Design and experimental performance of local entanglement witness operators

Amaro, David; Müller, Markus

doi:10.1103/physreva.101.012317

Cited by 13 publications

(10 citation statements)

References 90 publications

(147 reference statements)

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“…In 2000, Terhal first introduced the term entanglement witness (EW) by indicating that a violation of a Bell inequality can be expressed as a witness for entanglement [18]. Recently, more and more EWs have been implemented with local measurements [19][20][21][22]. Nowadays, EWs are a fundamental tool for the detection of entanglement both theoretically and experimentally [4].…”

Section: Introductionmentioning

confidence: 99%

Inertias of entanglement witnesses

Shen,

Chen,

Zhao

2020

Preprint

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Entanglement witnesses (EWs) are a fundamental tool for the detection of entanglement. We study the matrix inertias of EWs with a focus on the EWs constructed by the partial transposition of states with non-positive partial transposes. We provide a method to generate more inertias from a given inertia by the relevance between inertias. Based on that we exhaust all the inertias for EWs in each qubit-qudit system. We apply our results to propose a separability criterion in terms of the rank of the partial transpose of state. We also connect our results to tripartite genuinely entangled states and the classification of states with non-positive partial transposes. Additionally, the inertias of EWs constructed by X-states are clarified.

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Section: Introductionmentioning

confidence: 99%

Inertias of entanglement witnesses

Shen,

Chen,

Zhao

2020

Preprint

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“…In this chapter we describe our work on entanglement witnesses and localisable entanglement (LE), which resulted in three publications [3,4,7]. In Ref.…”

Section: Local Entanglement Witnessesmentioning

confidence: 99%

“…In Ref. [7] we propose local witness operators for stabiliser states, study their relations and resistance to noise, provide two methods to construct these operators, and apply them to the existing experimental realisation of the seven-qubit color code with trapped ions. Then, in Ref.…”

Section: Local Entanglement Witnessesmentioning

confidence: 99%

“…Here we test the performance of local witnesses and the tools that we developed in Refs. [3,4,7] to obtain the behaviour of LE as a function of the qubit distance. The state chosen to perform this test is a large color code (with hundreds of qubits) defined on a hexagonal lattice, and affected by depolarising and phase-flip noise.…”

Section: Entanglement Vs Distancementioning

confidence: 99%

“…• "Design and experimental performance of local entanglement witness operators", David Amaro and Markus Müller, Physical Review A 101, 012317 (accepted on December 2019 and published on January 2020) [7].…”

Section: Introductionmentioning

confidence: 99%

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Characterization and implementation of robust quantum information processing

Amaro¹

Self Cite

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Quantum information processing has practical applications like exponential speed ups in optimisation problems or the simulation of complex quantum systems. However, well controlled quantum systems realised experimentally to process the information are sensitive to noise. The progress in leading experimental platforms like superconducting qubits or trapped ions has al-lowed the realisation of high-fidelity quantum processors known as Noisy Intermediate-Scale Quantum (NISQ) devices with roughly 50 qubits. NISQ devices are meant to be large enough to show, despite their imperfections, an advantage over classical processors in some computational tasks and pro-vide a rich playground to prove principles for future quantum algorithms and protocols. However, quantum processors need to be scaled up to imple-ment quantum algorithms that are relevant for practical applications. For this purpose, Quantum Error Correction (QEC) codes, which encode the information in multi-partite quantum states that are generally highly en-tangled, become crucial to eliminate the errors introduced by noise sources like qubit loss. Here we introduce a protocol to correct qubit loss, i.e., the impossibility to access the information encoded in a qubit, in the color code, a leading candidate for fault-tolerant quantum computation. We show that the achieved tolerance of 46(1)% to qubit loss is related to a novel percola-tion problem on three coupled lattices. Our work shows the high robustness of the color under our protocol and has practical importance for implemen-tations of fault-tolerant QEC. In our second line of research we propose and analyse local entanglement witnesses as efficient and platform-agnostic detectors of the entanglement between qubit subsystems, providing a de-scription of the entanglement structure in, in principle, arbitrarily large quantum systems. Since entanglement is a genuinely quantum property used as a resource in most quantum algorithms, local witnesses, which can be implemented with current technology, are of interest for current and future quantum processors.

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Inertia of two-qutrit entanglement witnesses

Feng

Chen

et al. 2022

Linear and Multilinear Algebra

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Design and experimental performance of local entanglement witness operators

Cited by 13 publications

References 90 publications

Inertias of entanglement witnesses

Inertias of entanglement witnesses

Characterization and implementation of robust quantum information processing

Inertia of two-qutrit entanglement witnesses

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