92,078 research outputs found
Strategies for optimal single-shot discrimination of quantum measurements
In this work we study the problem of single-shot discrimination of von
Neumann measurements, which we associate with measure-and-prepare channels.
There are two possible approaches to this problem. The first one is simple and
does not utilize entanglement. We focus only on the discrimination of classical
probability distributions, which are outputs of the channels. We find necessary
and sufficient criterion for perfect discrimination in this case. A more
advanced approach requires the usage of entanglement. We quantify the distance
between two measurements in terms of the diamond norm (called sometimes the
completely bounded trace norm). We provide an exact expression for the optimal
probability of correct distinction and relate it to the discrimination of
unitary channels. We also state a necessary and sufficient condition for
perfect discrimination and a semidefinite program which checks this condition.
Our main result, however, is a cone program which calculates the distance
between the measurements and hence provides an upper bound on the probability
of their correct distinction. As a by-product, the program finds a strategy
(input state) which achieves this bound. Finally, we provide a full description
for the cases of Fourier matrices and mirror isometries.Comment: 13 pages, 4 figure
Collaborative Representation based Classification for Face Recognition
By coding a query sample as a sparse linear combination of all training
samples and then classifying it by evaluating which class leads to the minimal
coding residual, sparse representation based classification (SRC) leads to
interesting results for robust face recognition. It is widely believed that the
l1- norm sparsity constraint on coding coefficients plays a key role in the
success of SRC, while its use of all training samples to collaboratively
represent the query sample is rather ignored. In this paper we discuss how SRC
works, and show that the collaborative representation mechanism used in SRC is
much more crucial to its success of face classification. The SRC is a special
case of collaborative representation based classification (CRC), which has
various instantiations by applying different norms to the coding residual and
coding coefficient. More specifically, the l1 or l2 norm characterization of
coding residual is related to the robustness of CRC to outlier facial pixels,
while the l1 or l2 norm characterization of coding coefficient is related to
the degree of discrimination of facial features. Extensive experiments were
conducted to verify the face recognition accuracy and efficiency of CRC with
different instantiations.Comment: It is a substantial revision of a previous conference paper (L.
Zhang, M. Yang, et al. "Sparse Representation or Collaborative
Representation: Which Helps Face Recognition?" in ICCV 2011
Revisiting spatial vision: toward a unifying model
We report contrast detection, contrast increment, contrast masking, orientation discrimination, and spatial frequency discrimination thresholds for spatially localized stimuli at 4° of eccentricity. Our stimulus geometry emphasizes interactions among overlapping visual filters and differs from that used in previous threshold measurements, which also admits interactions among distant filters. We quantitatively account for all measurements by simulating a small population of overlapping visual filters interacting through divisive inhibition. We depart from previous models of this kind in the parameters of divisive inhibition and in using a statistically efficient decision stage based on Fisher information. The success of this unified account suggests that, contrary to Bowne [Vision Res. 30, 449 (1990)], spatial vision thresholds reflect a single level of processing, perhaps as early as primary visual cortex
Single-shot discrimination of quantum unitary processes
We formulate minimum-error and unambiguous discrimination problems for
quantum processes in the language of process positive operator valued measures
(PPOVM). In this framework we present the known solution for minimum-error
discrimination of unitary channels. We derive a "fidelity-like" lower bound on
the failure probability of the unambiguous discrimination of arbitrary quantum
processes. This bound is saturated (in a certain range of apriori
probabilities) in the case of unambiguous discrimination of unitary channels.
Surprisingly, the optimal solution for both tasks is based on the optimization
of the same quantity called completely bounded process fidelity.Comment: 11 pages, 1 figur
Single-shot discrimination of quantum unitary processes
We formulate minimum-error and unambiguous discrimination problems for
quantum processes in the language of process positive operator valued measures
(PPOVM). In this framework we present the known solution for minimum-error
discrimination of unitary channels. We derive a "fidelity-like" lower bound on
the failure probability of the unambiguous discrimination of arbitrary quantum
processes. This bound is saturated (in a certain range of apriori
probabilities) in the case of unambiguous discrimination of unitary channels.
Surprisingly, the optimal solution for both tasks is based on the optimization
of the same quantity called completely bounded process fidelity.Comment: 11 pages, 1 figur
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