Southwest Quantum Information and Technology

Fourteenth Annual Meeting, February 16-19, 2012
Albuquerque, New Mexico

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SESSION 4: Quantum Information Theory - Alvarado "D"
Session Chair:
10:30am-11:15am	Luiz Davidovich, Universidade Federal do Rio de Janeiro (invited)
	Quantum metrology with noisy systems
	Abstract. The estimation of parameters characterizing dynamical processes is central for science and technology. The estimation error decreases with the number N of resources employed in the experiment (which could quantify, for instance, the number of probes or the probing energy). For independent probes, it scales as one over the square root of N. Quantum strategies may improve the precision for noiseless processes, so that it scales as 1/N. For noisy processes, it is not known in general if and when this improvement can be achieved. This talk will introduce some basic aspects of quantum metrology, and present a recent proposal [1,2] of a general framework for obtaining attainable and useful lower bounds for the ultimate limit of precision in noisy systems. This method is applied to estimate precision bounds, which are independent of the initial state of the probes, for lossy optical interferometry and atomic spectroscopy in the presence of dephasing. These bounds capture the main features of the transition from the 1/N to the one over square root of N behavior as N increases. References [1] B. M. Escher, R. L. de Matos Filho, and L. Davidovich, General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology, Nature Physics vol. 7, 406 (2011). [2] B. M. Escher, R. L. de Matos Filho, and L. Davidovich, Quantum metrology for noisy systems, Brazilian Journal of Physics, vol. 41, 229 (2011).
11:15am-11:45am	Wim van Dam, University of California, Santa Barbara
	Mutually unbiased bases for quantum states defined over p-adic numbers
	Abstract. We describe sets of mutually unbiased bases (MUBs) for quantum states defined over the p-adic numbers Q_p, i.e. the states that can be described as elements of the (rigged) Hilbert space L2(Q_p). We find that for every prime >2 there are at least p+1 MUBs, which is in contrast with the situation for quantum states defined over the real line R for which only 3 MUBs are known. We comment on the possible reason for the difference regarding MUBs between these two infinite dimensional Hilbert spaces. This is joint work with Alexander Russell. http://arxiv.org/abs/1109.0060
11:45am-12:15pm	Gilad Gour, Institute for Quantum Information Science
	Local additivity of the minimum entropy output of a quantum channel
	Abstract. In this talk I will show that the minimum von-Neumann entropy output of a quantum channel is locally additive. Hasting's counterexample for the global additivity conjecture, makes this result somewhat surprising. In particular, it indicates that the non-additivity of the minimum entropy output is related to a global effect of quantum channels. I will end with few related open problems.