Southwest Quantum Information and Technology

Tenth Annual Meeting, February 14-17, 2008
University of New Mexico, Santa Fe, New Mexico

Full Program | Thursday Tutorials | Friday | Saturday | Sunday

SESSION 3: Information Theory
Session Chair: Cris Moore
13:45-14:30	Patrick Hayden, McGill University (invited)
	Black Holes as Mirrors
	Abstract. I'll discuss information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and also assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the "half-way" point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis.
15:00-15:30	Gregory Crosswhite, University of Washington, Department of Physics
	Using the cutting edge of matrix product state techniques to slice infinitely large entangled systems down to size
	Abstract. The numerical simulation of quantum systems is inherently very difficult because the presence of entanglement means that one is faced with a state space exponentially large with respect to the number of particles. The only hope one has to get around this is to employ a clever form of representation that approximates quantum states of interest adequately while remaining small enough to be tractable. Matrix product states have garnered much interest over the past decade because they have these properties. In particular, matrix product states make an excellent ansatz for using the variational method to determine properties of the ground state. In my talk, I shall present an algorithm which uses a local direct variational optimization algorithm to obtain a translationally invariant representation of ground states for infinitely large one-dimensional systems.
15:30-16:00	Jon Walgate, Perimeter Institute for Theoretical Physics
	Generic local distinguishability and completely entangled subspaces
	Abstract. The geometry of Hilbert space entails many necessary and generic properties of quantum systems. In fact, expressing quantum information theoretic questions in geometric terms can transform apparently complex problems into exceedingly simple results. We present an example - a theorem concerning subspaces of projective Hilbert space with immediate and surprising consequences for entanglement and local state distinguishability. A subspace of a multipartite Hilbert space is completely entangled if it contains no product states. Such subspaces can be large with a known maximum size, S, approaching the full dimension of the system, D. We show that almost all subspaces with dimension less than or equal to S are completely entangled, and then use this fact to prove that n random pure quantum states are unambiguously locally distinguishable if and only if n does not exceed D-S. This condition holds for almost all sets of states of all multipartite systems, and reveals something unexpected. The criterion is identical for separable and for nonseparable states: entanglement makes no difference.