Quantum parameter estimation with imperfect reference frames

Abstract

Quantum metrology studies quantum strategies which enable us to outperform their classical counterparts. In this framework, the existence of perfect classical reference frames is usually assumed. However, such ideal reference frames might not always be available. The reference frames required in metrology strategies can either degrade or become misaligned during the estimation process. We investigate how the imperfectness of reference frames leads to noise which in general affects the ultimate precision limits in measurement of physical parameters. Moreover, since quantum parameter estimation can be phrased as a quantum communication protocol between two parties, our results provide deeper insight into quantum communication protocols with misaligned reference frames. Our framework allows for the study of noise on the efficiency of such schemes.2 system or a quantum harmonic oscillator as carrier of her message. The message can be encoded as a phase parameter in the state of the spin − 1 2 particle or in the state of the quantum harmonic oscillator. Bob then performs a measurement on the system in order to decode the message, i.e. the encoded phase parameter. The quality of this communication protocol can be improved by optimization of both stages of the protocol, namely Alice's encoding process and Bob's decoding process. However, standard approaches to quantum communication, such as encoding qubits into polarization degree of freedom of photons, require that all parties have knowledge of a shared reference frame. This means that in the absence of such knowledge, the involved parties need to initially establish aligned reference frames. Despite the considerable amount of progress in the development of protocols for aligning reference frames such as clock synchronization and Cartesian frame alignment [4], maintaining aligned reference frames is still a large obstacle in achieving such tasks. For instance when the

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Quantizing time: Interacting clocks and systems

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