873 research outputs found
Quantum cryptography over non-Markovian channels
A set of schemes for secure quantum communication are analyzed under the
influence of non-Markovian channels. By comparing with the corresponding
Markovian cases, it is seen that the average fidelity in all these schemes can
be maintained for relatively longer periods of time. The effects of
non-Markovian noise on a number of facets of quantum cryptography, such as
quantum secure direct communication, deterministic secure quantum communication
and their controlled counterparts, quantum dialogue, quantum key distribution,
quantum key agreement, etc., have been extensively investigated. Specifically,
a scheme for controlled quantum dialogue (CQD) is analyzed over damping,
dephasing and depolarizing non-Markovian channels, and subsequently, the effect
of these non-Markovian channels on the other schemes of secure quantum
communication is deduced from the results obtained for CQD. The damped
non-Markovian channel causes, a periodic revival in the fidelity; while
fidelity is observed to be sustained under the influence of the dephasing
non-Markovian channel. The depolarizing channel, as well as the other
non-Markovian channels discussed here, show that the obtained average fidelity
subjected to noisy environment depends on the strength of coupling between the
quantum system with its surroundings and the number of rounds of quantum
communication involved in a particular scheme.Comment: 11 pages, 6 figure
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
Finite-Block-Length Analysis in Classical and Quantum Information Theory
Coding technology is used in several information processing tasks. In
particular, when noise during transmission disturbs communications, coding
technology is employed to protect the information. However, there are two types
of coding technology: coding in classical information theory and coding in
quantum information theory. Although the physical media used to transmit
information ultimately obey quantum mechanics, we need to choose the type of
coding depending on the kind of information device, classical or quantum, that
is being used. In both branches of information theory, there are many elegant
theoretical results under the ideal assumption that an infinitely large system
is available. In a realistic situation, we need to account for finite size
effects. The present paper reviews finite size effects in classical and quantum
information theory with respect to various topics, including applied aspects
The sudden change phenomenon of quantum discord
Even if the parameters determining a system's state are varied smoothly, the
behavior of quantum correlations alike to quantum discord, and of its classical
counterparts, can be very peculiar, with the appearance of non-analyticities in
its rate of change. Here we review this sudden change phenomenon (SCP)
discussing some important points related to it: Its uncovering,
interpretations, and experimental verifications, its use in the context of the
emergence of the pointer basis in a quantum measurement process, its appearance
and universality under Markovian and non-Markovian dynamics, its theoretical
and experimental investigation in some other physical scenarios, and the
related phenomenon of double sudden change of trace distance discord. Several
open questions are identified, and we envisage that in answering them we will
gain significant further insight about the relation between the SCP and the
symmetry-geometric aspects of the quantum state space.Comment: Lectures on General Quantum Correlations and their Applications, F.
F. Fanchini, D. O. Soares Pinto, and G. Adesso (Eds.), Springer (2017), pp
309-33
Non-Markovianity of Gaussian Channels
We introduce a necessary and sufficient criterion for the non-Markovianity of
Gaussian quantum dynamical maps based on the violation of divisibility. The
criterion is derived by defining a general vectorial representation of the
covariance matrix which is then exploited to determine the condition for the
complete positivity of partial maps associated to arbitrary time intervals.
Such construction does not rely on the Choi-Jamiolkowski representation and
does not require optimization over states.Comment: 5 pages, 1 figure. Published versio
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