Characterizing correlation within multipartite quantum systems via local randomized measurements

Liu, Zhenhuan; Zeng, Pei; Zhou, Y.; Gu, Mile

doi:10.1103/physreva.105.022407

Cited by 15 publications

(4 citation statements)

References 76 publications

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“…This protocol with Pauli measurements mainly works for 2-degree functions and is proved infeasible for higher-degree ones 14 . With the hybrid framework here, one can make it feasible for the 3-degree function P 3 and also reproduce the same variance scaling of P 2 in the original protocol 16,35 , indicating the advantage again.…”

Section: Application For the Moment Estimationmentioning

confidence: 78%

“…which is general and includes, such as the state overlap and fidelity [15][16][17] , the purity and higher-order moments 18,19 , quantum Fisher information 20 , outof-time-ordered correlators 21,22 , and topological invariants 23,24 . For simplicity, hereafter we mainly adopt the moment function P m to illustrate the framework, where O i ¼ I d and ρ i = ρ in Eq.…”

mentioning

confidence: 99%

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A hybrid framework for estimating nonlinear functions of quantum states

Zhou,

Liu

2024

npj Quantum Inf

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Estimating nonlinear functions of quantum states, such as the moment $${{{\rm{tr}}}}({\rho }^{m})$$ tr ( ρ m ) , is of fundamental and practical interest in quantum science and technology. Here we show a quantum-classical hybrid framework to measure them, where the quantum part is constituted by the generalized swap test, and the classical part is realized by postprocessing the result from randomized measurements. This hybrid framework utilizes the partial coherent power of the intermediate-scale quantum processor and, at the same time, dramatically reduces the number of quantum measurements and the cost of classical postprocessing. We demonstrate the advantage of our framework in the tasks of state-moment estimation and quantum error mitigation.

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Section: Application For the Moment Estimationmentioning

confidence: 78%

mentioning

confidence: 99%

A hybrid framework for estimating nonlinear functions of quantum states

Zhou,

Liu

2024

npj Quantum Inf

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“…Unitary t-designs are therefore used as an efficient substitute in many important applications (the resources required to implement an approximate t-design scale polynomially with the number of qubits [2,3]). In particular, 1-designs are used for encrypting quantum data [4,5]; and 2-designs are used for randomised benchmarking [6][7][8][9][10][11], characterising correlations within multipartite quantum systems [12] and formulating quantum mechanical models of black holes [13]. Furthermore, 3-designs are used for solving black-box problems [14]; and 4-designs are used for quantum state distinction [15] and estimating the self-adjointness of quantum noise [16].…”

Section: Introductionmentioning

confidence: 99%

Investigating the effect of noise channels on the quality of unitary t-designs

Strydom¹,

Tame²

2022

Preprint

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Unitary t-designs have a wide variety of applications in quantum information theory, such as quantum data encryption and randomised benchmarking. However, experimental realisations of t-designs are subject to noise. Here we investigate the effect of noise channels on the quality of single-qubit t-designs. The noise channels we study are bit flips, phase flips, bit and phase flips, phase damping, amplitude damping and depolarising noise. We consider two noise models: the first has noise applied before the t-design unitary operations, while the second has noise applied after the unitary operations. We show that for single qubits the 1-design is completely unaffected by an arbitrary noise channel, for both noise models, while numeric results obtained for the 2-, 3-, 4and 5-design suggest that a 2t-design is significantly more sensitive to noise than a (2t − 1)-design and that, with the exception of amplitude damping, a (2t + 1)-design is as sensitive to noise as a 2t-design. Numeric results also reveal substantial variations in sensitivity to noise throughout the Bloch sphere. In particular, t-designs appear to be most sensitive to noise when acting on pure states and least sensitive to noise for the maximally mixed state. For depolarising noise, we show that our two noise models are equivalent, and for the other noise channels, numeric results suggest that applying a noise channel after the unitary operations effectively transforms the channel into a depolarising channel, an effect exploited in randomised benchmarking with 2-designs.

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“…Huang's protocol 24 is hereafter referred as shadow tomography. Shadow tomography is efficient in estimation of quantities in terms of observable (polynomial), including nonlinear observables such as purity and R enyi entropy [25][26][27][28] , which is of particular interest in detecting multipartite…”

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confidence: 99%

Efficient characterizations of multiphoton states with an ultra-thin optical device

An,

Liu,

Zhang

et al. 2024

Nat Commun

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Metasurface enables the generation and manipulation of multiphoton entanglement with flat optics, providing a more efficient platform for large-scale photonic quantum information processing. Here, we show that a single metasurface optical device would allow more efficient characterizations of multiphoton entangled states, such as shadow tomography, which generally requires fast and complicated control of optical setups to perform information-complete measurements, a demanding task using conventional optics. The compact and stable device here allows implementations of general positive operator valued measures with a reduced sample complexity and significantly alleviates the experimental complexity to implement shadow tomography. Integrating self-learning and calibration algorithms, we observe notable advantages in the reconstruction of multiphoton entanglement, including using fewer measurements, having higher accuracy, and being robust against experimental imperfections. Our work unveils the feasibility of metasurface as a favorable integrated optical device for efficient characterization of multiphoton entanglement, and sheds light on scalable photonic quantum technologies with ultra-thin optical devices.

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Characterizing correlation within multipartite quantum systems via local randomized measurements

Cited by 15 publications

References 76 publications

A hybrid framework for estimating nonlinear functions of quantum states

A hybrid framework for estimating nonlinear functions of quantum states

Investigating the effect of noise channels on the quality of unitary t-designs

Efficient characterizations of multiphoton states with an ultra-thin optical device

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