[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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