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Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits and Many-Body Systems

Data: Sexta-Feira 19/06/2015, Sala A5-01, 11 am.

Palestrante: Eduardo R. Mucciolo (University of Central Florida)

Título: Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits and Many-Body Systems


We show that in a quantum system evolving unitarily under a stochastic quantum circuit the notions of irreversibility, universality of computation, and entanglement are closely related. As the state evolves from an initial product state, it gets asymptotically maximally entangled. We define irreversibility as the failure of searching for a disentangling circuit using a Metropolis-like algorithm. We show that irreversibility corresponds to Wigner-Dyson statistics in the level spacing of the entanglement eigenvalues, and that this is obtained from a quantum circuit made from a set of universal gates for quantum computation. If, on the other hand, the system is evolved with a non-universal set of gates, the statistics of the entanglement level spacing deviate from Wigner-Dyson and the disentangling algorithm succeeds. The type of reversible gate (real permutation for universal classical computations or complex unitary operation for universal quantum computations) defines the symmetry class of the Wigner-Dyson ensemble governing the spectral statistics (orthogonal or unitary classes). These results open a new way to characterize irreversibility in quantum systems, regardless of whether they are governed by time-dependent or time-independent Hamiltonians. In particular, we show how entanglement spectrum statistics identify integrability (or lack thereof) in systems submitted to a quantum quench and how it is affected by many-body localization in disordered spin chains.


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