95 research outputs found
Some Nearly Quantum Theories
We consider possible non-signaling composites of probabilistic models based
on euclidean Jordan algebras. Subject to some reasonable constraints, we show
that no such composite exists having the exceptional Jordan algebra as a direct
summand. We then construct several dagger compact categories of such
Jordan-algebraic models. One of these neatly unifies real, complex and
quaternionic mixed-state quantum mechanics, with the exception of the
quaternionic "bit". Another is similar, except in that (i) it excludes the
quaternionic bit, and (ii) the composite of two complex quantum systems comes
with an extra classical bit. In both of these categories, states are morphisms
from systems to the tensor unit, which helps give the categorical structure a
clear operational interpretation. A no-go result shows that the first of these
categories, at least, cannot be extended to include spin factors other than the
(real, complex, and quaternionic) quantum bits, while preserving the
representation of states as morphisms. The same is true for attempts to extend
the second category to even-dimensional spin-factors. Interesting phenomena
exhibited by some composites in these categories include failure of local
tomography, supermultiplicativity of the maximal number of mutually
distinguishable states, and mixed states whose marginals are pure.Comment: In Proceedings QPL 2015, arXiv:1511.0118
Composites and Categories of Euclidean Jordan Algebras
We consider possible non-signaling composites of probabilistic models based
on euclidean Jordan algebras (EJAs), satisfying some reasonable additional
constraints motivated by the desire to construct dagger-compact categories of
such models. We show that no such composite has the exceptional Jordan algebra
as a direct summand, nor does any such composite exist if one factor has an
exceptional summand, unless the other factor is a direct sum of one-dimensional
Jordan algebras (representing essentially a classical system). Moreover, we
show that any composite of simple, non-exceptional EJAs is a direct summand of
their universal tensor product, sharply limiting the possibilities.
These results warrant our focussing on concrete Jordan algebras of hermitian
matrices, i.e., euclidean Jordan algebras with a preferred embedding in a
complex matrix algebra}. We show that these can be organized in a natural way
as a symmetric monoidal category, albeit one that is not compact closed. We
then construct a related category InvQM of embedded euclidean Jordan algebras,
having fewer objects but more morphisms, that is not only compact closed but
dagger-compact. This category unifies finite-dimensional real, complex and
quaternionic mixed-state quantum mechanics, except that the composite of two
complex quantum systems comes with an extra classical bit.
Our notion of composite requires neither tomographic locality, nor
preservation of purity under tensor product. The categories we construct
include examples in which both of these conditions fail. In such cases, the
information capacity (the maximum number of mutually distinguishable states) of
a composite is greater than the product of the capacities of its constituents.Comment: 60 pages, 3 tables. Substantially revised, with some new result
Locally Tomographic Shadows (Extended Abstract)
Given a monoidal probabilistic theory -- a symmetric monoidal category
of systems and processes, together with a functor
assigning concrete probabilistic models to objects of -- we
construct a locally tomographic probabilistic theory
LT -- the locally tomographic shadow of
-- describing phenomena observable by local agents
controlling systems in , and able to pool information about joint
measurements made on those systems. Some globally distinct states become
locally indistinguishable in LT, and we restrict the
set of processes to those that respect this indistinguishability. This
construction is investigated in some detail for real quantum theory.Comment: In Proceedings QPL 2023, arXiv:2308.1548
Finding dex-1 Phenotype Suppressing Components
Caenorhabditis elegans is a species of microscopic round worm that has been used as a genetic model for over forty years. When in an adverse environment, C. elegans larvae cease reproductive development and enter the stress-resistant dauer stage.
dex-1 mutants of C. elegans are deficient in this protein, resulting in shortened dendrites and a sensitivity to sodium dodecyl sulfate (SDS). SDS will kill any non-dauer C. elegans, but wild type dauers will survive well past the standard concentration of 1% SDS. Thus, treatment with SDS is commonly how labs isolate dauers. By contrast, dex-1 dauers (Fig.3) will die when exposed to 1% SDS, but can potentially survive when exposed to less.
The focus of this lab is to characterize the genetic pathways that facilitate morphological changes that occur during the dauer stage by finding potential interactors of dex-1 during dauer when conducting a suppressor screen
Generalized No-Broadcasting Theorem
We prove a generalized version of the no-broadcasting theorem, applicable to essentially any nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with ‘‘superquantum’’ correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem
A generalized no-broadcasting theorem
We prove a generalized version of the no-broadcasting theorem, applicable to
essentially \emph{any} nonclassical finite-dimensional probabilistic model
satisfying a no-signaling criterion, including ones with ``super-quantum''
correlations. A strengthened version of the quantum no-broadcasting theorem
follows, and its proof is significantly simpler than existing proofs of the
no-broadcasting theorem.Comment: 4 page
Entropy and Information Causality in General Probabilistic Theories
We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality (IC) recently proposed by Pawlowski et al (2009 arXiv:0905.2292). We consider two entropic quantities, which we term measurement and mixing entropy. In the context of classical and quantum theory, these coincide, being given by the Shannon and von Neumann entropies, respectively; in general, however, they are very different. In particular, while measurement entropy is easily seen to be concave, mixing entropy need not be. In fact, as we show, mixing entropy is not concave whenever the state space is a non-simplicial polytope. Thus, the condition that measurement and mixing entropies coincide is a strong constraint on possible theories. We call theories with this property monoentropic.
Measurement entropy is subadditive, but not in general strongly subadditive. Equivalently, if we define the mutual information between two systems A and B by the usual formula I (A : B) = H(A) + H(B)− H(AB), where H denotes the measurement entropy and AB is a non-signaling composite of A and B, then it can happen that I (A : BC) \u3c I (A : B). This is relevant to IC in the sense of Pawlowski et al: we show that any monoentropic non-signaling theory in which measurement entropy is strongly subadditive, and also satisfies a version of the Holevo bound, is informationally causal, and on the other hand we observe that Popescu–Rohrlich boxes, which violate IC, also violate strong subadditivity. We also explore the interplay between measurement and mixing entropy and various natural conditions on theories that arise in quantum axiomatics
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