52,867 research outputs found
Quantum Kolmogorov Complexity Based on Classical Descriptions
We develop a theory of the algorithmic information in bits contained in an
individual pure quantum state. This extends classical Kolmogorov complexity to
the quantum domain retaining classical descriptions. Quantum Kolmogorov
complexity coincides with the classical Kolmogorov complexity on the classical
domain. Quantum Kolmogorov complexity is upper bounded and can be effectively
approximated from above under certain conditions. With high probability a
quantum object is incompressible. Upper- and lower bounds of the quantum
complexity of multiple copies of individual pure quantum states are derived and
may shed some light on the no-cloning properties of quantum states. In the
quantum situation complexity is not sub-additive. We discuss some relations
with ``no-cloning'' and ``approximate cloning'' properties.Comment: 17 pages, LaTeX, final and extended version of quant-ph/9907035, with
corrections to the published journal version (the two displayed equations in
the right-hand column on page 2466 had the left-hand sides of the displayed
formulas erroneously interchanged
How Events Come Into Being: EEQT, Particle Tracks, Quantum Chaos, and Tunneling Time
In sections 1 and 2 we review Event Enhanced Quantum Theory (EEQT). In
section 3 we discuss applications of EEQT to tunneling time, and compare its
quantitative predictions with other approaches, in particular with
B\"uttiker-Larmor and Bohm trajectory approach. In section 4 we discuss quantum
chaos and quantum fractals resulting from simultaneous continuous monitoring of
several non-commuting observables. In particular we show self-similar,
non-linear, iterated function system-type, patterns arising from quantum jumps
and from the associated Markov operator. Concluding remarks pointing to
possible future development of EEQT are given in section 5.Comment: latex, 27 pages, 7 postscript figures. Paper submitted to Proc.
Conference "Mysteries, Puzzles And Paradoxes In Quantum Mechanics, Workshop
on Entanglement And Decoherence, Palazzo Feltrinelli, Gargnano, Garda Lake,
Italy, 20-25 September, 199
Taking Heisenberg's Potentia Seriously
It is argued that quantum theory is best understood as requiring an
ontological duality of res extensa and res potentia, where the latter is
understood per Heisenberg's original proposal, and the former is roughly
equivalent to Descartes' 'extended substance.' However, this is not a dualism
of mutually exclusive substances in the classical Cartesian sense, and
therefore does not inherit the infamous 'mind-body' problem. Rather, res
potentia and res extensa are proposed as mutually implicative ontological
extants that serve to explain the key conceptual challenges of quantum theory;
in particular, nonlocality, entanglement, null measurements, and wave function
collapse. It is shown that a natural account of these quantum perplexities
emerges, along with a need to reassess our usual ontological commitments
involving the nature of space and time.Comment: Final version, to appear in International Journal of Quantum
Foundation
Quantitative Treatment of Decoherence
We outline different approaches to define and quantify decoherence. We argue
that a measure based on a properly defined norm of deviation of the density
matrix is appropriate for quantifying decoherence in quantum registers. For a
semiconductor double quantum dot qubit, evaluation of this measure is reviewed.
For a general class of decoherence processes, including those occurring in
semiconductor qubits, we argue that this measure is additive: It scales
linearly with the number of qubits.Comment: Revised version, 26 pages, in LaTeX, 3 EPS figure
A framework for bounding nonlocality of state discrimination
We consider the class of protocols that can be implemented by local quantum
operations and classical communication (LOCC) between two parties. In
particular, we focus on the task of discriminating a known set of quantum
states by LOCC. Building on the work in the paper "Quantum nonlocality without
entanglement" [BDF+99], we provide a framework for bounding the amount of
nonlocality in a given set of bipartite quantum states in terms of a lower
bound on the probability of error in any LOCC discrimination protocol. We apply
our framework to an orthonormal product basis known as the domino states and
obtain an alternative and simplified proof that quantifies its nonlocality. We
generalize this result for similar bases in larger dimensions, as well as the
"rotated" domino states, resolving a long-standing open question [BDF+99].Comment: 33 pages, 7 figures, 1 tabl
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