Mapping the spatial distribution of entanglement in optical lattices

Alba, Emilio; Tóth, G.; García-Ripoll, Juan José

doi:10.1103/physreva.82.062321

Cited by 11 publications

(20 citation statements)

References 27 publications

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“…For instance, in Ref. [70] the authors construct modified witnesses for bi-colorable graph states, where one measurement setting consists in measuring X on every even qubit and Z on every odd qubit, and vice versa for the second measurement setting. These operators are witnesses because their expectation value is larger than the expectation value of the standard genuine witness for any state [61,62],…”

Section: Standard and Modified Genuine Witnesses For Stabilizer Stmentioning

confidence: 99%

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Design and experimental performance of local entanglement witness operators

Amaro

Müller

2020

Phys. Rev. A

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Entanglement is a central concept in quantum information and a key resource for many quantum protocols. In this work we propose and analyze a class of entanglement witnesses that detect the presence of entanglement in subsystems of experimental multi-qubit stabilizer states. The witnesses we propose can be decomposed into sums of Pauli operators and can be efficiently evaluated by either two measurement settings only or at most a number of measurements that only depends on the size of the subsystem of interest. We provide two constructive methods to design the local witness operators, the first one based on the local unitary equivalence between graph and stabilizer states, and the second one based on sufficient and necessary conditions that the respective set of constituent Pauli operators needs to fulfill. We theoretically establish the noise tolerance of the proposed witnesses and benchmark their practical performance by analyzing the local entanglement structure of an experimental seven-qubit quantum error correction code.

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Section: Standard and Modified Genuine Witnesses For Stabilizer Stmentioning

confidence: 99%

“…The local witnesses we propose are constructed for stabilizer states and represent a generalization of the local witnesses proposed in [70] for graph states. Stabilizer states play a role in many areas of quantum information, e.g.…”

Section: Introductionmentioning

confidence: 99%

Design and experimental performance of local entanglement witness operators

Amaro

Müller

2020

Phys. Rev. A

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“…An entanglement witness [70][71][72][73][74][75][76]  is an operator with non-negative expectation values in all separable states, implying that a negative expectation value (Tr…”

Section: Witness-and Measurement-based Lower Boundsmentioning

confidence: 99%

“…We adopt two different, yet related approaches to obtain computable lower bounds for localizable entanglement in the case of mixed quantum states. The first approach is based on entanglement witnesses [70][71][72][73][74][75][76] that are local observables whose expectation value signals the presence of entanglement. We use a class of witnesses, called local witnesses [74][75][76], and we show how they can be used to estimate a lower bound of the value of localizable entanglement in subsystems of qubits.…”

Section: Introductionmentioning

confidence: 99%

“…The first approach is based on entanglement witnesses [70][71][72][73][74][75][76] that are local observables whose expectation value signals the presence of entanglement. We use a class of witnesses, called local witnesses [74][75][76], and we show how they can be used to estimate a lower bound of the value of localizable entanglement in subsystems of qubits. Lower bounds of the localizable entanglement can be computed from the expectation values of the witness operators evaluated in the noisy quantum state [77][78][79][80][81].…”

Section: Introductionmentioning

confidence: 99%

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Estimating localizable entanglement from witnesses

2018

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Computing localizable entanglement for noisy many-particle quantum states is difficult due to the optimization over all possible sets of local projection measurements. Therefore, it is crucial to develop lower bounds, which can provide useful information about the behaviour of localizable entanglement, and which can be determined by measuring a limited number of operators, or by performing the least number of measurements on the state, preferably without performing a full state tomography. In this paper, we adopt two different yet related approaches to obtain a witness-based, and a measurementbased lower bounds for localizable entanglement. The former is determined by the minimal amount of entanglement that can be present in a subsystem of the multipartite quantum state, which is consistent with the expectation value of an entanglement witness. Determining this bound does not require any information about the state beyond the expectation value of the witness operator, which renders this approach highly practical in experiments. The latter bound of localizable entanglement is computed by restricting the local projection measurements over the qubits outside the subsystem of interest to a suitably chosen basis. We discuss the behaviour of both lower bounds against local physical noise on the qubits, and discuss their dependence on noise strength and system size. We also analytically determine the measurement-based lower bound in the case of graph states under local uncorrelated Pauli noise.

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Scalable characterization of localizable entanglement in noisy topological quantum codes

2020

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Topological quantum error correcting codes have emerged as leading candidates towards the goal of achieving large-scale fault-tolerant quantum computers. However, quantifying entanglement in these systems of large size in the presence of noise is a challenging task. In this paper, we provide two different prescriptions to characterize noisy stabilizer states, including the surface and the color codes, in terms of localizable entanglement over a subset of qubits. In one approach, we exploit appropriately constructed entanglement witness operators to estimate a witness-based lower bound of localizable entanglement, which is directly accessible in experiments. In the other recipe, we use graph states that are local unitary equivalent to the stabilizer state to determine a computable measurement-based lower bound of localizable entanglement. If used experimentally, this translates to a lower bound of localizable entanglement obtained from single-qubit measurements in specific bases to be performed on the qubits outside the subsystem of interest. Towards computing these lower bounds, we discuss in detail the methodology of obtaining a local unitary equivalent graph state from a stabilizer state, which includes a new and scalable geometric recipe as well as an algebraic method that applies to general stabilizer states of arbitrary size. Moreover, as a crucial step of the latter recipe, we develop a scalable graph-transformation algorithm that creates a link between two specific nodes in a graph using a sequence of local complementation operations. We develop open-source Python packages for these transformations, and illustrate the methodology by applying it to a noisy topological color code, and study how the witness and measurement-based lower bounds of localizable entanglement varies with the distance between the chosen qubits.

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Mapping the spatial distribution of entanglement in optical lattices

Cited by 11 publications

References 27 publications

Design and experimental performance of local entanglement witness operators

Design and experimental performance of local entanglement witness operators

Estimating localizable entanglement from witnesses

Scalable characterization of localizable entanglement in noisy topological quantum codes

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