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 101: Special Thursday Tutorials
Session Chair:
10:00-12:00	Steven van Enk, University of Oregon (invited)
	Entanglement and Verification
	Abstract. Besides giving a general and simple introduction to bipartite entanglement, the main idea of the tutorial is to illustrate the differences between the theory and practice of entanglement verification. Outline of Tutorial: I. Bipartite entanglement: Definition Convex sets LOCC Entanglement monotones Why do we need entanglement anyway? Entanglement in infinite dimensions II. Verifying entanglement, theory: Convex sets and entanglement witnesses Optimal & nonoptimal witnesses Bell inequality violations as a nonoptimal witness III. Different sorts of entanglement in experiments: a priori Heralded a posteriori IV. Verifying entanglement in experiments: What could possibly go wrong? Criteria for entanglement verification Security of quantum key distribution as guideline Filtering data Assumptions about generated state Assumptions about measurements
13:30-15:30	John Martinis, University of California, Santa Barbara (invited)
	Beyond T₁: Measuring Coherence with State and Process Tomography
	Abstract. The tutorial would review the physics and mathematics behind the metrology of qubit coherence, using specific examples from recent experiments on superconducting qubits. Outline of Tutorial I. Qubit basics Two-state quantum system Time evolution of state with external control Simple physical picture of decoherence Example: Josephson phase qubit II. T₁- and T₂-ology T₁, T₂, polarization describes memory of practically all qubits T2 is approximate concept, depends on details Why are simple T₁, T₂ measurements not sufficient? III. Single-qubit: state and process tomography Density matrix description How measured - two methods Dynamic errors (to other states) measured to 10^-4 via "Ramsey filtering" Errors in memory storage described by process tomography Research issue: going from matrix to "what needs fixing" IV. Two-qubit: state and process tomography Density matrix description How measured from single qubit rotatins Experiment to demonstrate entanglement, measure matrix Process tomography Bell-violation experiment V. Multi-qubit state and process tomography - the problem
16:00-18:00	Howard Barnum, Los Alamos National Laboratory (invited)
	Convexity and Positivity in Quantum Information: Part I
	Abstract. Convex sets and convex cones occur frequently in quantum information theory. For example, normalized density matrices, completely positive maps, separable states, and POVMs all form convex sets. Finding an optimal quantum information processing protocol can often be cast as minimizing a linear function over a compact convex set, a problem for which much is known. This tutorial will cover some of the basic theory of convex sets and optimization over them, and applications to quantum information processing. The first half of the tutorial will be given by Howard Barnum and will focus on the basic theory in finite dimensions, with topics selected for their applicability to quantum information. It will cover the following: Outline of Tutorial: I. Basic definitions and facts Definition of convex and affine sets. Compact convex sets, preservation of convexity by affine maps. Krein-Milman theorem. Brief note on infinite vs. finite dimension. Caratheodory's theorem. Suspending d-dimensional convex sets as cone bases in d+1 real dimensions. Regular (convex, pointed, full, closed) cones. Ordered linear spaces, equivalence of OLS's to spaces with distinguished regular cones. Examples: positive orthant, Lorentz cones, and positive semidefinite matrices. Quantum information examples: unentangled states, positive maps, and completely positive maps. II. Separation and duality Separating hyperplanes, separation theorems. Definition of dual cone. Exposed points. Order units and operational theories. Direct sums of cones. Simplices: equivalent definitions, simplices as state-spaces of classical theories. Homogeneity, self-duality, examples. Koecher-Vinberg characterization of self-dual homogeneous cones. III. Optimization and applications Basic results about optimizing convex and concave functions over compact convex sets. General conic convex programming with linear objective function. Linear, quadratic, and semidefinite programming. Different presentations of programs. Sufficient conditions for efficient algorithms; ellipsoid and other methods; LP/SDP/quadratic examples. NP-hard examples. Hard convex-set membership problems and Gurvits' proof of NP-hardness of entanglement testing. Quantum applications of SDP. Reducing dimension with symmetry. Duality in convex conic optimization, lower bounds on query complexity via relaxation and duality (if time permits).
16:00-18:00	Andrew Landahl, University of New Mexico (invited)
	Convexity and Positivity in Quantum Information: Part II
	Abstract. Convex sets and convex cones occur frequently in quantum information theory. For example, normalized density matrices, completely positive maps, separable states, and POVMs all form convex sets. Finding an optimal quantum information processing protocol can often be cast as minimizing a linear function over a compact convex set, a problem for which much is known. This tutorial will cover some of the basic theory of convex sets and optimization over them, and applications to quantum information processing. The second half of the tutorial will be given by Andrew Landahl and will focus on some concrete applications of semidefinite programming in quantum information: Outline of Tutorial: I. Optimal quantum error correction Convexity of quantum process distance measures. Optimal optimal encoding and recovery as convex optimization problems. Semidefinite program (SDP) formulation for some distance measures. Comparison to stabilizer coding. II. Optimal quantum protocols for weak coin flipping Definition of weak coin flipping (WCF). Maximum cheating bias in a quantum WCF protocol as an SDP. Minimum bias over all quantum WCF protocols as an SDP. Why incorporating cheat detection makes problem nonconvex. III. Optimal quantum state discrimination Definition of quantum state discrimination problems. Optimal minimum-error state discrimination measurement as an SDP. Optimal unambiguous state discrimination measurement as an SDP. Optimal "hybrid" state discrimination measurement as an SDP.