Many-body quantum magic

Liu, Zi-Wen; Winter, Andreas

doi:10.48550/arxiv.2010.13817

Cited by 8 publications

(12 citation statements)

References 55 publications

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“…Our CB-SD-ST protocol given as Protocol 1 can be used for the proof of magic under the IID scenario where the device's functionality is the same for each repetition of the protocol. To measure the magic, we focus on the max-relative entropy of magic [40]. We adopt this measure for simplicity, but our arguments can be applied to any reasonable measure of the magic.…”

Section: Classical Verifiermentioning

confidence: 99%

Computational self-testing for entangled magic states

Mizutani,

Takeuchi,

Hiromasa

et al. 2021

Preprint

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Section: Classical Verifiermentioning

confidence: 99%

Computational self-testing for entangled magic states

Mizutani,

Takeuchi,

Hiromasa

et al. 2021

Preprint

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“…state conversion and distillation rates [7,15,[34][35][36]. For this case, it is also known that the theory is asymptotically reversible [18]. Here, it would be interesting to study whether tasks like magic state distillation can show a gap in the achievable rates between CSP channels and stabiliser operations.…”

Section: Summary and Open Questionsmentioning

confidence: 99%

“…There, the total negativity in the Wigner function of a state is a resource monotone called mana, and non-zero mana is a necessary condition for a quantum speed-up [4][5][6][7][8][9][10]. In the more relevant case of qubits, this theory breaks down, which has led to a number of parallel developments [11][12][13][14][15][16][17][18]. A common element is that the finite set of stabiliser states, or more generally their convex hull, is taken as the set of free states.…”

Section: Introductionmentioning

confidence: 99%

The axiomatic and the operational approaches to resource theories of magic do not coincide

Heimendahl¹,

Heinrich²,

Gross³

2020

Preprint

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Stabiliser operations occupy a prominent role in the theory of fault-tolerant quantum computing. They are defined operationally: by the use of Clifford gates, Pauli measurements and classical control. Within the stabiliser formalism, these operations can be efficiently simulated on a classical computer, a result which is known as the Gottesman-Knill theorem. However, an additional supply of magic states is enough to promote them to a universal, fault-tolerant model for quantum computing. To quantify the needed resources in terms of magic states, a resource theory of magic has been developed during the last years. Stabiliser operations (SO) are considered free within this theory, however they are not the most general class of free operations. From an axiomatic point of view, these are the completely stabiliserpreserving (CSP) channels, defined as those that preserve the convex hull of stabiliser states. It has been an open problem to decide whether these two definitions lead to the same class of operations. In this work, we answer this question in the negative, by constructing an explicit counter-example. This indicates that recently proposed stabiliser-based simulation techniques of CSP maps are strictly more powerful than Gottesman-Knill-like methods. The result is analogous to a well-known fact in entanglement theory, namely that there is a gap between the class of local operations and classical communication (LOCC) and the class of separable channels. Along the way, we develop a number of auxiliary techniques which allow us to better characterise the set of CSP channels.

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“…Quantum resource theories (QRTs) [1,2] provide a unified framework for quantitatively analyzing quantum properties, which underlies the advantage of quantum information processing over classical information processing. The framework of QRTs was initially motivated by the entanglement theory [3], but similar formulations apply to enormous kinds of quantum properties such as coherence [4], magic states [5][6][7], discord [8], non-Markovianity [9,10], non-Gaussianity [11][12][13][14]. Recently, general frameworks to reveal the universal properties of these various resources have also been studied [2,[15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Asymptotically Consistent Measures of General Quantum Resources: Discord, Non-Markovianity, and Non-Gaussianity

Kuroiwa,

Yamasaki

2021

Preprint

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Quantitative analysis of inherent quantum properties using quantum resource theories reveals fundamental limitations and advantages of large-scale quantum information processing in various tasks. However, a conventional way of resource quantification by resource measures may contradict rates of asymptotic transformation between resourceful quantum states on a large scale due to an approximation in the transformation. In this paper, we investigate consistent resource measures, which quantify resources without contradicting the rates of the asymptotic resource transformation. We prove that relative entropic measures are consistent with the rates for a broad class of resources, i.e., all convex finite-dimensional resources, e.g., entanglement, coherence, and magic, and even some non-convex or infinite-dimensional resources such as quantum discord, non-Markovianity, and non-Gaussianity. These results show that consistent resource measures are widely applicable to the quantitative analysis of large-scale quantum information processing using various quantum resources.

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Many-body quantum magic

Cited by 8 publications

References 55 publications

Computational self-testing for entangled magic states

Computational self-testing for entangled magic states

The axiomatic and the operational approaches to resource theories of magic do not coincide

Asymptotically Consistent Measures of General Quantum Resources: Discord, Non-Markovianity, and Non-Gaussianity

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