International Conference on Quantum Information

Phase transitions of bipartite entanglement

Paolo Facchi A, Ugo Marzolino, Giorgio Parisi A, Saverio Pascazio, Antonello Scardicchio

Published Jan 1, 2008• 8 citations

Abstract

We study a random matrix model for the statistical properties of the purity of a bipartite quantum system. This enables us to write the generating function for the cumulants, for both balanced and unbalanced bipartitions. It also unveils an unexpected feature of the system, namely the existence of two phase transitions.

DOI: 10.1364/icqi.2008.qtua2

Related papers

Phase Transitions of Bipartite Entanglement

Paolo Facchi A, Ugo Marzolino, Giorgio Parisi A +2 more

We analyze the statistical properties of the entanglement of a large bipartite quantum system. By framing the problem in terms of random matrices and a fictitious temperature, we unveil the existence of two phase transitions, characterized by different spectra of the reduced density matrices.

arXiv:0712.0015Physical Review LettersJul 30, 200892 citations

Phase diagram of bipartite entanglement

Paolo Facchi A, Giorgio Parisi A, Saverio Pascazio +2 more

Abstract We investigate the features of the entanglement spectrum (distribution of the eigenvalues of the reduced density matrix) of a large quantum system in a pure state. We consider all Rényi entropies and recover purity and von Neumann entropy as particular cases. We construct the phase diagram of the theory and unveil the presence of two critical lines.

arXiv:1906.01269Journal of Physics A Mathematical and TheoreticalAug 30, 20196 citations

Statistical mechanics of multipartite entanglement

Paolo Facchi A, Giuseppe Florio, Ugo Marzolino +2 more

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over all balanced bipartitions. We search for those (maximally multipartite entangled) states whose purity is minimum for all bipartitions and recast this optimization problem into a problem of statistical mechanics.

arXiv:0803.4498Journal of Physics A Mathematical and TheoreticalJan 6, 200925 citations

Quantum Phase Transitions and Bipartite Entanglement

Lian-Ao Wu, M. S. Sarandy, Daniel A. Lidar

We develop a general theory of the relation between quantum phase transitions (QPTs) characterized by nonanalyticities in the energy and bipartite entanglement. We derive a functional relation between the matrix elements of two-particle reduced density matrices and the eigenvalues of general two-body Hamiltonians of d-level systems. The ground state energy eigenvalue and its derivatives, whose nonanalyticity characterizes a QPT, are directly tied to bipartite entanglement measures. We show that first-order QPTs are signaled by density matrix elements themselves and second-order QPTs by the first derivative of density matrix elements. Our general conclusions are illustrated via several quantum spin models.

arXiv:quant-ph/0407056Physical Review LettersDec 15, 2004484 citations

Phase transitions and metastability in the distribution of the bipartite entanglement of a large quantum system

Antonella De Pasquale, Paolo Facchi A, Giorgio Parisi A +2 more

We study the distribution of the Schmidt coefficients of the reduced density matrix of a quantum system in a pure state. By applying general methods of statistical mechanics, we introduce a fictitious temperature and a partition function and translate the problem in terms of the distribution of the eigenvalues of random matrices. We investigate the appearance of two phase transitions, one at a positive temperature, associated with very entangled states, and one at a negative temperature, signaling the appearance of a significant factorization in the many-body wave function. We also focus on the presence of metastable states (related to two-dimensional quantum gravity) and study the finite size corrections to the saddle point solution.

arXiv:0911.3888Physical Review AMay 19, 201052 citations

Statistical Distribution of Quantum Entanglement for a Random Bipartite State

J Stat Phys, Céline Nadal, Satya N. Majumdar +1 more

analytically the statistics of the Renyi and von Neumann entropies (standard measures of entanglement), for a random pure state in a large bipartite quantum system. The full probability distribution is computed by first mapping the problem to a random matrix model and then using a Coulomb gas method. We identify three different regimes in the entropy distribution, which correspond to two phase transitions in the asso-ciated Coulomb gas. The two critical points correspond to sudden changes in the shape of the Coulomb charge density: the appearance of an integrable singularity at the origin for the first critical point, and the detachment of the rightmost charge (largest eigenvalue) from the sea of the other charges at the second critical point. Analytical results are verified by Monte Carlo numerical simulations. A short account of part of these results appeared recently in Nadal et al. (Phys. Rev. Lett. 104:110501, 2010).

Jan 1, 201146 citations