29 research outputs found
A paradox about an atom and a photon
In this article we propose a new relativistic paradox concerning the
absorption of a photon by a hydrogen atom. We show that the actual cause of the
paradox is one of the hypotheses of Bohr model; therefore, in order to solve
the paradox, we have to move away from Bohr model. Our analysis is carried out
only in the special relativistic framework, so we are not interested in giving
a full quantum mechanical treatment of the problem. We derive some expressions
for emission and absorption of photons by atoms, which are in perfect agreement
with special relativity, although comparable to the classical Bohr formula with
an excellent degree of approximation. Quite interestingly, these expressions
are no more invariant under a global shift of energy levels, showing a breaking
of classical "gauge invariance" of energy. We stress that, to the best of our
knowledge, the present approach has never been considered in literature. At the
end we will be able to solve the proposed paradox.Comment: 10 pages, no figures. PACS number: 03.30.+p, 32.30.-r, 32.80.-tp
Keywords: relativistic paradox, photon emission, photon absorptio
Information-theoretic foundations of thermodynamics in general probabilistic theories
We study the informational underpinnings of thermodynamics and statistical
mechanics, using an abstract framework, general probabilistic theories, capable
of describing arbitrary physical theories. This allows one to abstract the
informational content of a theory from the concrete details of its formalism.
In this framework, we extend the treatment of microcanonical thermodynamics,
namely the thermodynamics of systems with a well-defined energy, beyond the
known cases of classical and quantum theory, formulating two necessary
requirements for a well-defined thermodynamics. We adopt the recent approach of
resource theories, where one studies the transitions between states that can be
accomplished with a restricted set of physical operations. We formulate three
different resource theories, differing in the choice of the restricted set of
physical operations. To bridge the gap between the objective dynamics of
particles and the subjective world of probabilities, one of the core issues in
the foundations of statistical mechanics, we propose four information-theoretic
axioms. They are satisfied by quantum theory and more exotic alternatives,
including a suitable extension of classical theory where classical systems
interact with each other creating entangled states. The axioms identify a class
of theories where every mixed state can be modelled as the reduced state of a
pure entangled state. In these theories it is possible to introduce
well-behaved notions of majorisation, entropy, and Gibbs states, allowing for
an information-theoretic derivation of Landauer's principle. The three resource
theories define the same notion of resource if and only if, on top of the four
axioms, the dynamics of the underlying theory satisfy a condition called
"unrestricted reversibility". Under this condition we derive a duality between
microcanonical thermodynamics and pure bipartite entanglement.Comment: DPhil (PhD) thesis, University of Oxford, October 2018. 230 pages, 11
figure
Reply to the Comment on `The operational foundations of PT-symmetric and quasi-Hermitian quantum theory'
This document is our reply to the Comment arXiv:2301.01215 on our recent work
titled `The operational foundations of PT-symmetric and quasi-Hermitian quantum
theory'. The original Comment consists of three addenda to our work. The first
addendum claims that our work is ill-motivated as the motivating question,
namely whether PT-symmetric quantum theory extends the standard quantum theory,
was already answered in the literature. The second addendum points to some
missing references in our work, and the third addendum suggests what
constraints could lead to an extension of standard quantum theory. In our
reply, we explain that the claim in the first addendum is a result of a
misinterpretation of our motivating question. When interpreted correctly, the
third addendum in the Comment in itself elaborates on why our motivating
question is interesting and relevant. We also briefly comment on the prospects
of an extension of standard quantum theory along the lines suggested in the
third addendum. As our response to the second addendum, we explain our
rationale behind citing certain references while leaving out others.Comment: 5 pages, reply to arXiv:2301.0121
Ruling out higher-order interference from purity principles
As first noted by Rafael Sorkin, there is a limit to quantum interference.
The interference pattern formed in a multi-slit experiment is a function of the
interference patterns formed between pairs of slits, there are no genuinely new
features resulting from considering three slits instead of two. Sorkin has
introduced a hierarchy of mathematically conceivable higher-order interference
behaviours, where classical theory lies at the first level of this hierarchy
and quantum theory theory at the second. Informally, the order in this
hierarchy corresponds to the number of slits on which the interference pattern
has an irreducible dependence. Many authors have wondered why quantum
interference is limited to the second level of this hierarchy. Does the
existence of higher-order interference violate some natural physical principle
that we believe should be fundamental? In the current work we show that such
principles can be found which limit interference behaviour to second-order, or
"quantum-like", interference, but that do not restrict us to the entire quantum
formalism. We work within the operational framework of generalised
probabilistic theories, and prove that any theory satisfying Causality, Purity
Preservation, Pure Sharpness, and Purification---four principles that formalise
the fundamental character of purity in nature---exhibits at most second-order
interference. Hence these theories are, at least conceptually, very "close" to
quantum theory. Along the way we show that systems in such theories correspond
to Euclidean Jordan algebras. Hence, they are self-dual and, moreover,
multi-slit experiments in such theories are described by pure projectors.Comment: 18+8 pages. Comments welcome. v2: Minor correction to Lemma 5.1, main
results are unchange
Quantum hypothesis testing between qubit states with parity
Quantum hypothesis testing (QHT) provides an effective method to discriminate
between two quantum states using a two-outcome positive operator-valued measure
(POVM). Two types of decision errors in a QHT can occur. In this paper we focus
on the asymmetric setting of QHT, where the two types of decision errors are
treated unequally, considering the operational limitations arising from the
lack of a reference frame for chirality. This reference frame is associated
with the group \bbZ_2 consisting of the identity transformation and the
parity transformation. Thus, we have to discriminate between two qubit states
by performing the \bbZ_2-invariant POVMs only. We start from the
discrimination between two pure states. By solving the specific optimization
problem we completely characterize the asymptotic behavior of the minimal
probability of type-II error which occurs when the null hypothesis is accepted
when it is false. Our results reveal that the minimal probability reduces to
zero in a finite number of copies, if the \bbZ_2-twirlings of such two pure
states are different. We further derive the critical number of copies such that
the minimal probability reduces to zero. Finally, we replace one of the two
pure states with a maximally mixed state, and similarly characterize the
asymptotic behavior of the minimal probability of type-II error.Comment: minor revisions, one-column to two-colum