Optimal Entanglement Certification from Moments of the Partial Transpose

Yu, Xiao-Dong; Imai, Satoya; Gühne, Otfried

doi:10.48550/arxiv.2103.06897

Cited by 4 publications

(6 citation statements)

References 38 publications

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“…(A12)], it simply amounts to change the corresponding variables into their opposite, which is again achieved by a change of basis. Our approach therefore represents a hierachy of conditions which are completely independent of the PPT-based criteria [32,33,38,39].…”

Section: General Formulation Of the Hierarchymentioning

confidence: 99%

“…Conceptually-different approaches, based on randomized measurements, have also been developed. Such approaches allow one to test bipartite entanglement criteria based on Rényi entropies [12,22], and PT-based criteria [32,33]. However, in addition to the very high experimental requirements underlying these approaches, they require a number of measurements scaling exponentially with N , severely limiting their scalability beyond a few tens of qubits.…”

Section: Introductionmentioning

confidence: 99%

“…Invariance under partial transposition. It is interesting to notice that our criteria are independent of the partial-transposition (PT) criteria [32,33,38,39]: a state ρ is compatible with Eq. ( 7) if and only if (iff) the state ρPT is compatible with Eq.…”

Section: Introductionmentioning

confidence: 99%

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Unveiling quantum entanglement in many-body systems from partial information

Frérot,

Baccari,

Acín

2021

Preprint

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Quantum entanglement is commonly assumed to be a central resource for quantum computing and quantum simulation. Nonetheless, the capability to detect it in many-body systems is severely limited by the absence of sufficiently scalable and flexible certification tools. This issue is particularly critical in situations where the structure of entanglement is a priori unknown, and where one cannot rely on existing entanglement witnesses. Here, we implement a scheme in which the knowledge of the mean value of arbitrary observables can be used to probe multipartite entanglement in a scalable, certified and systematic manner. Specifically, we rely on positive semidefinite conditions, independent of partial-transposition-based criteria, necessarily obeyed if the data can be reproduced by a separable state. The violation of any of these conditions yields a specific entanglement witness, tailored to the data of interest, revealing the salient features of the data which are impossible to reproduce without entanglement. We validate this approach by probing theoretical many-body states of several hundreds of qubits relevant to existing experiments: a single-particle quench in a one-dimensional XX chain; a many-body quench in a two-dimensional XX model with 1/r 3 interactions; and thermal equilibrium states of Heisenberg and transverse-field Ising chains. In all cases, these investigations have lead us to discover new entanglement witnesses, some of which could be characterized analytically, generalizing existing results in the literature. In summary, our paper introduces a flexible data-driven entanglement detection technique for uncharacterized quantum many-body states, of immediate relevance to experiments in a quantum advantage regime.

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Section: General Formulation Of the Hierarchymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Unveiling quantum entanglement in many-body systems from partial information

Frérot,

Baccari,

Acín

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The goal of the present work is to develop measurement protocols for SFF and pSFF in quantum spin models of arbitrary dimension, as realized for instance with trapped ions [4,6], Rydberg atoms [7] and superconducting qubits [8]. We extend the randomized measurement toolbox [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51], which infers SFF and pSFF from statistical correlations of local random operations applied at different times in a single experiment. This ability to measure pSFF and SFF in a quantum simulation experiment provides a unified and broadly applicable testbed of many-body quantum chaotic behavior, and can be readily implemented in existing experimental platforms [11,17,18,52].…”

Section: Introductionmentioning

confidence: 99%

Probing many-body quantum chaos with quantum simulators

Joshi,

Elben,

Vikram

et al. 2021

Preprint

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“…As the effort in building fault-tolerant quantum computers increases, the need for efficient benchmarking and characterization of these devices becomes more and more apparent. Several studies have been realized in the direction of gauging current Noisy Intermediate-Scale Quantum (NISQ) devices [1]: some of them focus on the analysis of the entanglement behaviour of these systems and ways of measuring it [2,3], others propose new efficient entanglement detectors to be used in experiments [4][5][6]. In this work, we want to exploit Bell's-like inequalities in time, dubbed Leggett-Garg's inequalities (LGI) [7,8], to test the quantum coherence of a quantum hardware.…”

Section: Introductionmentioning

confidence: 99%

Experimental violations of Leggett-Garg's inequalities on a quantum computer

Santini,

Vitale

2021

Preprint

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Leggett-Garg's inequalities predict sharp bounds for some classical correlation functions that address the quantum or classical nature of real-time evolutions. We experimentally observe the violations of these bounds on single-and multi-qubit systems, in different settings, exploiting the IBM Quantum platform. In the multi-qubit case we introduce the Leggett-Garg-Bell's inequalities as an alternative to the previous ones. Measuring these correlation functions, we find quantum error mitigation to be essential to spot inequalities violations. Accessing only two qubit readouts, we assess Leggett-Garg-Bell's inequalities to emerge as the most efficient quantum coherence witnesses to be used for investigating quantum hardware, as the complexity of their calculation does not scale with the number of constituents of the system. Our analysis highlights the limits of nowadays quantum platforms, showing that the above-mentioned correlation functions deviate from theoretical prediction as the number of qubits and the depth of the circuit grow.

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Optimal Entanglement Certification from Moments of the Partial Transpose

Cited by 4 publications

References 38 publications

Unveiling quantum entanglement in many-body systems from partial information

Unveiling quantum entanglement in many-body systems from partial information

Probing many-body quantum chaos with quantum simulators

Experimental violations of Leggett-Garg's inequalities on a quantum computer

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