100 research outputs found
Tomographically reconstructed master equations for any open quantum dynamics
Memory effects in open quantum dynamics are often incorporated in the
equation of motion through a superoperator known as the memory kernel, which
encodes how past states affect future dynamics. However, the usual prescription
for determining the memory kernel requires information about the underlying
system-environment dynamics. Here, by deriving the transfer tensor method from
first principles, we show how a memory kernel master equation, for any quantum
process, can be entirely expressed in terms of a family of completely positive
dynamical maps. These can be reconstructed through quantum process tomography
on the system alone, either experimentally or numerically, and the resulting
equation of motion is equivalent to a generalised Nakajima-Zwanzig equation.
For experimental settings, we give a full prescription for the reconstruction
procedure, rendering the memory kernel operational. When simulation of an open
system is the goal, we show how our procedure yields a considerable advantage
for numerically calculating dynamics, even when the system is arbitrarily
periodically (or transiently) driven or initially correlated with its
environment. Namely, we show that the long time dynamics can be efficiently
obtained from a set of reconstructed maps over a much shorter time.Comment: 10+4 pages, 5 figure
Tightening Quantum Speed Limits for Almost All States
Conventional quantum speed limits perform poorly for mixed quantum states:
They are generally not tight and often significantly underestimate the fastest
possible evolution speed. To remedy this, for unitary driving, we derive two
quantum speed limits that outperform the traditional bounds for almost all
quantum states. Moreover, our bounds are significantly simpler to compute as
well as experimentally more accessible. Our bounds have a clear geometric
interpretation; they arise from the evaluation of the angle between generalized
Bloch vectors.Comment: Updated and revised version; 5 pages, 2 figures, 1 page appendi
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
Non-Markovian memory in IBMQX4
We measure and quantify non-Markovian effects in IBM's Quantum Experience.
Specifically, we analyze the temporal correlations in a sequence of gates by
characterizing the performance of a gate conditioned on the gate that preceded
it. With this method, we estimate (i) the size of fluctuations in the
performance of a gate, i.e., errors due to non-Markovianity; (ii) the length of
the memory; and (iii) the total size of the memory. Our results strongly
indicate the presence of non-trivial non-Markovian effects in almost all gates
in the universal set. However, based on our findings, we discuss the potential
for cleaner computation by adequately accounting the non-Markovian nature of
the machine.Comment: 8 page
Tight, robust, and feasible quantum speed limits for open dynamics
Starting from a geometric perspective, we derive a quantum speed limit for
arbitrary open quantum evolution, which could be Markovian or non-Markovian,
providing a fundamental bound on the time taken for the most general quantum
dynamics. Our methods rely on measuring angles and distances between (mixed)
states represented as generalized Bloch vectors. We study the properties of our
bound and present its form for closed and open evolution, with the latter in
both Lindblad form and in terms of a memory kernel. Our speed limit is provably
robust under composition and mixing, features that largely improve the
effectiveness of quantum speed limits for open evolution of mixed states. We
also demonstrate that our bound is easier to compute and measure than other
quantum speed limits for open evolution, and that it is tighter than the
previous bounds for almost all open processes. Finally, we discuss the
usefulness of quantum speed limits and their impact in current research.Comment: Main: 11 pages, 3 figures. Appendix: 2 pages, 1 figur
Entanglement, non-Markovianity, and causal non-separability
Quantum mechanics, in principle, allows for processes with indefinite causal
order. However, most of these causal anomalies have not yet been detected
experimentally. We show that every such process can be simulated experimentally
by means of non-Markovian dynamics with a measurement on additional degrees of
freedom. Explicitly, we provide a constructive scheme to implement arbitrary
acausal processes. Furthermore, we give necessary and sufficient conditions for
open system dynamics with measurement to yield processes that respect causality
locally, and find that tripartite entanglement and nonlocal unitary
transformations are crucial requirements for the simulation of causally
indefinite processes. These results show a direct connection between three
counter-intuitive concepts: non-Markovianity, entanglement, and causal
indefiniteness.Comment: 14 pages, 8 figure
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