Machine learning on quantifying quantum steerability
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Machine learning on quantifying quantum steerability Ye-Qi Zhang1
· Li-Juan Yang1 · Qi-Liang He2 · Liang Chen1
Received: 8 January 2020 / Accepted: 15 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We apply the artificial neural network to quantify two-qubit steerability based on the steerable weight, which can be computed through semidefinite programming. Due to the fact that the optimal measurement strategy is unknown, it is still very difficult and time-consuming to efficiently obtain the steerability for an arbitrary quantum state. In this work, we show the method via machine learning technique which provides an effective way to quantify steerability. Furthermore, the generalization ability of the trained model is also demonstrated by applying to the Werner state and that in dephasing noise channel. Our findings provide an new way to obtain steerability efficiently and accurately, revealing effective application of the machine learning method on exploring quantum steering. Keywords Quantum steerability · Quantum correlations · Machine Learning · Artificial neural network
1 Introduction The concept of quantum steering can be traced back to Schrodinger in 1935 [1], who was attempting to formalize the “spook action at distance” discussed by Einstein, Podolsky, and Rosen [2]. It describes the phenomenon that ensembles of quantum states can be remotely prepared by performing local measurements at a distance. Being able to demonstrate steering certifies the presence of entanglement between a user with untrusted device and another user with trusted device [3]. In this sense, quantum steerable states constitute a subset of entangled states and a superset of Bell nonlocal states. Besides fundamental importance, quantum steering has been recognized as a resource in one-sided device-independent quantum key distribution
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Ye-Qi Zhang [email protected]
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Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
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School of Physics and Electronics, Guizhou Normal University, Guiyang 550001, China 0123456789().: V,-vol
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(1S-DI-QKD) [4], which has more loose experiment requirements than fully DI-QKD [5]. Due to the fact that one system is classical and the other is quantum in the scenario of steering, it can also be useful in the tasks such as randomness certification [6] and subchannel discrimination [7]. Now that quantum states with entanglement cannot guarantee the realization of quantum steering, it is crucial to detect and quantify the steerability for a given state shared by participants. In the formalization of entanglement certification task [3], one party Alice, who has access to an untrusted device, wants to convince another party Bob, who has a trusted quantum system that they share an entangled state. Alice’s device can be treated as a black box, which admits classical inputs and outputs, corresponding to her choices of measurement and the outcomes. The set of conditional ense
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