67 research outputs found
Subjective probability and quantum certainty
In the Bayesian approach to quantum mechanics, probabilities--and thus
quantum states--represent an agent's degrees of belief, rather than
corresponding to objective properties of physical systems. In this paper we
investigate the concept of certainty in quantum mechanics. Particularly, we
show how the probability-1 predictions derived from pure quantum states
highlight a fundamental difference between our Bayesian approach, on the one
hand, and Copenhagen and similar interpretations on the other. We first review
the main arguments for the general claim that probabilities always represent
degrees of belief. We then argue that a quantum state prepared by some physical
device always depends on an agent's prior beliefs, implying that the
probability-1 predictions derived from that state also depend on the agent's
prior beliefs. Quantum certainty is therefore always some agent's certainty.
Conversely, if facts about an experimental setup could imply agent-independent
certainty for a measurement outcome, as in many Copenhagen-like
interpretations, that outcome would effectively correspond to a preexisting
system property. The idea that measurement outcomes occurring with certainty
correspond to preexisting system properties is, however, in conflict with
locality. We emphasize this by giving a version of an argument of Stairs [A.
Stairs, Phil. Sci. 50, 578 (1983)], which applies the Kochen-Specker theorem to
an entangled bipartite system.Comment: 20 pages RevTeX, 1 figure, extensive changes in response to referees'
comment
Unknown Quantum States: The Quantum de Finetti Representation
We present an elementary proof of the quantum de Finetti representation
theorem, a quantum analogue of de Finetti's classical theorem on exchangeable
probability assignments. This contrasts with the original proof of Hudson and
Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies on advanced
mathematics and does not share the same potential for generalization. The
classical de Finetti theorem provides an operational definition of the concept
of an unknown probability in Bayesian probability theory, where probabilities
are taken to be degrees of belief instead of objective states of nature. The
quantum de Finetti theorem, in a closely analogous fashion, deals with
exchangeable density-operator assignments and provides an operational
definition of the concept of an ``unknown quantum state'' in quantum-state
tomography. This result is especially important for information-based
interpretations of quantum mechanics, where quantum states, like probabilities,
are taken to be states of knowledge rather than states of nature. We further
demonstrate that the theorem fails for real Hilbert spaces and discuss the
significance of this point.Comment: 30 pages, 2 figure
Bayesian Conditioning, the Reflection Principle, and Quantum Decoherence
The probabilities a Bayesian agent assigns to a set of events typically
change with time, for instance when the agent updates them in the light of new
data. In this paper we address the question of how an agent's probabilities at
different times are constrained by Dutch-book coherence. We review and attempt
to clarify the argument that, although an agent is not forced by coherence to
use the usual Bayesian conditioning rule to update his probabilities, coherence
does require the agent's probabilities to satisfy van Fraassen's [1984]
reflection principle (which entails a related constraint pointed out by
Goldstein [1983]). We then exhibit the specialized assumption needed to recover
Bayesian conditioning from an analogous reflection-style consideration.
Bringing the argument to the context of quantum measurement theory, we show
that "quantum decoherence" can be understood in purely personalist
terms---quantum decoherence (as supposed in a von Neumann chain) is not a
physical process at all, but an application of the reflection principle. From
this point of view, the decoherence theory of Zeh, Zurek, and others as a story
of quantum measurement has the plot turned exactly backward.Comment: 14 pages, written in memory of Itamar Pitowsk
North Carolina Law Enforcement Assisted Diversion (LEAD): Considerations For Optimizing Eligibility and Referral
Facts, Values and Quanta
Quantum mechanics is a fundamentally probabilistic theory (at least so far as
the empirical predictions are concerned). It follows that, if one wants to
properly understand quantum mechanics, it is essential to clearly understand
the meaning of probability statements. The interpretation of probability has
excited nearly as much philosophical controversy as the interpretation of
quantum mechanics. 20th century physicists have mostly adopted a frequentist
conception. In this paper it is argued that we ought, instead, to adopt a
logical or Bayesian conception. The paper includes a comparison of the orthodox
and Bayesian theories of statistical inference. It concludes with a few remarks
concerning the implications for the concept of physical reality.Comment: 30 pages, AMS Late
Electromagnetic channel capacity for practical purposes
We give analytic upper bounds to the channel capacity C for transmission of
classical information in electromagnetic channels (bosonic channels with
thermal noise). In the practically relevant regimes of high noise and low
transmissivity, by comparison with know lower bounds on C, our inequalities
determine the value of the capacity up to corrections which are irrelevant for
all practical purposes. Examples of such channels are radio communication,
infrared or visible-wavelength free space channels. We also provide bounds to
active channels that include amplification.Comment: 6 pages, 3 figures. NB: the capacity bounds are constructed by
generalizing to the multi-mode case the minimum-output entropy bounds of
arXiv:quant-ph/0404005 [Phys. Rev. A 70, 032315 (2004)
Market competition, earnings management, and persistence in accounting profitability around the world
Deformation Responses of a Physically Cross-Linked High Molecular Weight Elastin-Like Protein Polymer
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