We propose a procedure for defining all single-photon observables in terms of Positive-Operator Valued Measures (POVMs), in particular spin and position. We identify the suppression of $0$ -helicity photon states as a projection from an extended Hilbert space onto the photon Hilbert space. We show that all single-photon observables are in general described by POVMs, obtained by applying this projection to opportune Projection-Valued Measures (PVMs), defined on the extended Hilbert space. The POVMs associated to momentum and helicity reduce to PVMs, unlike those associated to position and spin, this fact reflecting the intrinsic unsharpness of these observables. We finally extensively study the preparation uncertainty relations for position and momentum and the probability distribution of spin, exploring single photon Gaussian states for several choices of spin and polarization.We propose a procedure for defining all single-photon observables in terms of Positive-Operator Valued Measures (POVMs), in particular spin and position. We identify the suppression of $0$-helicity photon states as a projection from an extended Hilbert space onto the photon Hilbert space. We show that all single-photon observables are in general described by POVMs, obtained by applying this projection to opportune Projection-Valued Measures (PVMs), defined on the extended Hilbert space. The POVMs associated to momentum and helicity reduce to PVMs, unlike those associated to position and spin, this fact reflecting the intrinsic unsharpness of these observables. We finally extensively study the preparation uncertainty relations for position and momentum and the probability distribution of spin, exploring single photon Gaussian states for several choices of spin and polarization.

arXiv:1403.6405Journal of Physics A Mathematical and TheoreticalJun 12, 20156 citations

Photon position measure

Margaret Hawton

The positive operator valued measure (POVM) for a photon counting array detector is derived and found to equal photon flux density integrated over pixel area and measurement time. Since photon flux density equals number density multiplied by the speed of light, this justifies theoretically the observation that a photon counting array provides a coarse-grained measurement of photon position. The POVM obtained here can be written as a set of projectors onto a basis of localized states, consistent with the description of photon position in a recent quantum imaging proposal [Tsang, Phys. Rev. Lett. 102, 253601 (2009)]. The wave function that describes a photon counting experiment is the projection of the photon state vector onto this localized basis. Collapse is to the electromagnetic vacuum and not to a localized state, thus violating the textbook rules of quantum mechanics but compatible with the theory of generalized observables and the nonlocalizability of an incoming photon.The positive operator valued measure (POVM) for a photon counting array detector is derived and found to equal photon flux density integrated over pixel area and measurement time. Since photon flux density equals number density multiplied by the speed of light, this justifies theoretically the observation that a photon counting array provides a coarse-grained measurement of photon position. The POVM obtained here can be written as a set of projectors onto a basis of localized states, consistent with the description of photon position in a recent quantum imaging proposal [Tsang, Phys. Rev. Lett. 102, 253601 (2009)]. The wave function that describes a photon counting experiment is the projection of the photon state vector onto this localized basis. Collapse is to the electromagnetic vacuum and not to a localized state, thus violating the textbook rules of quantum mechanics but compatible with the theory of generalized observables and the nonlocalizability of an incoming photon.

arXiv:1007.0460Physical Review AJul 30, 20108 citations

A new position operator for the photon

J. Bertrand

Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fieldsMay 1, 19737 citations

On the photon vector potential

B. I. Makshantsev, V.B. Makshantsev

Chemical PhysicsSep 1, 20011 citation

From the observer to the photon, from time to eternity

Guillermo Omar Decoppet

The null interval of light implies that the photon's journey accumulates no time: emission, path and absorption are a single instant. This does not mean that the photon is everywhere without direction: it is present throughout its path at once, outside time, and its trajectory has direction; the succession of positions does not occur in its proper time ---which it does not possess--- but in the proper time of observers. From this structure it follows that the simultaneity of positions is only possible outside time, and that the photon is its typical case: a complete journey that manifests as a localized event when measured.The null interval of light implies that the photon's journey accumulates no time: emission, path and absorption are a single instant. This does not mean that the photon is everywhere without direction: it is present throughout its path at once, outside time, and its trajectory has direction; the succession of positions does not occur in its proper time ---which it does not possess--- but in the proper time of observers. From this structure it follows that the simultaneity of positions is only possible outside time, and that the photon is its typical case: a complete journey that manifests as a localized event when measured.

Oct 19, 20260 citations

We propose a procedure for defining all single-photon observables in terms of Positive-Operator Valued Measures (POVMs), in particular spin and position. We identify the suppression of

0

-helicity photon states as a projection from an extended Hilbert space onto the photon Hilbert space. We show that all single-photon observables are in general described by POVMs, obtained by applying this projection to opportune Projection-Valued Measures (PVMs), defined on the extended Hilbert space. The POVMs associated to momentum and helicity reduce to PVMs, unlike those associated to position and spin, this fact reflecting the intrinsic unsharpness of these observables. We finally extensively study the preparation uncertainty relations for position and momentum and the probability distribution of spin, exploring single photon Gaussian states for several choices of spin and polarization.