Quantum Theory from Rules on Information Acquisition

Hoehn, Philipp A.

doi:10.3390/e19030098

Cited by 31 publications

(72 citation statements)

References 23 publications

(137 reference statements)

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“…Whether or not a consistency among different observers' descriptions can be used in a reconstruction of quantum theory remains an open question. In fact, meanwhile, the formalism has been reconstructed without it, while still being compatible with relational quantum mechanics [54,77] (see [78] for a summary). 12 However, in line with our perspective-neutral approach of sec.…”

Section: Discussionmentioning

confidence: 99%

A change of perspective: switching quantum reference frames via a perspective-neutral framework

Vanrietvelde

Hoehn

Giacomini

et al. 2020

Quantum

119

247

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Treating reference frames fundamentally as quantum systems is inevitable in quantum gravity and also in quantum foundations once considering laboratories as physical systems. Both fields thereby face the question of how to describe physics relative to quantum reference systems and how the descriptions relative to different such choices are related. Here, we exploit a fruitful interplay of ideas from both fields to begin developing a unifying approach to transformations among quantum reference systems that ultimately aims at encompassing both quantum and gravitational physics. In particular, using a gravity inspired symmetry principle, which enforces physical observables to be relational and leads to an inherent redundancy in the description, we develop a perspectiveneutral structure, which contains all frame perspectives at once and via which they are changed. We show that taking the perspective of a specific frame amounts to a fixing of the symmetry related redundancies in both the classical and quantum theory and that changing perspective corresponds to a symmetry transformation. We implement this using the language of constrained systems, which naturally encodes symmetries. Within a simple one-dimensional model, we recover some of the quantum frame transformations of [1], embedding them in a perspective-neutral framework. Using them, we illustrate how entanglement and classicality of an observed system depend on the quantum frame perspective. Our operational language also inspires a new interpretation of Dirac and reduced quantized theories as perspective-neutral and perspectival quantum theories, respectively, and reveals the link between them. In this light, we suggest a new take on the relation between a 'quantum general covariance' and the diffeomorphism symmetry in quantum gravity. * p.hoehn@univie.ac.at arXiv:1809.00556v2 [quant-ph]

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Section: Discussionmentioning

confidence: 99%

A change of perspective: switching quantum reference frames via a perspective-neutral framework

Vanrietvelde

Hoehn

Giacomini

et al. 2020

Quantum

119

247

View full text Add to dashboard Cite

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“…If some points on the sphere were not valid states, then there would exist additional measurements that would violate further natural postulates like Hardy's [25] "Subspaces" axiom. This argumentation or others along similar lines [25][26][27][28][29][30][31][32][33][34][35][36] lead to Euclidean balls as the most natural state spaces of a generalized bit.…”

Section: A Single Gbitsmentioning

confidence: 89%

Quantum computation is the unique reversible circuit model for which bits are balls

Krumm

Müller

2019

npj Quantum Inf

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The computational efficiency of quantum mechanics can be defined in terms of the qubit circuit model, which is characterized by a few simple properties: each computational gate is a reversible transformation in a connected matrix group; single wires carry quantum bits, i.e. states of a threedimensional Bloch ball; states on two or more wires are uniquely determined by local measurement statistics and their correlations. In this paper, we ask whether other types of computation are possible if we relax one of those characteristics (and keep all others), namely, if we allow wires to be described by d-dimensional Bloch balls, where d is different from three. Theories of this kind have previously been proposed as possible generalizations of quantum physics, and it has been conjectured that some of them allow for interesting multipartite reversible transformations that cannot be realized within quantum theory. However, here we show that all such potential beyond-quantum models of computation are trivial: if d is not three, then the set of reversible transformations consists entirely of single-bit gates, and not even classical computation is possible. In this sense, qubit quantum computation is an island in theoryspace.that tomographic locality forces computations to be contained in a class called AWPP [15,16], and that in some theories (satisfying additional axioms) higher-order interference does not lead to a speed-up in Grover's algorithm [17]. Further examples can be found e.g. in [18][19][20][21].

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“…The binary question framework in its present form is limited to reconstructing qubit (and rebit [1,44]) quantum theory and requires a generalization in order to be applicable to arbitrary n-level quantum systems. A treatment of mechanical systems may even necessitate an entirely novel approach.…”

Section: Discussionmentioning

confidence: 99%

“…It is our task to derive what the triple (Q N , Σ N , T N ) compatible with the rules is. As shown in [1], there are only two solutions to these five principles within the established landscape of theories: in this manuscript we shall complete the proof that one solution is standard qubit quantum theory and, as exhibited in a companion paper [44], the second solution is rebit quantum theory, i.e. two level systems over real Hilbert spaces.…”

Section: The Quantum Principles As Rules On Information Acquisitionmentioning

confidence: 99%

Quantum theory from questions

2017

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We reconstruct the explicit formalism of qubit quantum theory from elementary rules on an observer's information acquisition. Our approach is purely operational: we consider an observer O interrogating a system S with binary questions and define S's state as O's 'catalogue of knowledge' about S. From the rules we derive the state spaces for N elementary systems and show that (a) they coincide with the set of density matrices over an N -qubit Hilbert space C 2 N ; (b) states evolve unitarily under the group PSU(2 N ) according to the von Neumann evolution equation; and (c) O's binary questions correspond to projective Pauli operator measurements with outcome probabilities given by the Born rule. As a by-product, this results in a propositional formulation of quantum theory. Aside from offering an informational explanation for the theory's architecture, the reconstruction also unravels new structural insights. We show that, in a derived quadratic information measure, (d) qubits satisfy inequalities which bound the information content in any set of mutually complementary questions to 1 bit; and (e) maximal sets of mutually complementary questions for one and two qubits must carry precisely 1 bit of information in pure states. The latter relations constitute conserved informational charges which define the unitary groups and, together with their conservation conditions, the sets of pure quantum states. These results highlight information as a 'charge of quantum theory' and the benefits of this informational approach. This work emphasizes the sufficiency of restricting to an observer's information to reconstruct the theory and completes the quantum reconstruction initiated in [1].

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Quantum Theory from Rules on Information Acquisition

Cited by 31 publications

References 23 publications

A change of perspective: switching quantum reference frames via a perspective-neutral framework

A change of perspective: switching quantum reference frames via a perspective-neutral framework

Quantum computation is the unique reversible circuit model for which bits are balls

Quantum theory from questions

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