24 research outputs found
Inadequacy of Modal Logic in Quantum Settings
We test the principles of classical modal logic in fully quantum settings.
Modal logic models our reasoning in multi-agent problems, and allows us to
solve puzzles like the muddy children paradox. The Frauchiger-Renner thought
experiment highlighted fundamental problems in applying classical reasoning
when quantum agents are involved; we take it as a guiding example to test the
axioms of classical modal logic. In doing so, we find a problem in the original
formulation of the Frauchiger-Renner theorem: a missing assumption about
unitarity of evolution is necessary to derive a contradiction and prove the
theorem. Adding this assumption clarifies how different interpretations of
quantum theory fit in, i.e., which properties they violate. Finally, we show
how most of the axioms of classical modal logic break down in quantum settings,
and attempt to generalize them. Namely, we introduce constructions of trust and
context, which highlight the importance of an exact structure of trust
relations between agents. We propose a challenge to the community: to find
conditions for the validity of trust relations, strong enough to exorcise the
paradox and weak enough to still recover classical logic.Comment: In Proceedings QPL 2018, arXiv:1901.0947
Thermalisation and entropy in Heisenberg spin chains
Mestrado em Engenharia FísicaEste projecto tem como objectivo estudar o comportamento de medidas de entropia quântica em pequenos sistemas quânticos, de forma a se obter uma intuição sobre o assunto que veja a ser útil para um futuro projecto dedicado ao desenvolvimento de uma termodinâmica para pequenos sistemas quânticos baseada em entropias quânticas.
Mostramos como modelar sistemas quânticos que interagem entre si.
Introduzimos a noção de entropia quântica e discutimos o significado físico de algumas medidas de entropia, bem como as relações entre si.
Apresentamos uma abordagem do ponto de vista da informação quântica ao problema da termalização e equilíbrio. De seguida introduzimos e discutimos os sistemas modelo estudados, cadeias de spin de Heisenberg.
Para contribuir para esta linha de trabalho, desenvolvemos e executamos simulações numéricas nestas cadeias de spin, de forma a estudar o comportamento de várias medidas de entropia à medida que pequenos subsistemas termalizavam.
Entre outras coisas, concluímos que as diferentes medidas de entropia apresentam diferentes tempos de saturação. Apenas a medida de entropia
mais lenta constitui um indicador adequado acerca do estado de termalização do sistema.
ABSTRACT: The goal of this project is to study the behaviour of quantum entropy measures in small quantum systems, in order to get an intuition for the subject that may help to orientate a future project dedicated to the development of a thermodynamic theory of small quantum systems based on quantum entropies.
We show how to model composite (in particular interacting) quantum systems.
We introduce the notion of quantum entropy and discuss the physical meaning of some entropy measures and the relations between them.
We present a quantum-information framework to the phenomena of thermalisation and equilibration and recall state-of-the-art results in this topic.
Then we introduce the toy systems of study, Heisenberg spin chains, from the most basic principles of spin and exchange interaction. We discuss their physical meaning and how they behave under the action of the XXZ Hamiltonian. To contribute to that body of work we finally develop and perform numerical simulations in those spin chains in order to study the behaviour of
several entropy measures as small systems thermalised.
Amongst other things, we find that distinct entropy measures saturate at different times. Only the slowest of these measures is appropriate to indicate
whether a system has equilibrated
The role of quantum information in thermodynamics --- a topical review
This topical review article gives an overview of the interplay between
quantum information theory and thermodynamics of quantum systems. We focus on
several trending topics including the foundations of statistical mechanics,
resource theories, entanglement in thermodynamic settings, fluctuation theorems
and thermal machines. This is not a comprehensive review of the diverse field
of quantum thermodynamics; rather, it is a convenient entry point for the
thermo-curious information theorist. Furthermore this review should facilitate
the unification and understanding of different interdisciplinary approaches
emerging in research groups around the world.Comment: published version. 34 pages, 6 figure
Toys can't play: physical agents in Spekkens' theory
Information is physical, and for a physical theory to be universal, it should
model observers as physical systems, with concrete memories where they store
the information acquired through experiments and reasoning. Here we address
these issues in Spekkens' toy theory, a non-contextual epistemically restricted
model that partially mimics the behaviour of quantum mechanics. We propose a
way to model physical implementations of agents, memories, measurements,
conditional actions and information processing. We find that the actions of toy
agents are severely limited: although there are non-orthogonal states in the
theory, there is no way for physical agents to consciously prepare them. Their
memories are also constrained: agents cannot forget in which of two arbitrary
states a system is. Finally, we formalize the process of making inferences
about other agents' experiments and model multi-agent experiments like Wigner's
friend. Unlike quantum theory or box world, in the toy theory there are no
inconsistencies when physical agents reason about each other's knowledge.Comment: 18 + 19 page
Fitch's knowability axioms are incompatible with quantum theory
How can we consistently model the knowledge of the natural world provided by
physical theories? Philosophers frequently use epistemic logic to model
reasoning and knowledge abstractly, and to formally study the ramifications of
epistemic assumptions. One famous example is Fitch's paradox, which begins with
minimal knowledge axioms and derives the counter-intuitive result that "every
agent knows every true statement." Accounting for knowledge that arises from
physical theories complicates matters further. For example, quantum mechanics
allows observers to model other agents as quantum systems themselves, and to
make predictions about measurements performed on each others' memories.
