63,171 research outputs found
Born in an Infinite Universe: a Cosmological Interpretation of Quantum Mechanics
We study the quantum measurement problem in the context of an infinite,
statistically uniform space, as could be generated by eternal inflation. It has
recently been argued that when identical copies of a quantum measurement system
exist, the standard projection operators and Born rule method for calculating
probabilities must be supplemented by estimates of relative frequencies of
observers. We argue that an infinite space actually renders the Born rule
redundant, by physically realizing all outcomes of a quantum measurement in
different regions, with relative frequencies given by the square of the wave
function amplitudes. Our formal argument hinges on properties of what we term
the quantum confusion operator, which projects onto the Hilbert subspace where
the Born rule fails, and we comment on its relation to the oft-discussed
quantum frequency operator. This analysis unifies the classical and quantum
levels of parallel universes that have been discussed in the literature, and
has implications for several issues in quantum measurement theory. It also
shows how, even for a single measurement, probabilities may be interpreted as
relative frequencies in unitary (Everettian) quantum mechanics. We also argue
that after discarding a zero-norm part of the wavefunction, the remainder
consists of a superposition of indistinguishable terms, so that arguably
"collapse" of the wavefunction is irrelevant, and the "many worlds" of
Everett's interpretation are unified into one. Finally, the analysis suggests a
"cosmological interpretation" of quantum theory in which the wave function
describes the actual spatial collection of identical quantum systems, and
quantum uncertainty is attributable to the observer's inability to self-locate
in this collection.Comment: 17 pages, 2 figures; revised version to match published version,
including authorship change. Abstract is abridge
A simple proof of Born’s rule for statistical interpretation of quantum mechanics
The Born’s rule to interpret the square of wave function as the probability to get a specific value in measurement has been accepted as a postulate in foundations of quantum mechanics. Although there have been so many attempts at deriving this rule theoretically using different approaches such as frequency operator approach, many-world theory, Bayesian probability and envariance, literature shows that arguments in each of these methods are circular. In view of absence of a convincing theoretical proof, recently some researchers have carried out experiments to validate the rule up-to maximum possible accuracy using multi-order interference (Sinha et al, Science, 329, 418 [2010]). But, a convincing analytical proof of Born’s rule will make us understand the basic process responsible for exact square dependency of probability on wave function. In this paper, by generalizing the method of calculating probability in common experience into quantum mechanics, we prove the Born’s rule for statistical interpretation of wave function
Securing coherence rephasing with a pair of adiabatic rapid passages
Coherence rephasing is an essential step in quantum storage protocols that
use echo-based strategies. We present a thorough analysis on how two adiabatic
rapid passages (ARP) are able to rephase atomic coherences in an
inhomogeneously broadened ensemble. We consider both the cases of optical and
spin coherences, rephased by optical or radio-frequency (rf) ARPs,
respectively. We show how a rephasing sequence consisting of two ARPs in a
double-echo scheme is equivalent to the identity operator (any state can be
recovered), as long as certain conditions are fulfilled. Our mathematical
treatment of the ARPs leads to a very simple geometrical interpretation within
the Bloch sphere that permits a visual comprehension of the rephasing process.
We also identify the conditions that ensure the rephasing, finding that the
phase of the optical or rf ARP fields plays a key role in the capability of the
sequence to preserve the phase of the superposition state. This settles a
difference between optical and rf ARPs, since field phase control is not
readily guaranteed in the former case. We also provide a quantitative
comparison between -pulse and ARP rephasing efficiencies, showing the
superiority of the latter. We experimentally verify the conclusions of our
analysis through rf ARP rephasing sequencies performed on the rare-earth
ion-doped crystal Tm:YAG, of interest in quantum memories.Comment: 24 pages, 7 figure
Quantum mechanics: Myths and facts
A common understanding of quantum mechanics (QM) among students and practical
users is often plagued by a number of "myths", that is, widely accepted claims
on which there is not really a general consensus among experts in foundations
of QM. These myths include wave-particle duality, time-energy uncertainty
relation, fundamental randomness, the absence of measurement-independent
reality, locality of QM, nonlocality of QM, the existence of well-defined
relativistic QM, the claims that quantum field theory (QFT) solves the problems
of relativistic QM or that QFT is a theory of particles, as well as myths on
black-hole entropy. The fact is that the existence of various theoretical and
interpretational ambiguities underlying these myths does not yet allow us to
accept them as proven facts. I review the main arguments and counterarguments
lying behind these myths and conclude that QM is still a
not-yet-completely-understood theory open to further fundamental research.Comment: 51 pages, pedagogic review, revised, new references, to appear in
Found. Phy
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