An operational approach to spacetime symmetries: Lorentz transformations from quantum communication

Hoehn, Philipp A.; Müller, Markus P.

doi:10.1088/1367-2630/18/6/063026

Cited by 24 publications

(37 citation statements)

References 44 publications

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“…For n = 2 parties with m = 2 measurements and k = 2 outcomes each, our result provides a characterization of the quantum set. Although Theorem 3 cannot be extended to general (m, n, k)-behaviours [36] without modification, this result shows that our framework of G-boxes offers a very natural perspective on physical correlations, and reinforces earlier observations that hint at a deep fundamental link between the structures of spacetime and quantum theory [37][38][39][40].…”

Section: Example: Characterizing Quantum Correlationssupporting

confidence: 82%

Semi-device-independent information processing with spatiotemporal degrees of freedom

Garner

Krumm

Müller

2020

Phys. Rev. Research

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Nonlocality, as demonstrated by the violation of Bell inequalities, enables device-independent cryptographic tasks that do not require users to trust their apparatus. In this article, we consider devices whose inputs are spatiotemporal degrees of freedom, e.g. orientations or time durations. Without assuming the validity of quantum theory, we prove that the devices' statistical response must respect their input's symmetries, with profound foundational and technological implications. We exactly characterize the bipartite binary quantum correlations in terms of local symmetries, indicating a fundamental relation between spacetime and quantum theory. For Bell experiments characterized by two input angles, we show that the correlations are accounted for by a local hidden variable model if they contain enough noise, but conversely must be nonlocal if they are pure enough. This allows us to construct a "Bell witness" that certifies nonlocality with fewer measurements than possible without such spatiotemporal symmetries, suggesting a new class of semi-device-independent protocols for quantum technologies. arXiv:1907.09274v1 [quant-ph]

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Section: Example: Characterizing Quantum Correlationssupporting

confidence: 82%

Semi-device-independent information processing with spatiotemporal degrees of freedom

Garner

Krumm

Müller

2020

Phys. Rev. Research

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“…Given the transformations (36)(37)(38), it is also clear that (ψ phys ,Ô ψ phys ) phys ≡ (ψ A,BC |T A,BCÔ (T A,BC ) † | ψ A,BC ) A,BC = ψ| BC|AÔBC|A |ψ BC|A ,…”

Section: Physical Inner Product For Dirac Quantizationmentioning

confidence: 99%

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

Vanrietvelde

Hoehn

Giacomini

et al. 2020

Quantum

126

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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“…Given the popularity of approaches in which spacetime emerges in some way from an underlying quantum theory [59][60][61], this observation can perhaps be regarded as more than a coincidence. In fact, it has been argued more rigorously that the structures of quantum theory and spacetime mutually constrain each other [23,53,[62][63][64]. This suggests a slogan that also fits some other ideas from quantum information [65]: the limits of computation are the limits of our world.…”

Section: Discussionmentioning

confidence: 96%

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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An operational approach to spacetime symmetries: Lorentz transformations from quantum communication

Cited by 24 publications

References 44 publications

Semi-device-independent information processing with spatiotemporal degrees of freedom

Semi-device-independent information processing with spatiotemporal degrees of freedom

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

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