Moreover, complex thought experiments in which agents' memories are modelled as
quantum systems show that multi-agent reasoning chains can yield paradoxical
results.
Here, we bridge the gap between quantum paradoxes and foundational problems
in epistemic logic, by relating the assumptions behind the recent
Frauchiger-Renner quantum thought experiment and the axioms for knowledge used
in Fitch's knowability paradox. Our results indicate that agents' knowledge of
quantum systems must violate at least one of the following assumptions: it
cannot be distributive over conjunction, have a kind of internal continuity,
and yield a constructive interpretation all at once. Indeed, knowledge provided
by quantum mechanics apparently contradicts traditional notions of how
knowledge behaves; for instance, it may not be possible to universally assign
objective truth values to claims about agent knowledge. We discuss the
relations of this work to results in quantum contextuality and explore possible
modifications to standard epistemic logic that could make it consistent with
quantum theory.Comment: 22 + 7 page
Operational locality in global theories
Within a global physical theory, a notion of locality allows us to find and justify information-processing primitives, like non-signalling between distant agents. Here, we propose exploring the opposite direction: to take agents as the basic building blocks through which we test a physical theory, and recover operational notions of locality from signalling conditions. First, we introduce an operational model for the effective state spaces of individual agents, as well as the range of their actions. We then formulate natural secrecy conditions between agents and identify the aspects of locality relevant for signalling. We discuss the possibility of taking commutation of transformations as a primitive of physical theories, as well as applications to quantum theory and generalized probability frameworks. This ‘it from bit’ approach establishes an operational connection between local actions and local observations, and gives a global interpretation to concepts like discarding a subsystem or composing local functions.ISSN:1364-503XISSN:1471-296
Operational locality in global theories
Within a global physical theory, a notion of locality allows us to find and justify information-processing primitives, like non-signalling between distant agents. Here, we propose exploring the opposite direction: to take agents as the basic building blocks through which we test a physical theory, and recover operational notions of locality from signalling conditions. First, we introduce an operational model for the effective state spaces of individual agents, as well as the range of their actions. We then formulate natural secrecy conditions between agents and identify the aspects of locality relevant for signalling. We discuss the possibility of taking commutation of transformations as a primitive of physical theories, as well as applications to quantum theory and generalized probability frameworks. This ‘it from bit’ approach establishes an operational connection between local actions and local observations, and gives a global interpretation to concepts like discarding a subsystem or composing local functions.ISSN:1364-503XISSN:1471-296
Composable security in relativistic quantum cryptography
Relativistic protocols have been proposed to overcome certain impossibility results in classical and
quantum cryptography. In such a setting, one takes the location of honest players into account, and
uses the signalling limit given by the speed of light to constraint the abilities of dishonest agents.
However, composing such protocols with each other to construct new cryptographic resources is
known to be insecure in some cases. To make general statements about such constructions, a
composable framework for modelling cryptographic security in Minkowski space is required.
Here, we introduce a framework for performing such a modular security analysis of classical and
quantum cryptographic schemes in Minkowski space. As an application, we show that (1) fair and
unbiased coin flipping can be constructed from a simple resource called channel with delay; (2)
biased coin flipping, bit commitment and channel with delay through any classical, quantum or
post-quantum relativistic protocols are all impossible without further setup assumptions; (3) it is
impossible to securely increase the delay of a channel, given several short-delay channels as
ingredients. Results(1) and (3) imply in particular the non-composability of existing relativistic bit
commitment and coin flipping protocols
The thermodynamic meaning of negative entropy
Landauer's erasure principle exposes an intrinsic relation between
thermodynamics and information theory: the erasure of information stored in a
system, S, requires an amount of work proportional to the entropy of that
system. This entropy, H(S|O), depends on the information that a given observer,
O, has about S, and the work necessary to erase a system may therefore vary for
different observers. Here, we consider a general setting where the information
held by the observer may be quantum-mechanical, and show that an amount of work
proportional to H(S|O) is still sufficient to erase S. Since the entropy H(S|O)
can now become negative, erasing a system can result in a net gain of work (and
a corresponding cooling of the environment).Comment: Added clarification on non-cyclic erasure and reversible computation
(Appendix E). For a new version of all technical proofs see the Supplementary
Information of the journal version (free access