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Abstract
A major outstanding problem for many quantum clock synchronization protocols is the hidden assumption of a common phase reference between the parties to be synchronized. In general, the definition of the quantum states between two parties do not have consistent phase definitions, which can lead to an unknown systematic error. We show that despite prior arguments to the contrary, it is possible to remove this unknown phase via entanglement purification. This closes the loophole for entanglement based quantum clock synchronization protocols, which is a non-local approach to synchronize two clocks independent of the properties of the intervening medium. Starting with noisy Bell pairs, we show that the scheme produces a singlet state for any combination of (i) differing basis conventions for Alice and Bob; (ii) an overall time offset in the execution of the purification algorithm; and (iii) the presence of a noisy channel. Error estimates reveal that better performance than existing classical Einstein synchronization protocols should be achievable using current technology.
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Details
1 State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai, China; New York University Shanghai, Pudong, Shanghai, China; Department of Physics, School of Physical Sciences, Federal University of Technology, Owerri, Nigeria
2 New York University Shanghai, Pudong, Shanghai, China; RIKEN Cluster for Pioneering Research, Wako-Shi, Saitama, Japan
3 NYU-ECNU Institute of Physics at NYU Shanghai, Shanghai, China; Hearne Institute for Theoretical Physics, Department of Physics & Astronomy, Louisiana State University, Baton Rouge, Louisiana, USA; CAS-Alibaba Quantum Computing Laboratory, University of Science and Technology of China, Shanghai, China
4 State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai, China; New York University Shanghai, Pudong, Shanghai, China; NYU-ECNU Institute of Physics at NYU Shanghai, Shanghai, China; National Institute of Informatics, Chiyoda-ku, Tokyo, Japan; Department of Physics, New York University, New York, NY, USA