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Journal of Physics B Atomic Molecular and Optical Physics

Open-loop and closed-loop control of flying qubits

Marco Lucamarini, Giovanni Di Giuseppe, David Vitali, P. Tombesi

Published Jul 25, 2011• 7 citations
Publisher

Abstract

We describe two recent techniques, along with related experiments, to control and reduce the noise affecting a photon polarization qubit. The first is based on the open-loop 'bang–bang' method, where suitably tailored pulses are implemented on the system to prevent polarization decoherence. This requires only passive elements when the physical system is a photon and the operation is performed in space rather than in time. The second technique is based on closed-loop 'asymmetric feedback', where some quantities are measured and used for a real-time correction of the system dynamics. This technique necessarily requires active electronics to work.

DOI
10.1088/0953-4075/44/15/154005

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We describe two recent techniques, along with related experiments, to control and reduce the noise affecting a photon polarization qubit. The first is based on the open-loop 'bang–bang' method, where suitably tailored pulses are implemented on the system to prevent polarization decoherence. This requires only passive elements when the physical system is a photon and the operation is performed in space rather than in time. The second technique is based on closed-loop 'asymmetric feedback', where some quantities are measured and used for a real-time correction of the system dynamics. This technique necessarily requires active electronics to work.
In recent years the interest in the manipulation of quantum systems has furthered new strategies for maintaining their coherence, continuously threatened by unwanted and uncontrollable interactions with the environment. Photons interact weakly with the surroundings. Even so decoherence may significantly affect their polarization state during the propagation within dispersive media because of the unavoidable presence of more than a single frequency in the envelope of the photon pulse. Here we report on a suppression of the polarization decoherence in a ring cavity obtained by properly retooling for the photon qubit the "bang-bang" protection technique already employed for nuclear spins and nuclear-quadrupole qubits. Our results show that bang-bang control can be profitably extended to all quantum information processes involving flying polarization qubits.
Experimental suppression of polarization decoherence in a ring cavity uses a simple open-loop control technique known as bang-bang decou-pling. In recent years new strategies for maintaining the coherence (i.e., constant relative phase) of quantum systems have appeared.1, 2 Even if photons interact weakly with their surroundings, the re-sulting decoherence (i.e., randomization of the relative phase) may significantly affect their polarization state during propaga-tion within dispersive media. We show how the polarization de-coherence of a photon circling in a ring cavity can be suppressed by adapting to the field of quantum optics the open-loop pro-tection technique known as bang-bang (BB). This method is al-ready being employed for nuclear spins and nuclear-quadrupole qubits. It has potential practical application in the field of optical fibers.
Decoherence may significantly affect the polarization state of optical pulses propagating in dispersive media because of the unavoidable presence of more than a single frequency in the envelope of the pulse. Here we report on the suppression of polarization decoherence in a ring cavity obtained by properly retooling for photonic qubits the "bang-bang" protection technique already employed for nuclear spins and nuclear-quadrupole qubits. Our results show that bang-bang control can be profitably extended to quantum information processes involving flying polarization qubits.
We present an open-loop (bang–bang) scheme which drives an open two-level quantum system to any target state, while maintaining quantum coherence throughout the process. The control is illustrated by a realistic simulation for both adiabatic and thermal decoherence. In the thermal decoherence regime, the control achieved by the proposed scheme is qualitatively similar, at the ensemble level, to the control realized by the quantum feedback scheme of Wang, Wiseman and Milburn (2001 Phys. Rev. A 64 063810) for the spontaneous emission of a two-level atom. The performance of the open-loop scheme compares favourably against the quantum feedback scheme with respect to robustness, target fidelity and transition times.
One of the fundamental limitations to high bit rate, long distance, telecommunication in optical fibers is Polarization Mode Dispersion (PMD). Here we show how one can adapt bang-bang control techniques for suppressing the decoherence of polarization states in optical fibers by carrying out controlled rotations of polarization at predetermined locations along the fiber. We propose an experimental proof-ofprinciple demonstration of the idea based on the propagation of polarization qubits in a ring-cavity containing birefringent crystals and wave-plates.
The paper first briefly introduces the current research on quantum control. Then the quantum open-loop control (no measurement introduced) and the closed-loop control (measurement introduced) was compared through a standard model of coherent control. When using quantum closed-loop control, we need measurement which inevitably brings in the reduction noise. This is different from the classical control systems. On the other hand, measurement-based feedback can reduce the influence of the system uncertainties. Thus, there is a tradeoff between the noise influence brought in by the measurement and the information got by the measurement. The paper demonstrate that in the case without decoherence, the quantum closed-loop control is superior to the open-loop control in dealing with the uncertainty in some sense. In the case with decoherence, we discuss the controllability of the quantum control through two performance indices.