10,248 research outputs found
Quantum Discord, Decoherence and Quantum Phase Transitions
Quantum discord is a more general measure of quantum correlations than
entanglement and has been proposed as a resource in certain quantum information
processing tasks. The computation of discord is mostly confined to two-qubit
systems for which an analytical calculational scheme is available. The
utilization of quantum correlations in quantum information-based applications
is limited by the problem of decoherence, i.e., the loss of coherence due to
the inevitable interaction of a quantum system with its environment. The
dynamics of quantum correlations due to decoherence may be studied in the Kraus
operator formalism for different types of quantum channels representing
system-environment interactions. In this review, we describe the salient
features of the dynamics of classical and quantum correlations in a two-qubit
system under Markovian (memoryless) time evolution. The two-qubit state
considered is described by the reduced density matrix obtained from the ground
state of a spin model. The models considered include the transverse-field XY
model in one dimension, a special case of which is the transverse-field Ising
model, and the spin chain. The quantum channels studied include the
amplitude damping, bit-flip, bit-phase-flip and phase-flip channels. The Kraus
operator formalism is briefly introduced and the origins of different types of
dynamics discussed. One can identify appropriate quantities associated with the
dynamics of quantum correlations which provide signatures of quantum phase
transitions in the spin models. Experimental observations of the different
types of dynamics are also mentioned.Comment: 20 pages, 6 figures, To appear in Int. J. Mod. Phys. B, special issue
"Classical Vs Quantum correlations in composite systems" edited by L. Amico,
S. Bose, V. Korepin and V. Vedra
Non-Markovianity and Quantum Correlations in Qubit-Systems
In this Thesis I discuss the exact dynamics of simple non-Markovian systems. I focus on fundamental questions at the core of non-Markovian theory and investigate the dynamics of quantum correlations under non-Markovian decoherence.
In the first context I present the connection between two different non-Markovian approaches, and compare two distinct definitions of non-Markovianity. The general aim is to characterize in exemplary cases which part of the environment is responsible for the feedback of information typical of non- Markovian dynamics. I also show how such a feedback of information is not always described by certain types of master equations commonly used to tackle non-Markovian dynamics.
In the second context I characterize the dynamics of two qubits in a common non-Markovian reservoir, and introduce a new dynamical effect in a wellknown model, i.e., two qubits under depolarizing channels. In the first model the exact solution of the dynamics is found, and the entanglement behavior is extensively studied. The non-Markovianity of the reservoir and reservoirmediated-interaction between the qubits cause non-trivial dynamical features.
The dynamical interplay between different types of correlations is also investigated. In the second model the study of quantum and classical correlations demonstrates the existence of a new effect: the sudden transition between classical and quantum decoherence. This phenomenon involves the complete preservation of the initial quantum correlations for long intervals of time of the order of the relaxation time of the system.Siirretty Doriast
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
Frozen and Invariant Quantum Discord under Local Dephasing Noise
In this chapter, we intend to explore and review some remarkable dynamical
properties of quantum discord under various different open quantum system
models. Specifically, our discussion will include several concepts connected to
the phenomena of time invariant and frozen quantum discord. Furthermore, we
will elaborate on the relation of these two phenomena to the non-Markovian
features of the open system dynamics and to the usage of dynamical decoupling
protocols.Comment: 29 pages, 8 figure
The rise and fall of quantum and classical correlations in open-system dynamics
Interacting quantum systems evolving from an uncorrelated composite initial
state generically develop quantum correlations -- entanglement. As a
consequence, a local description of interacting quantum system is impossible as
a rule. A unitarily evolving (isolated) quantum system generically develops
extensive entanglement: the magnitude of the generated entanglement will
increase without bounds with the effective Hilbert space dimension of the
system. It is conceivable, that coupling of the interacting subsystems to local
dephasing environments will restrict the generation of entanglement to such
extent, that the evolving composite system may be considered as approximately
disentangled. This conjecture is addressed in the context of some common models
of a bipartite system with linear and nonlinear interactions and local coupling
to dephasing environments. Analytical and numerical results obtained imply that
the conjecture is generally false. Open dynamics of the quantum correlations is
compared to the corresponding evolution of the classical correlations and a
qualitative difference is found.Comment: 35 pages, 10 figures. Revised according to comments of the referees.
Accepted for publication in Phys. Rev.
Non-Markovian dynamics in open quantum systems
The dynamical behavior of open quantum systems plays a key role in many
applications of quantum mechanics, examples ranging from fundamental problems,
such as the environment-induced decay of quantum coherence and relaxation in
many-body systems, to applications in condensed matter theory, quantum
transport, quantum chemistry and quantum information. In close analogy to a
classical Markov process, the interaction of an open quantum system with a
noisy environment is often modelled by a dynamical semigroup with a generator
in Lindblad form, which describes a memoryless dynamics leading to an
irreversible loss of characteristic quantum features. However, in many
applications open systems exhibit pronounced memory effects and a revival of
genuine quantum properties such as quantum coherence and correlations. Here,
recent results on the rich non-Markovian quantum dynamics of open systems are
discussed, paying particular attention to the rigorous mathematical definition,
to the physical interpretation and classification, as well as to the
quantification of memory effects. The general theory is illustrated by a series
of examples. The analysis reveals that memory effects of the open system
dynamics reflect characteristic features of the environment which opens a new
perspective for applications, namely to exploit a small open system as a
quantum probe signifying nontrivial features of the environment it is
interacting with. This article further explores the various physical sources of
non-Markovian quantum dynamics, such as structured spectral densities, nonlocal
correlations between environmental degrees of freedom and correlations in the
initial system-environment state, in addition to developing schemes for their
local detection. Recent experiments on the detection, quantification and
control of non-Markovian quantum dynamics are also discussed.Comment: 26 pages, 10 figure
The relation between the quantum discord and quantum teleportation: the physical interpretation of the transition point between different quantum discord decay regimes
We study quantum teleportation via Bell-diagonal mixed states of two qubits
in the context of the intrinsic properties of the quantum discord. We show that
when the quantum-correlated state of the two qubits is used for quantum
teleportation the character of the teleportation efficiency changes
substantially depending on the Bell-diagonal-state parameters, which can be
seen when the worst-case-scenario or best-case-scenario fidelity is studied.
Depending on the parameter range, one of two types of single qubit states is
hardest/easiest to teleport. The transition between these two parameter ranges
coincides exactly with the transition between the range of classical
correlation decay and quantum correlation decay characteristic for the
evolution of the quantum discord. The correspondence provides a physical
interpretation for the prominent feature of the decay of the quantum discord.Comment: 6 page
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