[quantum-info] John Calsamiglia @ IQC, Thursday, August 4

Marco Piani marcopiani at gmail.com
Wed Aug 3 13:31:05 EDT 2011


Who: John Calsamiglia, Universitat Autònoma de Barcelona

Where: IQC, RAC1 2009

When: Thursday, August 4, noon

What:

"Local vs Collective measurements in statistical inference"

Abstract:

I will present three problems in quantum statistical inference that  
all stem from the difference between local and collective measurements  
on multipartite states.
The first one is that of hiding a secret direction in a multipartite  
state with the promise that the parties cannot learn the direction if  
they perform local operations and classical communication, but can  
accurately retrieve it if they perform collective measurements.
The second is that of giving the probability of discriminating between  
a large number of copies of two given quantum states. This leads to  
the identification of the Quantum Chernoff bound, which gives a  
natural operational distinguishability measure between quantum states.  
The question remains whether the bound can be attained by LOCC  
measurments or, on the contrary, collective operations on an  
assymptotically large number of copies are necessary. Our results  
indicate that the gap between collective and LOCC operations persists  
even in the asymptotic limit: in order for LOCC and collective  
protocols to achieve the same accuracy, the former requires up to  
twice the number of copies of the latter.
Finally, if time permits, I will present a quantum learning machine  
which classifies an unknown qubit after being trained with a number of  
already classified qubits. We prove that quantum memory is not  
required for optimal performance (i.e. quantum correlations between  
the training qubits and the classified qubit are of no aid here). In  
this sense, we show how to physically separate the protocol in two  
steps: training and discrimination, where the information gathered in  
the former is stored in a (finite) classical memory to be used for the  
latter. This 2-step functioning implies also the ability of having  
time-like separation between training and testing stages. Moreover, as  
the memory needed is classical, such a machine can be reused for the  
classification of any number of additional qubits without retraining.





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