136,689 research outputs found
Distance measures to compare real and ideal quantum processes
With growing success in experimental implementations it is critical to
identify a "gold standard" for quantum information processing, a single measure
of distance that can be used to compare and contrast different experiments. We
enumerate a set of criteria such a distance measure must satisfy to be both
experimentally and theoretically meaningful. We then assess a wide range of
possible measures against these criteria, before making a recommendation as to
the best measures to use in characterizing quantum information processing.Comment: 15 pages; this version in line with published versio
Compression of quantum measurement operations
We generalize recent work of Massar and Popescu dealing with the amount of
classical data that is produced by a quantum measurement on a quantum state
ensemble. In the previous work it was shown how spurious randomness generally
contained in the outcomes can be eliminated without decreasing the amount of
knowledge, to achieve an amount of data equal to the von Neumann entropy of the
ensemble. Here we extend this result by giving a more refined description of
what constitute equivalent measurements (that is measurements which provide the
same knowledge about the quantum state) and also by considering incomplete
measurements. In particular we show that one can always associate to a POVM
with elements a_j, an equivalent POVM acting on many independent copies of the
system which produces an amount of data asymptotically equal to the entropy
defect of an ensemble canonically associated to the ensemble average state and
the initial measurement (a_j). In the case where the measurement is not
maximally refined this amount of data is strictly less than the von Neumann
entropy, as obtained in the previous work. We also show that this is the best
achievable, i.e. it is impossible to devise a measurement equivalent to the
initial measurement (a_j) that produces less data. We discuss the
interpretation of these results. In particular we show how they can be used to
provide a precise and model independent measure of the amount of knowledge that
is obtained about a quantum state by a quantum measurement. We also discuss in
detail the relation between our results and Holevo's bound, at the same time
providing a new proof of this fundamental inequality.Comment: RevTeX, 13 page
Kak's three-stage protocol of secure quantum communication revisited: Hitherto unknown strengths and weaknesses of the protocol
Kak's three-stage protocol for quantum key distribution is revisited with
special focus on its hitherto unknown strengths and weaknesses. It is shown
that this protocol can be used for secure direct quantum communication.
Further, the implementability of this protocol in the realistic situation is
analyzed by considering various Markovian noise models. It is found that the
Kak's protocol and its variants in their original form can be implemented only
in a restricted class of noisy channels, where the protocols can be transformed
to corresponding protocols based on logical qubits in decoherence free
subspace. Specifically, it is observed that Kak's protocol can be implemented
in the presence of collective rotation and collective dephasing noise, but
cannot be implemented in its original form in the presence of other types of
noise, like amplitude damping and phase damping noise. Further, the performance
of the protocol in the noisy environment is quantified by computing average
fidelity under various noise models, and subsequently a set of preferred states
for secure communication in noisy environment have also been identified.Comment: Kak's protocol is not suitable for quantum cryptography in presence
of nois
Purification-based metric to measure the distance between quantum states and processes
In this work we study the properties of an purification-based entropic metric
for measuring the distance between both quantum states and quantum processes.
This metric is defined as the square root of the entropy of the average of two
purifications of mixed quantum states which maximize the overlap between the
purified states. We analyze this metric and show that it satisfies many
appealing properties, which suggest this metric is an interesting proposal for
theoretical and experimental applications of quantum information.Comment: 11 pages, 2 figures. arXiv admin note: text overlap with
arXiv:quant-ph/0408063, arXiv:1107.1732 by other author
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