Hyper-decoherence in Density Hypercubes

Hefford, James; Gogioso, Stefano

doi:10.48550/arxiv.2003.08318

Cited by 6 publications

(12 citation statements)

References 20 publications

(44 reference statements)

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“…In doing so, we explicitly construct an infinite family of related probabilistic theories with interesting and complex decoherence towers. This effort fits squarely within a recent surge of interest in hyperdecoherence [38,27,28,21,23] and resource theories of coherence [31].…”

Section: Introductionmentioning

confidence: 63%

“…we recover the folding of density hypercubes [21,23], double dilation [37] and double mixing [2,9,29]. In all three cases the environment structure contains the caps from the original CPM construction (i.e.…”

Section: Definition 4 (Environment Structurementioning

confidence: 99%

“…For density hypercubes one additionally picks the caps induced by a special commutative †-Frobenius algebra; for double dilation the caps induced by the action of the folding functor on the caps of the original CPM construction; and for double mixing a spider induced by a special commutative †-Frobenius algebra. Note that the additional caps for density hypercubes and double-dilation are wired differently, see discussion in [23].…”

Section: Definition 4 (Environment Structurementioning

confidence: 99%

“…A limitation of this group theoretic approach is that it does not tell us whether double dilation and density hypercubes coincide; by other means, it is in fact known that they do not [23]. This also means that theories generated by the same folding and using discarding maps from isomorphic subgroups of G do not, in general, need to be equivalent: the G-action itself plays an important role in this.…”

Section: Environment Structures From Classical Structuresmentioning

confidence: 99%

“…This generalisation expands upon the inherent symmetries of the original CPM construction to produce categories with more exotic properties, captured by an essential invariance under the action of a group of monoidal autofunctors. These categories have found uses in quantum natural language processing, where they capture multiple degrees of linguistic ambiguity [2,29,9,37], and in CQM, where they have been found to exhibit higher-order interference, hyper-decoherence and a rich phase group structure [21,23].…”

Section: Introductionmentioning

confidence: 99%

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CPM Categories for Galois Extensions

Hefford

Gogioso

2021

Electron. Proc. Theor. Comput. Sci.

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Hashberg Quantum, London, UK quantum(at)hashberg(dot)io By considering a generalisation of the CPM construction, we develop an infinite hierarchy of probabilistic theories, exhibiting compositional decoherence structures which generalise the traditional quantum-to-classical transition. Analogously to the quantum-to-classical case, these decoherences reduce the degrees of freedom in physical systems, while at the same time restricting the fields over which the systems are defined. These theories possess fully fledged operational semantics, allowing both categorical and GPT-style approaches to their study.

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Section: Introductionmentioning

confidence: 63%

Section: Definition 4 (Environment Structurementioning

confidence: 99%

Section: Definition 4 (Environment Structurementioning

confidence: 99%

Section: Environment Structures From Classical Structuresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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CPM Categories for Galois Extensions

Hefford

Gogioso

2021

Electron. Proc. Theor. Comput. Sci.

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Computation in a general physical setting

Gilligan-Lee

2021

J. Phys. A: Math. Theor.

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The computational abilities of theories within the generalised probabilistic theory framework has been the subject of much recent study. Such investigations aim to gain an understanding of the possible connections between physical principles and computation. Moreover, comparing and contrasting the computational properties of quantum theory with other operationally-sensible theories could shed light on the strengths and limitations of quantum computation. This paper reviews and extends some of these results, deriving new bounds on the computational ability of theories satisfying n-local tomography, and theories in which states are represented as generalised superpositions. It moreover provides a refined version of the conjecture that a quantum computer can simulate the computation in any theory within a certain sub-class of generalised probabilistic theories with at most polynomial overhead. The paper ends by describing an important relation between this conjecture and delegated computation, similar to the relation between quantum non-locality and device-independent cryptography.

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Unscrambling the omelette of causation and inference: The framework of causal-inferential theories

Schmid,

Selby,

Spekkens

2020

Preprint

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Using a process-theoretic formalism, we introduce the notion of a causal-inferential theory: a triple consisting of a theory of causal influences, a theory of inferences (of both the Boolean and Bayesian varieties), and a specification of how these interact. Recasting the notions of operational and realist theories in this mold clarifies what a realist account of an experiment offers beyond an operational account. It also yields a novel characterization of the assumptions and implications of standard no-go theorems for realist representations of operational quantum theory, namely, those based on Bell's notion of locality and those based on generalized noncontextuality. Moreover, our process-theoretic characterization of generalised noncontextuality is shown to be implied by an even more natural principle which we term Leibnizianity. Most strikingly, our framework offers a way forward in a research program that seeks to circumvent these no-go results. Specifically, we argue that if one can identify axioms for a realist causal-inferential theory such that the notions of causation and inference can differ from their conventional (classical) interpretations, then one has the means of defining an intrinsically quantum notion of realism, and thereby a realist representation of operational quantum theory that salvages the spirit of locality and of noncontextuality. CONTENTS

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Hyper-decoherence in Density Hypercubes

Cited by 6 publications

References 20 publications

CPM Categories for Galois Extensions

CPM Categories for Galois Extensions

Computation in a general physical setting

Unscrambling the omelette of causation and inference: The framework of causal-inferential theories

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