which we prove a new inequality. We explore the optimal measurement strategy for spin chains and two-dimensional conformal field theory, focusing on the task of distinguishing reduced density matrices of subsystems. The optimal strategy turns out to be somewhat cumbersome to implement in practice, and we discuss a possible alternative strategy and the corresponding errors.
We present a method to show that low-energy states of quantum many-body interacting systems in one spatial dimension are nonlocal. We assign a Bell inequality to the Hamiltonian of the system in a natural way and we efficiently find its classical bound using dynamic programming. The Bell inequality is such that its quantum value for a given state, and for appropriate observables, corresponds to the energy of the state. Thus, the presence of nonlocal correlations can be certified for states of low enough energy. The method can also be used to optimize certain Bell inequalities: in the translationally invariant (TI) case, we provide an exponentially faster computation of the classical bound and analytically closed expressions of the quantum value for appropriate observables and Hamiltonians. The power and generality of our method is illustrated through four representative examples: a tight TI inequality for 8 parties, a quasi TI uniparametric inequality for any even number of parties, ground states of spin-glass systems, and a non-integrable interacting XXZ-like Hamiltonian. Our work opens the possibility for the use of low-energy states of commonly studied Hamiltonians as multipartite resources for quantum information protocols that require nonlocality.
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