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Quantum Information and Computation

Feedback control for communication with non-orthogonal states

JacobsKurt

Published Jan 1, 2007• 0 citations
Publisher

Abstract

Communicating classical information with a quantum system involves the receiver making a measurement on the system so as to distinguish as well as possible the alphabet of states used by the sender...
DOI
10.5555/2011706.2011714

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In the conventional picture of quantum feedback control, sensors perform measurements on the system, a classical controller processes the results of the measurements, and actuators supply semiclassical potentials to alter the behavior of the quantum system. In this picture, the sensors tend to destroy coherence in the process of making measurements, and although the controller can use the actuators to act coherently on the quantum system, it is processing and feeding back classical information. This paper proposes an alternative method for quantum feedback control, in which the sensors, controller, and actuators are quantum systems that interact coherently with the system to be controlled. In this picture, the controller gets, processes, and feeds back quantum information. Controllers that operate using such quantum feedback loops can perform tasks such as entanglement transfer that are not possible using classical feedback. Necessary and sufficient conditions are presented for Hamiltonian quantum systems to be controllable and observable using both classical and quantum feedback.
Communicating classical information with a quantum system involves the receiver making a measurement on the system so as to distinguish as well as possible the alphabet of states used by the sender. We consider the situation in which this measurement takes an appreciable time. In this case the measurement must be described by a continuous measurement process. We consider a continuous implementation of the optimal measurement for distinguishing between two non-orthogonal states, and show that feedback control can be used during this measurement to increase the rate at which the information regarding the initial preparation is obtained. We show that while the maximum obtainable increase is modest, the effect is purely quantum mechanical in the sense that the enhancement is only possible when the initial states are non-orthogonal. We find further that the enhancement in the rate of information gain is achieved at the expense of reducing the total information which the measurement can extract in the long-time limit.
Quantum communication protocols require efficient detection schemes to maximize the information transfer rate between the sender and the receiver. To this aim, we have demonstrated that weak-field receivers, merging wave-like and particle-like features, can be considered as a valid alternative to already existing receivers, such as optical homodyne detection. To better emphasize the potential of our receiver, in this work we consider a proof of concept for quaternary communication based on coherent states with the same amplitude and different phase values. The encoding in phase requires a fine control of phase noise obtained through a feedback system. The results achieved in terms of mutual information and secret key generation rate encourage further increase of the alphabet towards an approximately continuous phase modulation.
Quantum systems may be used to transmit classical information. To do this the sender encodes information by preparing the system in one of an alphabet of possible states, and sends it to the receiver. The receiver then performs a measurement on the system in order to obtain information about which state was sent. Here we describe a general bound on the information which is accessible to the receiver in such a channel when the receivers measurement is noisy. In addition to extracting classical information, measurements also reduce the entropy of a quantum system. This is important, for example, in quantum feedback control. We discuss two corollaries of the information bound that involve this entropy reduction.