Geometry of Einstein-Podolsky-Rosen Correlations

H. Chau Nguyen, Huy-Viet Nguyen, and Otfried Gühne
Phys. Rev. Lett. 122, 240401 – Published 17 June 2019
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Abstract

Correlations between distant particles are central to many puzzles and paradoxes of quantum mechanics and, at the same time, underpin various applications such as quantum cryptography and metrology. Originally in 1935, Einstein, Podolsky, and Rosen (EPR) used these correlations to argue against the completeness of quantum mechanics. To formalize their argument, Schrödinger subsequently introduced the notion of quantum steering. Still, the question of which quantum states can be used for EPR steering and which cannot remained open. Here we show that quantum steering can be viewed as an inclusion problem in convex geometry. For the case of two spin-1/2 particles, this approach completely characterizes the set of states leading to EPR steering. In addition, we discuss the generalization to higher-dimensional systems as well as generalized measurements. Our results find applications in various protocols in quantum information processing, and moreover they are linked to quantum mechanical phenomena such as uncertainty relations and the question of which observables in quantum mechanics are jointly measurable.

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  • Received 26 November 2018
  • Revised 17 April 2019

DOI:https://doi.org/10.1103/PhysRevLett.122.240401

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

H. Chau Nguyen1,*, Huy-Viet Nguyen2,†, and Otfried Gühne1,‡

  • 1Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
  • 2Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Hanoi, Vietnam

  • *chau.nguyen@uni-siegen.de
  • nhviet@iop.vast.ac.vn
  • otfried.guehne@uni-siegen.de

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Issue

Vol. 122, Iss. 24 — 21 June 2019

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