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

It has been argued [T. Rudolph and B.C. Sanders, Phys. Rev. Lett. {\bf 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, {\bf 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 {\bf 60}, 4083 (1999)] and Berry and myself [Phys. Rev. A {\bf 65}, 043803 (2002)] to show that a Heisenberg-limited laser with a mean photon number $\mu$ can synchronize $M$ independent clocks each with a mean-square error of $\sqrt{M}/4\mu$ radians$^2$.Comment: 14 pages, no figures, some equations this time. For proceedings of SPIE conference "Fluctuations and Noise 2003

Maximum information gain in weak or continuous measurements of qudits: complementarity is not enough

To maximize average information gain for a classical measurement, all outcomes of an observation must be equally likely. The condition of equally likely outcomes may be enforced in quantum theory by ensuring that one's state $\rho$ is maximally different, or complementary, to the measured observable. This requires the ability to perform unitary operations on the state, conditioned on the results of prior measurements. We consider the case of measurement of a component of angular momentum for a qudit (a $D$-dimensional system, with $D=2J+1$). For weak or continuous-in-time (i.e. repeated weak) measurements, we show that the complementarity condition ensures an average improvement, in the rate of purification, of only 2. However, we show that by choosing the optimal control protocol of this type, one can attain the best possible scaling, $O(D^{2})$, for the average improvement. For this protocol the acquisition of information is nearly deterministic. Finally we contrast these results with those for complementarity-based protocols in a register of qbits.Comment: 21 pages, 21 figures. V2 published versio

Quantum feedback for rapid state preparation in the presence of control imperfections

Quantum feedback control protocols can improve the operation of quantum devices. Here we examine the performance of a purification protocol when there are imperfections in the controls. The ideal feedback protocol produces an $x$ eigenstate from a mixed state in the minimum time, and is known as rapid state preparation. The imperfections we examine include time delays in the feedback loop, finite strength feedback, calibration errors, and inefficient detection. We analyse these imperfections using the Wiseman-Milburn feedback master equation and related formalism. We find that the protocol is most sensitive to time delays in the feedback loop. For systems with slow dynamics, however, our analysis suggests that inefficient detection would be the bigger problem. We also show how system imperfections, such as dephasing and damping, can be included in model via the feedback master equation.Comment: 15 pages, 6 figures and 2 tables. V2 the published version, fig. 1 corrected and some minor changes to the tex

Reply to Norsen's paper "Are there really two different Bell's theorems?"

Yes. That is my polemical reply to the titular question in Travis Norsen's self-styled "polemical response to Howard Wiseman's recent paper." Less polemically, I am pleased to see that on two of my positions --- that Bell's 1964 theorem is different from Bell's 1976 theorem, and that the former does not include Bell's one-paragraph heuristic presentation of the EPR argument --- Norsen has made significant concessions. In his response, Norsen admits that "Bell's recapitulation of the EPR argument in [the relevant] paragraph leaves something to be desired," that it "disappoints" and is "problematic". Moreover, Norsen makes other statements that imply, on the face of it, that he should have no objections to the title of my recent paper ("The Two Bell's Theorems of John Bell"). My principle aim in writing that paper was to try to bridge the gap between two interpretational camps, whom I call 'operationalists' and 'realists', by pointing out that they use the phrase "Bell's theorem" to mean different things: his 1964 theorem (assuming locality and determinism) and his 1976 theorem (assuming local causality), respectively. Thus, it is heartening that at least one person from one side has taken one step on my bridge. That said, there are several issues of contention with Norsen, which we (the two authors) address after discussing the extent of our agreement with Norsen. The most significant issues are: the indefiniteness of the word 'locality' prior to 1964; and the assumptions Einstein made in the paper quoted by Bell in 1964 and their relation to Bell's theorem.Comment: 13 pages (arXiv version) in http://www.ijqf.org/archives/209