60,401 research outputs found
An introduction to operational quantum dynamics
In the summer of 2016, physicists gathered in Torun, Poland for the 48th
annual Symposium on Mathematical Physics. This Symposium was special; it
celebrated the 40th anniversary of the discovery of the
Gorini-Kossakowski-Sudarshan-Lindblad master equation, which is widely used in
quantum physics and quantum chemistry. This article forms part of a Special
Volume of the journal Open Systems & Information Dynamics arising from that
conference; and it aims to celebrate a related discovery -- also by Sudarshan
-- that of Quantum Maps (which had their 55th anniversary in the same year).
Nowadays, much like the master equation, quantum maps are ubiquitous in physics
and chemistry. Their importance in quantum information and related fields
cannot be overstated. In this manuscript, we motivate quantum maps from a
tomographic perspective, and derive their well-known representations. We then
dive into the murky world beyond these maps, where recent research has yielded
their generalisation to non-Markovian quantum processes.Comment: Submitted to Special OSID volume "40 years of GKLS
A pedagogical overview of quantum discord
Recent measures of nonclassical correlations are motivated by different
notions of classicality and operational means. Quantum discord has received a
great deal of attention in studies involving quantum computation, metrology,
dynamics, many-body physics, and thermodynamics. In this article I show how
quantum discord is different from quantum entanglement from a pedagogical point
of view. I begin with a pedagogical introduction to quantum entanglement and
quantum discord, followed by a historical review of quantum discord. Next, I
give a novel definition of quantum discord in terms of any classically
extractable information, a approach that is fitting for the current avenues of
research. Lastly, I put forth several arguments for why discord is an
interesting quantity to study and why it is of interest to so many researchers
in the community.Comment: 17 pages, 6 figures, to appear in special OSID volume of on open
system
Density-operator evolution: Complete positivity and the Keldysh real-time expansion
We study the reduced time-evolution of open quantum systems by combining
quantum-information and statistical field theory. Inspired by prior work [EPL
102, 60001 (2013) and Phys. Rev. Lett. 111, 050402 (2013)] we establish the
explicit structure guaranteeing the complete positivity (CP) and
trace-preservation (TP) of the real-time evolution expansion in terms of the
microscopic system-environment coupling.
This reveals a fundamental two-stage structure of the coupling expansion:
Whereas the first stage defines the dissipative timescales of the system
--before having integrated out the environment completely-- the second stage
sums up elementary physical processes described by CP superoperators. This
allows us to establish the nontrivial relation between the (Nakajima-Zwanzig)
memory-kernel superoperator for the density operator and novel memory-kernel
operators that generate the Kraus operators of an operator-sum. Importantly,
this operational approach can be implemented in the existing Keldysh real-time
technique and allows approximations for general time-nonlocal quantum master
equations to be systematically compared and developed while keeping the CP and
TP structure explicit.
Our considerations build on the result that a Kraus operator for a physical
measurement process on the environment can be obtained by 'cutting' a group of
Keldysh real-time diagrams 'in half'. This naturally leads to Kraus operators
lifted to the system plus environment which have a diagrammatic expansion in
terms of time-nonlocal memory-kernel operators. These lifted Kraus operators
obey coupled time-evolution equations which constitute an unraveling of the
original Schr\"odinger equation for system plus environment. Whereas both
equations lead to the same reduced dynamics, only the former explicitly encodes
the operator-sum structure of the coupling expansion.Comment: Submission to SciPost Physics, 49 pages including 6 appendices, 13
figures. Significant improvement of introduction and conclusion, added
discussions, fixed typos, no results change
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