891 research outputs found
Kraus representation of quantum evolution and fidelity as manifestations of Markovian and non-Markovian avataras
It is shown that the fidelity of the dynamically evolved system with its
earlier time density matrix provides a signature of non-Markovian dynamics.
Also, the fidelity associated with the initial state and the dynamically
evolved state is shown to be larger in the non-Markovian evolution compared to
that in the corresponding Markovian case. Starting from the Kraus
representation of quantum evolution, the Markovian and non-Markovian features
are discerned in its short time structure. These two features are in
concordance with each other and they are illustrated with the help of four
models of interaction of the system with its environment.Comment: 7 pages, 5 eps figures; Discussion on recent characterizations of
non-Markovianity included in this versio
Interplay of quantum stochastic and dynamical maps to discern Markovian and non-Markovian transitions
It is known that the dynamical evolution of a system, from an initial tensor
product state of system and environment, to any two later times, t1,t2 (t2>t1),
are both completely positive (CP) but in the intermediate times between t1 and
t2 it need not be CP. This reveals the key to the Markov (if CP) and nonMarkov
(if it is not CP) avataras of the intermediate dynamics. This is brought out
here in terms of the quantum stochastic map A and the associated dynamical map
B -- without resorting to master equation approaches. We investigate these
features with four examples which have entirely different physical origins (i)
a two qubit Werner state map with time dependent noise parameter (ii)
Phenomenological model of a recent optical experiment (Nature Physics, 7, 931
(2011)) on the open system evolution of photon polarization. (iii) Hamiltonian
dynamics of a qubit coupled to a bath of qubits and (iv) two qubit unitary
dynamics of Jordan et. al. (Phys. Rev. A 70, 052110 (2004)) with initial
product states of qubits. In all these models, it is shown that the
positivity/negativity of the eigenvalues of intermediate time dynamical B map
determines the Markov/non-Markov nature of the dynamics.Comment: 6 pages, 5 figures, considerably extended version of arXiv:1104.456
Aspects of the Second Law of Thermodynamics from Quantum Statistical Mechanics to Quantum Information Theory
The Kullback-Leibler inequality is a way of comparing any two density
matrices. A technique to set up the density matrix for a physical system is to
use the maximum entropy principle, given the entropy as a functional of the
density matrix, subject to known constraints. In conjunction with the master
equation for the density matrix, these two ingredients allow us to formulate
the second law of thermodynamics in its widest possible setting. Thus problems
arising in both quantum statistical mechanics and quantum information can be
handled. Aspects of thermodynamic concepts such as the Carnot cycle will be
discussed. A model is examined to elucidate the role of entanglement in the
Landauer erasure problem.Comment: 6 page
Two Qubits in the Dirac Representation
A general two qubit system expressed in terms of the complete set of unit and
fifteen traceless, Hermitian Dirac matrices, is shown to exhibit novel features
of this system. The well-known physical interpretations associated with the
relativistic Dirac equation involving the symmetry operations of time-reversal
T, charge conjugation C, parity P, and their products are reinterpreted here by
examining their action on the basic Bell states. The transformation properties
of the Bell basis states under these symmetry operations also reveal that C is
the only operator that does not mix the Bell states whereas all others do. In a
similar fashion, expressing the various logic gates introduced in the subject
of quantum computers in terms of the Dirac matrices shows for example, that the
NOT gate is related to the product of time-reversal and parity operators.Comment: 11 page
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