Relativity of quantum states in entanglement swapping |
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| Institution: | 1. State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, China;2. New York University Shanghai, 1555 Century Ave, Pudong, Shanghai 200122, China;3. Department of Physics, New York University, New York, NY 10003, USA;4. Department of Physics, School of Physical Sciences, Federal University of Technology, P. M. B. 1526, Owerri, Imo State 460001, Nigeria;5. Centre for Quantum Software & Information (QSI), Faculty of Engineering & Information Technology, University of Technology Sydney, NSW 2007, Australia;6. Hearne Institute for Theoretical Physics and Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA;7. National Institute of Information and Communications Technology, 4-2-1, Nukui-Kitamachi, Koganei, Tokyo 184-8795, Japan;8. NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China;9. CAS-Alibaba Quantum Computing Laboratory, University of Science and Technology of China, Shanghai 201315, China;10. National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan |
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| Abstract: | The entanglement swapping protocol is analyzed in a relativistic setting, where shortly after the entanglement swapping is performed, a Bell test is performed. For an observer in the laboratory frame, a Bell violation is observed between the qubits with the swapped entanglement. In a moving frame, the order of the measurements is reversed, and a Bell violation is observed even though the particles are not entangled, directly or indirectly, or at any point in time. Although the measurement results are identical, the wavefunctions for the two frames are starkly different — one is entangled and the other is not. Furthermore, for boosts in a perpendicular direction, in the presence of decoherence, we show that the maximum Bell violation can occur across non-simultaneous points in time. This is a signature of entanglement that is spread across both space and time, showing both non-local and non-simultaneous aspects of entanglement. |
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| Keywords: | Quantum information Entanglement swapping Special relativity |
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