Experimental Greenberger–Horne–Zeilinger entanglement beyond qubits

Quantum entanglement is important for emerging quantum technologies such as quantum computation and secure quantum networks. To boost these technologies, a race is currently ongoing to increase the number of particles in multiparticle entangled states, such as Greenberger–Horne–Zeilinger (GHZ) states. An alternative route is to increase the number of entangled quantum levels. Here, we overcome present experimental and technological challenges to create a three-particle GHZ state entangled in three levels for every particle. The resulting qutrit-entangled states are able to carry more information than entangled states of qubits. Our method, inspired by the computer algorithm Melvin, relies on a new multi-port that coherently manipulates several photons simultaneously in higher dimensions. The realization required us to develop a new high-brightness four-photon source entangled in orbital angular momentum. Our results allow qualitatively new refutations of local-realistic world views. We also expect that they will open up pathways for a further boost to quantum technologies.A three-dimensionally entangled Greenberger–Horne–Zeilinger state, where all three photons reside in a qutrit space, is generated by developing a new multi-port in combination with a novel four-photon source entangled in orbital angular momentum.

[1]  Marek Żukowski,et al.  Multisetting Greenberger-Horne-Zeilinger theorem , 2013, 1303.7222.

[2]  H. Weinfurter,et al.  Multiphoton entanglement and interferometry , 2003, 0805.2853.

[3]  T. Monz,et al.  14-Qubit entanglement: creation and coherence. , 2010, Physical review letters.

[4]  Matej Pivoluska,et al.  Measurements in two bases are sufficient for certifying high-dimensional entanglement , 2017, Nature Physics.

[5]  A. Zeilinger,et al.  High-Dimensional Single-Photon Quantum Gates: Concepts and Experiments. , 2017, Physical review letters.

[6]  H. Weinfurter,et al.  Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement , 2000, Nature.

[7]  Jay Lawrence,et al.  Mermin inequalities for perfect correlations in many-qutrit systems , 2017, 1701.08331.

[8]  Valerio Scarani,et al.  Security proof for quantum key distribution using qudit systems , 2010, 1003.5464.

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

[10]  A. Zeilinger,et al.  Going Beyond Bell’s Theorem , 2007, 0712.0921.

[11]  Robert Fickler,et al.  Cyclic transformation of orbital angular momentum modes , 2015, 1512.02696.

[12]  Andrew Forbes,et al.  Simultaneous entanglement swapping of multiple orbital angular momentum states of light , 2016, Nature Communications.

[13]  S. Barnett,et al.  Measuring the orbital angular momentum of a single photon. , 2002, Physical review letters.

[14]  Marek Zukowski,et al.  Greenberger-Horne-Zeilinger theorem for N-partite quDits , 2013 .

[15]  A. Zeilinger,et al.  Multi-photon entanglement in high dimensions , 2015, Nature Photonics.

[16]  Weidong Tang,et al.  Multisetting Greenberger-Horne-Zeilinger paradoxes , 2013, 1303.6740.

[17]  John M. Martinis,et al.  State preservation by repetitive error detection in a superconducting quantum circuit , 2015, Nature.

[18]  Jian-Wei Pan,et al.  Experimental Ten-Photon Entanglement. , 2016, Physical review letters.

[19]  Jay Lawrence,et al.  Rotational covariance and Greenberger-Horne-Zeilinger theorems for three or more particles of any dimension , 2013, 1308.3808.

[20]  Mario Krenn,et al.  Orbital angular momentum of photons and the entanglement of Laguerre–Gaussian modes , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[21]  Jian-Wei Pan,et al.  10-Qubit Entanglement and Parallel Logic Operations with a Superconducting Circuit. , 2017, Physical review letters.

[22]  Robert W Boyd,et al.  Efficient separation of the orbital angular momentum eigenstates of light , 2013, Nature Communications.

[23]  A. Zeilinger,et al.  Automated Search for new Quantum Experiments. , 2015, Physical review letters.

[24]  Mario Krenn,et al.  Entanglement by Path Identity. , 2016, Physical review letters.

[25]  Martin Rötteler,et al.  Factoring with Qutrits: Shor's Algorithm on Ternary and Metaplectic Quantum Architectures , 2016, ArXiv.

[26]  Kiel T. Williams,et al.  Extreme quantum entanglement in a superposition of macroscopically distinct states. , 1990, Physical review letters.

[27]  Hong,et al.  Measurement of subpicosecond time intervals between two photons by interference. , 1987, Physical review letters.

[28]  J. P. Woerdman,et al.  Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[29]  A. Shimony,et al.  Bell’s theorem without inequalities , 1990 .

[30]  Ben Reichardt,et al.  Fault-Tolerant Quantum Computation , 2016, Encyclopedia of Algorithms.

[31]  B. Hiesmayr,et al.  Observation of Four-Photon Orbital Angular Momentum Entanglement. , 2015, Physical review letters.

[32]  V. Buzek,et al.  Quantum secret sharing , 1998, quant-ph/9806063.

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

[34]  Mario Krenn,et al.  Quantum Experiments and Graphs: Multiparty States as Coherent Superpositions of Perfect Matchings. , 2017, Physical review letters.

[35]  Marcus Huber,et al.  Structure of multidimensional entanglement in multipartite systems. , 2012, Physical review letters.

[36]  Mario Krenn,et al.  Quantum Experiments and Graphs II: Computation and State Generation with Probabilistic Sources and Linear Optics , 2018 .

[37]  Andrew Forbes,et al.  Engineering two-photon high-dimensional states through quantum interference , 2016, Science Advances.

[38]  M. J. Padgett,et al.  Bounds and optimisation of orbital angular momentum bandwidths within parametric down-conversion systems , 2011, 1112.3910.

[39]  Anton Zeilinger,et al.  A quantum router for high-dimensional entanglement , 2016, 1605.05947.

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

[41]  Zhengang Shi,et al.  Scheme for n phase gates operation and one-step preparation of highly entangled cluster state , 2012 .

[42]  Derryck T. Reid,et al.  Pure down-conversion photons through sub-coherence-length domain engineering , 2017, 1704.03683.

[43]  H. Weinfurter,et al.  Observation of three-photon Greenberger-Horne-Zeilinger entanglement , 1998, quant-ph/9810035.