Southwest Quantum Information and Technology

Thirteenth Annual Meeting, February 17-20, 2011
Boulder, Colorado

Full Program | Thursday | Friday | Saturday | Sunday | All Sessions

SESSION 4: Quantum Information Theory I
Session Chair:
1:45pm-2:30pm	Jonathan Oppenheim, University of Cambridge
	Uncertainty, nonlocality, & complementarity
	Abstract. Two central concepts of quantum mechanics are Heisenberg's uncertainty principle, and a subtle form of non-locality that Einstein famously called ``spooky action at a distance''. These two fundamental features have thus far been distinct concepts. Here we show that they are inextricably and quantitatively linked. Quantum mechanics cannot be more non-local with measurements that respect the uncertainty principle. In fact, the link between uncertainty and non-locality holds for all physical theories.More specifically, the degree of non-locality of any theory is determined by two factors -- the strength of the uncertainty principle, and the strength of a property called ``steering'', which determines which states can be prepared at one location given a measurement at another.
2:30pm-3:00pm	Jon Yard, Los Alamos National Laboratory
	Faithful squashed entanglement with applications to separability testing and quantum complexity
	Abstract. Squashed entanglement is a measure for the entanglement of bipartite quantum states. In this talk, I will present a new lower bound for squashed entanglement in terms of the distance to the set of separable states, along with several applications. I will first show how this implies that squashed entanglement is a faithful measure of entanglement, meaning it is positive on a state if and only if it is entangled. The bound also implies a new de Finetti-type bound for quantum states which, in turn, implies a quasipolynomial-time algorithm for deciding if a density matrix is entangled. The best known algorithms for this problem had been exponential. I will also show several applications in quantum complexity theory by giving new multi-prover characterizations of QMA, which is a quantum analog of NP. The bound follows from a sequence of new results about entanglement measures, whose proofs utilize some recent results in quantum information theory. These include an operational interpretation of quantum conditional mutual information as the optimal communication rate in quantum state redistribution, and an operational interpretation of the regularized relative entropy of entanglement as the optimal error rate for hypothesis testing with one-sided error. Another crucial aspect of the proof is the utilization of operationally-motivated norms on bipartite states that quantify distinguishability under local operations and classical communication. This is joint work (arXiv:1010.1750, 1011.2751) with Fernando Brandão and Matthias Christandl.
3:00pm-3:30pm	Steve Flammia, Caltech
	Tomography via Compressed Sensing
	Abstract. I will review past results and present current progress on using methods from the theory of compressed sensing to drastically reduce the number of measurements required for quantum tomography. These methods achieve a square root improvement in the number of measurement settings when the state in question is pure. Our methods have several features that make them amenable to experimental implementation: they require only simple Pauli measurements, use fast convex optimization, are stable against noise, can be applied to states that are only approximately pure, and can be extended to process tomography of nearly unitary channels. The acquired data can be used to certify that the state is indeed close to pure, so no a priori assumptions are needed.