Optical coherence and teleportation: Why a laser is a clock, not a quantum channel

摘要

It has been argued [T. Rudolph and B.C. Sanders, Phys. Rev. Lett. 87, 077903 (2001)] that continuous-variable quantum teleportation at optical frequencies has not been achieved because the source used (a laser) was not 'truly coherent'. Van Enk, and Fuchs [Phys. Rev. Lett, 88, 027902 (2002)], while arguing against Rudolph and Sanders, also accept that an 'absolute phase' is achievable, even if it has not been achieved yet. I will argue to the contrary that 'true coherence' or 'absolute phase' is always illusory, as the concept of absolute time on a scale beyond direct human experience is meaningless. All we can ever do is to use an agreed time standard. In this context, a laser beam is fundamentally as good a 'clock' as any other. I explain in detail why this claim is true, and defend my argument against various objections. In the process I discuss super-selection rules, quantum channels, and the ultimate limits to the performance of a laser as a clock. For this last topic I use some earlier work by myself [Phys. Rev. A 60, 4083 (1999)] and Berry and myself [Phys. Rev. A 65, 043803 (2002)] to show that a Heisenberg-limited laser with a mean photon number μ can synchronize M independent clocks each with a mean-square error of M~(1/2)/4μ radians.