1,844 research outputs found
Deriving the Qubit from Entropy Principles
The Heisenberg uncertainty principle is one of the most famous features of
quantum mechanics. However, the non-determinism implied by the Heisenberg
uncertainty principle --- together with other prominent aspects of quantum
mechanics such as superposition, entanglement, and nonlocality --- poses deep
puzzles about the underlying physical reality, even while these same features
are at the heart of exciting developments such as quantum cryptography,
algorithms, and computing. These puzzles might be resolved if the mathematical
structure of quantum mechanics were built up from physically interpretable
axioms, but it is not. We propose three physically-based axioms which together
characterize the simplest quantum system, namely the qubit. Our starting point
is the class of all no-signaling theories. Each such theory can be regarded as
a family of empirical models, and we proceed to associate entropies, i.e.,
measures of information, with these models. To do this, we move to phase space
and impose the condition that entropies are real-valued. This requirement,
which we call the Information Reality Principle, arises because in order to
represent all no-signaling theories (including quantum mechanics itself) in
phase space, it is necessary to allow negative probabilities (Wigner [1932]).
Our second and third principles take two important features of quantum
mechanics and turn them into deliberately chosen physical axioms. One axiom is
an Uncertainty Principle, stated in terms of entropy. The other axiom is an
Unbiasedness Principle, which requires that whenever there is complete
certainty about the outcome of a measurement in one of three mutually
orthogonal directions, there must be maximal uncertainty about the outcomes in
each of the two other directions.Comment: 8 pages, 3 figure
Team Decision Problems with Classical and Quantum Signals
We study team decision problems where communication is not possible, but
coordination among team members can be realized via signals in a shared
environment. We consider a variety of decision problems that differ in what
team members know about one another's actions and knowledge. For each type of
decision problem, we investigate how different assumptions on the available
signals affect team performance. Specifically, we consider the cases of
perfectly correlated, i.i.d., and exchangeable classical signals, as well as
the case of quantum signals. We find that, whereas in perfect-recall trees
(Kuhn [1950], [1953]) no type of signal improves performance, in
imperfect-recall trees quantum signals may bring an improvement. Isbell [1957]
proved that in non-Kuhn trees, classical i.i.d. signals may improve
performance. We show that further improvement may be possible by use of
classical exchangeable or quantum signals. We include an example of the effect
of quantum signals in the context of high-frequency trading.Comment: 18 pages, 16 figure
The non-existence of a universal topological type space
The concept of types was introduced by Harsányi[8]. In the literature there are two approaches for formalizing types, type spaces: the purely measurable and the topological models. In the former framework Heifetz and Samet [11] showed that the universal type space exists and later Meier[13] proved that it is complete. In this paper we examine the topological approach and conclude that there is no universal topological type space in the category of topological type spaces
No-Signalling Is Equivalent To Free Choice of Measurements
No-Signalling is a fundamental constraint on the probabilistic predictions
made by physical theories. It is usually justified in terms of the constraints
imposed by special relativity. However, this justification is not as clear-cut
as is usually supposed. We shall give a different perspective on this condition
by showing an equivalence between No-Signalling and Lambda Independence, or
"free choice of measurements", a condition on hidden-variable theories which is
needed to make no-go theorems such as Bell's theorem non-trivial. More
precisely, we shall show that a probability table describing measurement
outcomes is No-Signalling if and only if it can be realized by a
Lambda-Independent hidden-variable theory of a particular canonical form, in
which the hidden variables correspond to non-contextual deterministic
predictions of measurement outcomes. The key proviso which avoids contradiction
with Bell's theorem is that we consider hidden-variable theories with signed
probability measures over the hidden variables - i.e. negative probabilities.
Negative probabilities have often been discussed in the literature on quantum
mechanics. We use a result proved previously in "The Sheaf-theoretic Structure
of Locality and Contextuality" by Abramsky and Brandenburger, which shows that
they give rise to, and indeed characterize, the entire class of No-Signalling
behaviours. In the present paper, we put this result in a broader context,
which reveals the surprising consequence that the No-Signalling condition is
equivalent to the apparently completely different notion of free choice of
measurements.Comment: In Proceedings QPL 2013, arXiv:1412.791
Method for thermal monitoring subcutaneous tissue
A noninvasive accurate method for measuring the temperature of tissue beneath the surface of a living body is described. Ultrasonic signals are directed into beads of a material that are inserted into the tissue with a syringe. The reflected signals indicate the acoustic impedance or resonance frequency of the beads which in turn indicates the temperature of the tissue. A range of temperatures around the melting temperature of the material can be measured by this method
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