Southwest Quantum Information and Technology

Sixteenth Annual Meeting, February 20-22, 2014
Santa Fe, New Mexico

Full Program | Thursday | Friday | Saturday | All Sessions

SESSION 7: Quantum Information Theory I
10:30am - 11:15am	Patrick Hayden, Stanford University (invited)
	Spacetime, quantum cloning and black holes
	Abstract. Reconciling black hole evaporation with the unitarity of quantum mechanics is an endeavour frought with conceptual difficulties. Not least among them is the apparent need for quantum cloning or, equivalently, violations of the monogamy of entanglement. The most recent and confusing incarnation of this problem is the so-called firewall paradox, which interprets monogamy violations as an indication that black holes may not have interiors. This talk will begin with a more pedestrian question: understanding all the ways in which quantum information can be replicated in Minkowski spacetime. It turns out that there is an amazing variety, perhaps an indication that we should not be so worried about apparent violations of no-cloning in situations in which the causal structure of spacetime is itself in doubt. Towards the end, I will return to the black hole firewall problem and sketch some of the quantum information theoretic ideas that have been proposed as possible resolutions.
11:15am - 11:45am	Mankei Tsang, National University of Singapore
	Mismatched quantum filtering and entropic information
	Abstract. Quantum filtering is a signal processing technique that estimates the posterior state of a quantum system under continuous measurements and has become a standard tool in quantum information processing, with applications in quantum state preparation, quantum metrology, and quantum control. If the filter assumes a wrong model due to assumptions or approximations, however, the estimation accuracy is bound to suffer. I shall present formulas that relate the error penalty caused by quantum filter mismatch to the relative entropy between the true model and the nominal model, with one formula for Gaussian measurements, such as homodyne detection, and another for Poissonian measurements, such as photon counting. These formulas generalize recent seminal results in classical information theory and provide new operational meanings to relative entropy, mutual information, and channel capacity in the context of quantum experiments. See http://arxiv.org/abs/1310.0291 for details.
11:45am - 12:15pm	Beni Yoshida, California Institute of Technology
	Violation of the Arrhenius law for memory time below magnetic and topological transition temperature
	Abstract. When interacting spin systems possess non-zero magnetization or topological entanglement entropy below the transition temperature, they often serve as classical or quantum self-correcting memory whose memory time grows exponentially in the system size due to polynomially growing energy barrier. Here, we argue that this is not always the case; we demonstrate that memory time of classical clock model (a generalization of ferromagnet to q-state spins) or Zq Toric code may be only polynomially long even when the system possesses finite magnetization or topological entanglement entropy. This violation of the Arrhenius law occurs above the percolation temperature (but below the transition temperature) where excitation droplets percolate the entire lattice while the system as a whole still remains ordered. We present numerical evidences for polynomial scaling as well as analytical argument showing that energy barrier is effectively suppressed and is only logarithmically divergent. The models we study are physically natural as they converge to 2d XY model and U(1) gauge theory as q goes to infinity where excitations are vortex-like with logarithmically divergent excitation energy. We also derive an asymptotic formula of mutual information and topological entanglement entropy at finite temperature for 2d clock model and 3d toric code as a function of q, which is consistent with large q behaviors.