Resource theory of quantum uncomplexity

Halpern, Nicole Yunger; Kothakonda, Naga B. T.; Haferkamp, Jonas; Munson, Anthony; Eisert, Jens; Faist, Philippe

doi:10.48550/arxiv.2110.11371

Cited by 5 publications

(6 citation statements)

References 75 publications

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“…One point should be mentioned that the above-said resource theory is completely different the resource theory of quantum uncomplexity which is presented in the Ref. [23] and the fuzzy operations which are discussed in the Ref. [23] is quite different than our idea of fuzzifying processes.…”

Section: Discussionmentioning

confidence: 85%

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Quantifying unsharpness of observables in an outcome-independent way

Mitra¹

2022

Preprint

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Recently, a very beautiful measure of the unsharpness (fuzziness) of the observables is discussed in the paper [Phys. Rev. A 104, 052227 (2021)]. The measure which is defined in this paper is constructed via uncertainty and does not depend on the values of the outcomes. There exist several properties of a set of observables (e.g., incompatibility, non-disturbance) that do not depend on the values of the outcomes. Therefore, the approach in the above-said paper is consistent with the above-mentioned fact and is able to measure the intrinsic unsharpness of the observables. In this work, we also quantify the unsharpness of observables in an outcome-independent way. But our approach is different than the approach of the above-said paper. In this work, at first, we construct two Luder's instrument-based unsharpness measures and provide the tight upper bounds of those measures. Then we prove the monotonicity of the above-said measures under a class of fuzzifying processes (processes that make the observables more fuzzy). This is consistent with the resourcetheoretic framework. Then we relate our approach to the approach of the above-said paper. Next, we try to construct two instrument-independent unsharpness measures. In particular, we define two instrument-independent unsharpness measures and provide the tight upper bounds of those measures and then we derive the condition for the monotonicity of those measures under a class of fuzzifying processes and prove the monotonicity for dichotomic qubit observables. Then we show that for an unknown measurement, the values of all of these measures can be determined experimentally. Finally, we present the idea of the resource theory of the sharpness of the observables.

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Section: Discussionmentioning

confidence: 85%

“…[23] and the fuzzy operations which are discussed in the Ref. [23] is quite different than our idea of fuzzifying processes.…”

Section: Discussionmentioning

confidence: 90%

Quantifying unsharpness of observables in an outcome-independent way

Mitra¹

2022

Preprint

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“…Relation between symmetry and number of states of subsystems can be quantified using quantum complexity and its application as a resource [178,179]. If states of subsystems 1 and 2 can be prepared using n 1 and n 2 qubits, respectively, their maximum complexity C max in isolation is C max " 2 n 1 `2n 2 .…”

Section: B1 Dual Of Generators In Spherical Harmonic Representation O...mentioning

confidence: 99%

$SU(\infty)$-QGR: Emergence of Gravity in an Infinitely Divisible Quantum Universe

Ziaeepour¹

2023

Preprint

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SU p8q-QGR is a foundationally quantum approach to gravity. It assumes that Hilbert spaces of the Universe as a whole and its subsystems represent the symmetry group SU p8q. The Universe is divided to infinite number of subsystems based on an arbitrary finite rank symmetry group G, which arises due to quantum fluctuations and clustering of states. After selection of two arbitrary subsystems as clock and reference observer, subsystems acquire a relative dynamics, and gravity emerges as a SU p8q Yang-Mills quantum field theory, defined on the (3+1)-dimensional parameter space of Hilbert spaces of the subsystems. As a Yang-Mills model SU p8q-QGR is renormalizable and despite prediction of a spin-1 field for gravity at quantum level, when QGR effects are not detectable, it is perceived similar to Einstein gravity. The aim of the present work is to make the foundation of SU p8q-QGR more mathematically rigorous and fill the gaps in the construction of the model reported in earlier works. In particular, we show that the global SU p8q symmetry manifests itself through the entanglement of every subsystem with the rest of the Universe. Moreover, we demonstrate irrelevance of the geometry of parameter space, which can be gauged out by a SU p8q gauge transformation up to an irrelevant constant. Therefore, SU p8q-QGR deviates from gauge-gravity duality models, because the perceived classical spacetime is neither quantized, nor considered to be non-commutative. In fact, using quantum uncertainty relations, we demonstrate that the classical spacetime and its perceived geometry present the average path of the ensemble of quantum states of subsystems in their parameter space. Thus, SU p8q-QGR explains both the dimension and signature of the classical spacetime. We also briefly discuss SU p8q-QGR specific models for dark energy.

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“…In particular, the AdS/CFT correspondence [8] that connects quantum gravity in D-dimensional anti-de Sitter space to a conformal field theory living on its (D −1)dimensional boundary, also connects quantum complexity in the field theory to various quantities in the gravity side of the correspondence via the so-called complexity/volume and complexity/action conjectures [9]. Indeed, complexity as a resource in quantum information [10], has featured prominently in discussions on black hole firewall [11], fast scrambling near black hole horizons [9,[12][13][14], quantum chaos [15] and the properties of the holographic dictionary itself [16].…”

Section: Introductionmentioning

confidence: 99%

Spread complexity and topological transitions in the Kitaev chain

Caputa

Gupta

Haque

et al. 2023

J. High Energ. Phys.

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A number of recent works have argued that quantum complexity, a well-known concept in computer science that has re-emerged recently in the context of the physics of black holes, may be used as an efficient probe of novel phenomena such as quantum chaos and even quantum phase transitions. In this article, we provide further support for the latter, using a 1-dimensional p-wave superconductor — the Kitaev chain — as a prototype of a system displaying a topological phase transition. The Hamiltonian of the Kitaev chain manifests two gapped phases of matter with fermion parity symmetry; a trivial strongly-coupled phase and a topologically non-trivial, weakly-coupled phase with Majorana zero-modes. We show that Krylov-complexity (or, more precisely, the associated spread-complexity) is able to distinguish between the two and provides a diagnostic of the quantum critical point that separates them. We also comment on some possible ambiguity in the existing literature on the sensitivity of different measures of complexity to topological phase transitions.

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Resource theory of quantum uncomplexity

Cited by 5 publications

References 75 publications

Quantifying unsharpness of observables in an outcome-independent way

Quantifying unsharpness of observables in an outcome-independent way

$SU(\infty)$-QGR: Emergence of Gravity in an Infinitely Divisible Quantum Universe

Spread complexity and topological transitions in the Kitaev chain

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