One-way Einstein-Podolsky-Rosen Steering

Einstein-Podolsky-Rosen steering is a form of quantum nonlocality exhibiting an inherent asymmetry between the observers, Alice and Bob. A natural question is then whether there exist entangled states which are one-way steerable, that is, Alice can steer Bob's state, but it is impossible for Bob to steer the state of Alice. So far, such a phenomenon has been demonstrated for continuous variable systems, but with a strong restriction on allowed measurements, namely, considering only Gaussian measurements. Here we present a simple class of entangled two-qubit states which are one-way steerable, considering arbitrary projective measurements. This shows that the nonlocal properties of entangled states can be fundamentally asymmetrical.

[1]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[2]  E. Schrödinger.  Discussion of Probability Relations between Separated Systems , 1935, Mathematical Proceedings of the Cambridge Philosophical Society.

[3]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[4]  J. Bell.  On the Einstein-Podolsky-Rosen paradox , 1964 .

[5]  Werner,et al.  Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. , 1989, Physical review. A, General physics.

[6]  Reid,et al.  Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification. , 1989, Physical review. A, General physics.

[7]  Konrad Banaszek,et al.  TESTING QUANTUM NONLOCALITY IN PHASE SPACE , 1999 .

[8]  J. Barrett.  Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality , 2001, quant-ph/0107045.

[9]  A C Doherty,et al.  Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox. , 2007, Physical review letters.

[10]  G. Tóth,et al.  Noise robustness of the nonlocality of entangled quantum states. , 2007, Physical review letters.

[11]  W. P. Bowen,et al.  Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications , 2008, 0806.0270.

[12]  H. M. Wiseman,et al.  Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox , 2009, 0907.1109.

[13]  D. J. Saunders,et al.  Experimental EPR-steering using Bell-local states , 2009, 0909.0805.

[14]  A. Ferris,et al.  Asymmetric Gaussian steering: When Alice and Bob disagree , 2009, 0906.4851.

[15]  P. Drummond,et al.  Einstein-Podolsky-Rosen entanglement strategies in two-well Bose-Einstein condensates. , 2011, Physical review letters.

[16]  D. J. Saunders,et al.  Arbitrarily loss-tolerant Einstein-Podolsky-Rosen steering allowing a demonstration over 1 km of optical fiber with no detection loophole , 2011 .

[17]  Rupert Ursin,et al.  Loophole-free Einstein–Podolsky–Rosen experiment via quantum steering , 2011, 1111.0760.

[18]  V. Scarani,et al.  One-sided device-independent quantum key distribution: Security, feasibility, and the connection with steering , 2011, 1109.1435.

[19]  Sae Woo Nam,et al.  Conclusive quantum steering with superconducting transition-edge sensors , 2011, Nature Communications.

[20]  R. Werner,et al.  Observation of one-way Einstein–Podolsky–Rosen steering , 2012, Nature Photonics.

[21]  M. Olsen.  Asymmetric Gaussian harmonic steering in second-harmonic generation , 2013, 1308.4293.

[22]  M. Reid,et al.  Towards an Einstein–Podolsky–Rosen paradox between two macroscopic atomic ensembles at room temperature , 2013, 1310.7296.

[23]  Matthew F. Pusey,et al.  Negativity and steering: A stronger Peres conjecture , 2013, 1305.1767.

[24]  N. Brunner,et al.  Genuine hidden quantum nonlocality. , 2013, Physical review letters.

[25]  Miguel Navascués,et al.  Quantifying Einstein-Podolsky-Rosen steering. , 2013, Physical review letters.

[26]  M. Lewenstein,et al.  Quantum Entanglement , 2020, Quantum Mechanics.