Closed expressions are derived for the quantum measurement statistics of pre-and postselected Gaussian particle beams. The weakness of the preselection step is shown to compete with the nonorthogonality of postselection in a transparent way. The approach is shown to be useful in analyzing postselection-based signal amplification, allowing measurements to be extended far beyond the range of validity of the well-known Aharonov-Albert-Vaidman limit. Additionally, the present treatment connects postselected weak measurement to the topic of phase-contrast microscopy.

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The Born-Markov master equation analysis of the vibrating mirror and photon experiment proposed by Marshall, Simon, Penrose and Bouwmeester is completed by including the important issues of temperature and friction. We find that at the level of cooling available to date, visibility revivals are purely classical, and no quantum effect can be detected by the setup, no matter how strong the photon-mirror coupling is. Checking proposals of universal nonenvironmental decoherence is ruled out by dominating thermal decoherence; a conjectured coordinate-diffusion contribution to decoherence may become observable on reaching moderately low temperatures.PACS numbers: 03.65. Ta, 42.50.Xa, 03.65.Yz The nature of the quantum-classical border along the mass scale is still poorly defined. There remain some 10 orders of magnitude unexplored between the heaviest molecules for which c.o.m. interference has been observed [1], and the lightest nanomechanical objects, for which no quantum behavior has been seen [2]. In trying to close the gap top down, the primary experimental task is to find firm evidence, never seen so far, that the spatial motion of a mass as large as a nanomechanical object does follow the Schrödinger equation, notwithstanding environmental interactions, or noise, which would quickly decohere the wave function. Only having succeeded in suppressing that effect so that interference of a heavy object is detected beyond any doubt, can we turn to checking the presence of spontaneous (also called universal or intrinsic) decoherence [3] on top of the environmental one.An experimentally accessible system with potentialities to achieve the above goal is a photon in a high-quality resonating cavity, coupled by its radiation pressure to a nanomechanical oscillator, carrying one of the mirrors that close the cavity. After pioneering experiments [2] which did not detect any quantum effect on the mirror, as well as thoughtful theoretical analyses [4], a promising idea appeared for bridging the frequency gap and carrying out a genuine quantum test [5,6]. In that proposal, the vibrating mirror closes an optical cavity in arm A of a Michelson interferometer, arm B having another cavity with fixed mirrors. The vibrating mirror is expected to become entangled with a single photon traveling along both arms, the mirror being split into a kind of Schrödinger cat doublet. The interference of the photon is detected with the scope of extracting information about the quantum motion of the mirror. Since the vibrations of the mirror are much slower than the frequency of light, a shift of the interference pattern would be unobservable; the good chance is to record the visibility which is modulated by the motion of the mirror, creating revivals as the components of the superposition overlap again and again.Highly worth doing as it is, this is a very hard experiment, for various reasons. One thing is that high-quality optical resonators are needed to keep the photon alive for several, or at least one, return of the mirror; a less familiar ...

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Within Newton-Schrödinger quantum mechanics which allows gravitational self-interaction, it is shown that a no-split no-collapse measurement scenario is possible. A macroscopic pointer moves at low acceleration, controlled by the Ehrenfest-averaged force acting on it. That makes classicality self-sustaining, resolves Everett's paradox, and outlines a way to spontaneous emergence of quantum randomness. Numerical estimates indicate that enhanced short-range gravitational forces are needed for the scenario to work. The scheme fails to explain quantum nonlocality, including two-detector anticorrelations, which points towards the need of a nonlocal modification of the Newton-Schrödinger coupling scheme.