Continuous-Variable Quantum System

Ola Bratteli, Derek W. Robinson

Chenyang Li, Thomas van Himbeeck, Li Qian +1 more

Despite tremendous theoretical and experimental progress in continuous variable (CV) quantum key distribution (QKD), its security has not been rigorously established for practical systems with multiple imperfections. The idea of tagging is widely used in security proofs of discrete variable quantum key distribution with imperfect devices. In this paper, we generalize the tagging idea from discrete variable to continuous variable. Based on untagged signals, we prove the security of the imperfect quantum key distribution system in the most conservative case. By introducing a generic imperfection model, we can evaluate and further incorporate multiple imperfections in the different stages such as modulation, channel and detection. Finally, with this generic model and tagging idea, we can prove the security of continuous variable key distribution system with multiple imperfections. Our case study shows our proofs are able to provide secure keys in the presence of both modulation and detection flaws.

Ola Bratteli, Derek W. Robinson

Carles Rodó

This thesis deals with the study of quantum communication protocols with Continuous Variable (CV) systems. Continuous Variable systems are those described by canonical conjugated coordinates x and p endowed with infinite dimensional Hilbert spaces, thus involving a complex mathematical structure. A special class of CV states, are the so-called Gaussian states. With them, it has been possible to implement certain quantum tasks as quantum teleportation, quantum cryptography and quantum computation with fantastic experimental success. The importance of Gaussian states is two-fold; firstly, its structural mathematical description makes them much more amenable than any other CV system. Secondly, its production, manipulation and detection with current optical technology can be done with a very high degree of accuracy and control. Nevertheless, it is known that in spite of their exceptional role within the space of all Continuous Variable states, in fact, Gaussian states are not always the best candidates to perform quantum information tasks. Thus non-Gaussian states emerge as potentially good candidates for communication and computation purposes.

Victor V. Albert

Re-Bing Wu, Raj Chakrabarti, HERSCHEL A. RABITZ

The methodology of optimal control theory is applied to the problem of implementing quantum gates in continuous-variable (CV) systems with quadratic Hamiltonians. We demonstrate that it is possible to define a fidelity measure for CV gate optimization that is devoid of traps, such that the search for optimal control fields using local algorithms will not be hindered. The optimal control of several quantum computing gates, as well as that of algorithms composed of these primitives, is investigated using several typical physical models and compared for discrete-variable and continuous-variable quantum systems. Numerical simulations indicate that the optimization of generic CV quantum gates is inherently more expensive than that of generic discrete variable quantum gates, but can be routinely achieved for all the major classes of computing primitives. The exact-time controllability of CV systems, hitherto largely ignored in the design of information processing models, is shown to play an important role in determining the maximal achievable gate fidelity. Moreover, the ability to control interactions between qunits can be exploited to delimit the total control fluence. Future experimental model systems should carefully tune these parameters so as to enable the implementation of CV quantum information processing with optimal fidelity.