Non-destructive weak measurement of a photonic qubit
by
G J Pryde
Centre for Quantum Computer Technology, The University of Queensland, Brisbane, Qld, 4072, Australia
Coauthors: J. L. O’Brien, A. G. White, S. D. Bartlett and T. C. Ralph

Measuring the polarisation of a single photon typically results in its destruction. We propose, demonstrate, and completely characterise a non-deterministic, quantum non-demolition (QND) scheme for realising such a measurement non-destructively [1]. Our scheme uses linear optics and conditional projective measurement of a second meter photon to realise a QND measurement of the signal qubit, after the two qubits have interacted. The scheme is non-deterministic – it works with non-unit probability, but whenever a single photon is detected in the meter output it is known to have worked. We vary this QND measurement continuously into the weak regime, and use it to perform a non-destructive test of complementarity in quantum mechanics. Our scheme non-deterministically realises the most advanced general measurement of a qubit to date: it is non-destructive, can be made in any basis, and with arbitrary strength. Recently it has been recognized that linear optics QND measurements of photon number may be useful for scalable all-optical quantum computing [2].

At the heart of quantum mechanics is the principle that measuring a system perturbs it. QND measurements arrange for this measurement back-action to feed only into unwanted observables. The most advanced demonstrations have been in quantum optics, mostly continuous variable experiments. To date: there have been few discrete variable demonstrations; no measurement on a superposition state; and no universal set of QND measures exists. Here we propose and demonstrate a QND measurement of a polarisation encoded single-photon qubit, which can be prepared in any state. We introduce a universal set of fidelity measures which characterise how well the QND satisfies the requirements: (1) The measurement is correctly correlated with the input; (2) Repeated measurement gives the same result; and (3) The measurement does not alter the quantity being measured.

This QND measurement can be thought of as a interferometric “which path” measurement where the paths are the polarisation modes of the signal. An important application of this device is to realise a non-destructive weak measurement of photon polarisation. We have achieved this by rotating the polarisation of the meter photon from a state where an ideal QND measurement is realised to one where no measurement is made. We observe the effect of complementarity between “which path” knowledge and interferometric visibility. Finally we discuss how this non-destructive weak measurement could be used for quantum control of a single quantum system.

[1] G. J. Pryde, J. L. O'Brien, A. G. White, S. D. Bartlett and T. C. Ralph, Phys. Rev. Lett., in press (quant-ph/0312048)

[2] J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph and D. Branning, Nature, 426, 264 (2003)

Date received: March 31, 2004