Finite size mean-field models

Abstract

We characterize the two-site marginals of exchangeable states of a system of quantum spins in terms of a simple positivity condition. This result is used in two applications. We first show that the distance between two-site marginals of permutation invariant states on N spins and exchangeable states is of order 1/N. The second application relates the mean ground state energy of a mean-field model of composite spins interacting through a product pair interaction with the mean ground state energies of the components.

20 pages

References in corpus (4)

• Entanglement in a second order quantum phase transition
• Entanglement in a first order quantum phase transition
• A de Finetti representation for finite symmetric quantum states
• A de Finetti Representation Theorem for Quantum Process Tomography

Cited by in corpus (8)

• Entanglement and permutational symmetry
• Testing product states, quantum Merlin-Arthur games and tensor optimisation
• Quantum de Finetti theorem under fully-one-way adaptive measurements
• A quasipolynomial-time algorithm for the quantum separability problem
• Approximation algorithms for QMA-complete problems
• Many-Body Blow-Up Profile of Boson Stars with External Potentials
• On Exchangeable Continuous Variable Systems
• Additivity of the Renyi entropy of order 2 for positive-partial-transpose-inducing channels