We discuss upper bounds on the rate at which unitary evolution governed by a non-local Hamiltonian can generate entanglement in a bipartite system. Given a bipartite Hamiltonian H coupling two finite dimensional particles A and B, the entangling rate is shown to be upper bounded by where d is the smallest dimension of the Hilbert spaces describing A, B, and is the operator norm of H. Under certain restrictions on the initial state the same upper bound is shown to be valid for the ancilla-assisted entangling rate, that is, A and B can be extended by local ancillas a and b which are not acted on by H. The restriction is that the reduced density matrix of the subsystem aA (or Bb) has at most two distinct eigenvalues (each eigenvalue may have arbitrarily large multiplicity). We also describe a connection between entangling rate in a bipartite system and mixing rate in a one-party system.

By:* Sergey Bravyi*

Published in: Physical Review. A. General Physics, volume 76, (no 5), pages 052319-1-8 in 2007

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