High-dimensional entanglement between distant atomic-ensemble memories

Entangled quantum states in high-dimensional space show many advantages compared with entangled states in two-dimensional space. The former enable quantum communication with higher channel capacity, enable more efficient quantum-information processing and are more feasible for closing the detection loophole in Bell test experiments. Establishing high-dimensional entangled memories is essential for long-distance communication, but its experimental realization is lacking. We experimentally established high-dimensional entanglement in orbital angular momentum space between two atomic ensembles separated by 1 m. We reconstructed the density matrix for a three-dimensional entanglement and obtained an entanglement fidelity of (83.9±2.9)%. More importantly, we confirmed the successful preparation of a state entangled in more than three-dimensional space (up to seven-dimensional) using entanglement witnesses. Achieving high-dimensional entanglement represents a significant step toward a high-capacity quantum network.

[1]  Wolfgang Dür,et al.  Quantum Repeaters: The Role of Imperfect Local Operations in Quantum Communication , 1998 .

[2]  G. Guo,et al.  Single-photon-level quantum image memory based on cold atomic ensembles , 2013, Nature Communications.

[3]  G. Buller,et al.  Imaging high-dimensional spatial entanglement with a camera , 2012, Nature Communications.

[4]  Thomas Halfmann,et al.  Storage of images in atomic coherences in a rare-earth-ion-doped solid , 2010 .

[5]  Beatrix C. Hiesmayr,et al.  Complementarity reveals bound entanglement of two twisted photons , 2013 .

[6]  Quentin Glorieux,et al.  Temporally multiplexed storage of images in a gradient echo memory. , 2012, Optics express.

[7]  Félix Bussières,et al.  Quantum storage of photonic entanglement in a crystal , 2010, Nature.

[8]  A. Nicolas,et al.  A reversible optical memory for twisted photons , 2012, CLEO: 2013.

[9]  Charles H. Bennett,et al.  Concentrating partial entanglement by local operations. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[10]  M. Padgett,et al.  Advances in optical angular momentum , 2008 .

[11]  G. Tóth,et al.  Entanglement detection , 2008, 0811.2803.

[12]  Guang-Can Guo,et al.  Multiple image storage and frequency conversion in a cold atomic ensemble , 2013 .

[13]  A. Willner,et al.  Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers , 2013, Science.

[14]  Collapses and revivals of stored orbital angular momentum of light in a cold-atom ensemble , 2009, 0901.0939.

[15]  S. Massar,et al.  Bell inequalities for arbitrarily high-dimensional systems. , 2001, Physical review letters.

[16]  Jian-Wei Pan,et al.  Preparation and storage of frequency-uncorrelated entangled photons from cavity-enhanced spontaneous parametric downconversion , 2011 .

[17]  H. J. Kimble,et al.  The quantum internet , 2008, Nature.

[18]  D. Bruß Characterizing Entanglement , 2001, quant-ph/0110078.

[19]  M J Padgett,et al.  Optical ferris wheel for ultracold atoms. , 2007, Optics express.

[20]  A. Sørensen,et al.  High-capacity spatial multimode quantum memories based on atomic ensembles. , 2011, Physical review letters.

[21]  Stephen M. Barnett,et al.  Violation of Leggett inequalities in orbital angular momentum subspaces , 2010 .

[22]  N Davidson,et al.  Storing images in warm atomic vapor. , 2007, Physical review letters.

[23]  Toward high-dimensional-state quantum memory in a cold atomic ensemble , 2013, 1310.3092.

[24]  Wei Zhang,et al.  Quantum storage of orbital angular momentum entanglement in an atomic ensemble. , 2014, Physical review letters.

[25]  A. Zeilinger,et al.  Generation and confirmation of a (100 × 100)-dimensional entangled quantum system , 2013, Proceedings of the National Academy of Sciences.

[26]  Guangcan Guo,et al.  Realization of a Two-Dimensional Magneto-optical Trap with a High Optical Depth * , 2012 .

[27]  J. Laurat,et al.  Mapping photonic entanglement into and out of a quantum memory , 2007, Nature.

[28]  M. Koashi,et al.  Measuring qutrit-qutrit entanglement of orbital angular momentum states of an atomic ensemble and a photon. , 2009, Physical review letters.

[29]  John C Howell,et al.  Storage and retrieval of multimode transverse images in hot atomic Rubidium vapor. , 2008, Physical review letters.

[30]  Olivier Pinel,et al.  Spatial-mode storage in a gradient-echo memory , 2012, 1204.3981.

[31]  Adetunmise C. Dada,et al.  Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities , 2011, 1104.5087.

[32]  S. Brierley,et al.  Entanglement detection via mutually unbiased bases , 2012, 1202.5058.

[33]  A. Vaziri,et al.  Entanglement of the orbital angular momentum states of photons , 2001, Nature.

[34]  W. Munro,et al.  Qudit quantum-state tomography , 2002 .

[35]  G. Guo,et al.  Quantum Storage of Three-Dimensional Orbital-Angular-Momentum Entanglement in a Crystal. , 2014, Physical review letters.

[36]  A. Zeilinger,et al.  Twisted photon entanglement through turbulent air across Vienna , 2015, Proceedings of the National Academy of Sciences.

[37]  Observation of entanglement witnesses for orbital angular momentum states , 2012 .

[38]  M. Lewenstein,et al.  Detection of entanglement with few local measurements , 2002, quant-ph/0205089.

[39]  Stefano Pironio,et al.  Closing the detection loophole in Bell experiments using qudits. , 2009, Physical review letters.

[40]  F. Bussières,et al.  Broadband waveguide quantum memory for entangled photons , 2010, Nature.

[41]  A. Willner,et al.  Terabit free-space data transmission employing orbital angular momentum multiplexing , 2012, Nature Photonics.

[42]  Light storage based on four-wave mixing and electromagnetically induced transparency in cold atoms , 2012, 1204.0955.

[43]  Multimode image memory based on a cold atomic ensemble , 2012, 1204.1130.

[44]  M. Lewenstein,et al.  Schmidt number witnesses and bound entanglement , 2000, quant-ph/0009109.

[45]  M. Padgett,et al.  Orbital angular momentum: origins, behavior and applications , 2011 .

[46]  Wei Zhang,et al.  Raman quantum memory of photonic polarized entanglement , 2014, 1410.7101.

[47]  A. Nicolas,et al.  A quantum memory for orbital angular momentum photonic qubits , 2013, Nature Photonics.

[48]  Jian-Wei Pan,et al.  Holographic storage of biphoton entanglement. , 2012, Physical review letters.

[49]  Robert Fickler,et al.  Real-Time Imaging of Quantum Entanglement , 2012, Scientific Reports.

[50]  Jonathan Leach,et al.  Generation of orbital angular momentum Bell states and their verification via accessible nonlinear witnesses. , 2013, Physical review letters.