Theoretical investigation of hybrid approaches to quantum information processing and quantum communication utilizing both discrete and continuous quantum variables
Final Report Abstract
Theoretical research conducted in my Emmy Noether group has followed mainly two directions. One that aims at proposing feasible and relatively practical protocols for quantum communication over long distances, of the order of 1000 km and more. The other direction was devoted to implementations of small-scale quantum computing. In either of these advanced quantum applications, state-of-the-art quantum optical resources and techniques were to be employed. Specific approaches to these communication and computation protocols are those based upon quantum repeaters and cluster-state processing, respectively. Important side lines of the two above-mentioned main directions were concerned with the optical implementability of various types of quantum measurements, such as qubit Bell measurements (important for quantum repeaters) or non-Gaussian continuous-variable measurements (important for cluster computation), and with classifications and proposals of optical quantum error correction / detection schemes. Since quantum error correction and entanglement distillation are known to be impossible in the Gaussian regime, for these tasks, non-Gaussian measurements such as discrete photon number detections may be performed on Gaussian resource states. Similarly, such measurements enable one to achieve universal quantum-state processing through Gaussian cluster states. Ultimately, continuous and discrete encodings can be combined in a hybrid quantum repeater where atomic spins are used for storage and light fields for the distribution of quantum correlations. In general, this so-called hybrid approach, utilizing at the same time discrete and continuous encodings and measurements, has been pursued in our group in order to circumvent the known limitations on advanced quantum applications when only linear optical resources are available. Compared to my original Emmy Noether proposal, in work package block A.) on “Resource-related classification of quantum information tasks”, the main focus during the entire funding period has been on quantum error detection and correction, and most results have been obtained in that context. Various non-Gaussian extensions of the most practical schemes based upon Gaussian elements have been investigated such as photon subtraction on mixed Gaussian entangled states for entanglement distillation in quantum communication. In the context of small-scale quantum computation, we found that nonlinear bosonic quantum gates (such as the important Kerr interaction) can be decomposed into elementary linear and nonlinear gates much more efficiently than previously thought. Important results have been found concerning blocks B.) and C.) with regards to the optimization of optical hybrid approaches to quantum communication and computation, respectively. In the former case, for example, different variations of the original so-called hybrid quantum repeater scheme have been shown to significantly enhance the trade-off between through-put (distant-entangled pair creation rates) and output fidelities as well as feasibilities of potential realizations. In the context of small-scale computation, based upon our theory, an experiment was conducted at the University of Tokyo in which the ultimate building block for a linear, fully measurement-controlled, single-mode quantum information processor was demonstrated. Investigations towards more realistic manifestations of quantum communication and computation are still on the way after the end of the Emmy Noether project (2012) in the new group of the Emmy Noether grant holder at the University of Mainz. In particular, as envisaged in the original Emmy Noether proposal for block D.), an ultra-efficient distribution scheme for photonic entangled states or photonic qubit states through realistic optical fiber channels over long distances has been proposed now. As this scheme, in principle, approaches quantum communication rates as obtainable in classical communication, the temporal and spectral widths of the quantum–information carrying optical pulses become important. Therefore, dispersion and even nonlinear effects on the optical pulses traveling along the fiber channel are to be taken into account. This was originally intended for the final year of the Emmy Noether project, but will now be part of a broader research programme. What was achieved in the final year of the Emmy Noether project is, as initially proposed, a further investigation into optical quantum error correction codes and entanglement distillation schemes as well as a more conceptual study on the notion of genuinely hybrid entangled states (discrete-continuous entangled states with no finite-dimensional support).
Publications
- “Demonstration of a quantum nondemolition sum gate”, Phys. Rev. Lett. 101, 250501 (2008)
J. Yoshikawa, Y. Miwa, A. Huck, U. L. Andersen, P. van Loock, and A. Furusawa
- „Hybrid quantum computation in quantum optics“, Phys. Rev. A 78, 022303 (2008)
P. van Loock, W. J. Munro, Kae Nemoto, T. P. Spiller, S. L. Braunstein, G. J. Milburn
- “Demonstration of a universal one-way quantum quadratic phase gate”, Phys. Rev. A 80, 050303(R) (2009)
Y. Miwa, J. Yoshikawa, P. van Loock, and A. Furusawa
- “Quantum error correction beyond qubits”, Nature Physics 5, 541 (2009)
Takao Aoki, G. Takahashi, T. Kajiya, Jun-ichi Yoshikawa, S. L. Braunstein, P. van Loock, and Akira Furusawa
- “Near-unit-fidelity entanglement distribution scheme using Gaussian communication”, Phys. Rev. A 81, 060303(R) (2010)
L. Praxmeyer and P. van Loock
- “Universal linear Bogoliubov transformations through one-way quantum computation”, Phys. Rev. A 81, 032315 (2010)
R. Ukai, J. Yoshikawa, N. Iwata, P. van Loock, and A. Furusawa
- “Demonstration of unconditional one-way quantum computations for continuous variables”, Phys. Rev. Lett. 106, 240504 (2011)
Ryuji Ukai, Noriaki Iwata, Yuji Shimokawa, Seiji C. Armstrong, Alberto Politi, Jun-ichi Yoshikawa, P. van Loock, and Akira Furusawa
- “How to Decompose Arbitrary Continuous-Variable Quantum Operations”, Phys. Rev. Lett.107, 170501 (2011)
S. Sefi and P. van Loock
- “Classifying, quantifying, and witnessing qudit-qumode hybrid entanglement”, Phys. Rev. A 85, 032307 (2012)
Karsten Kreis and Peter van Loock
(See online at https://doi.org/10.1103/PhysRevA.85.032307) - “Unconditional generation of bright coherent non-Gaussian light from exciton-polariton condensates”, Phys. Rev. B 87, 201301(R) (2012)
Tim Byrnes, Yoshihisa Yamamoto, and Peter van Loock
(See online at https://doi.org/10.1103/PhysRevB.87.201301)
