Entanglement from longitudinal and scalar photons

Abstract

The covariant quantization of the electromagnetic field in the Lorentz gauge gives rise to longitudinal and scalar photons in addition to the usual transverse photons. It is shown here that the exchange of longitudinal and scalar photons can produce entanglement between two distant atoms or harmonic oscillators. The form of the entangled states produced in this way is very different from that obtained in the Coulomb gauge, where the longitudinal and scalar photons do not exist. A generalized gauge transformation is used to show that all physically observable effects are the same in the two gauges, despite the differences in the form of the entangled states. An approach of this kind may be useful for a covariant description of the dynamics of quantum information processing.

Macroscopic state interferometry over large distances using state discrimination

“…Decoherence due to photon loss is an important consideration in any approach for transmitting optical entangled states over large distances. Here we model the effects of photon loss by a series of beam splitters, although it can be shown that similar results would be obtained in the presence of absorption by two-level atoms [12,13]. A low rate of decoherence due to photon loss can be achieved for these Schrodinger-cat states when their separation in phase space is relatively small [14].…”

Time-bin-entangled photon holes

“…These states have now been observed in the laboratory [2], and their nonclassical properties have been experimentally demonstrated [3]. It has recently been shown that these states can be relatively insensitive to loss and amplification noise [4], which may be beneficial for quantum communication applications such as quantum key distribution [5].…”

“…Indeed, as the coherent state background is replaced by single-photon state back-ground, a basic time-bin EPH state becomes fully equivalent to an antisymmetric time-bin entangled photon-pair state. This relatively simple scenario provides insight into the properties of more general EPH states, such as energy-time EPH's in coherent-state background [1,4], which do not have direct equivalences with entangled photon-pair states.…”

Mathematical constraint on functions with continuous second partial derivatives

“…where ' ' f x x denotes the second partial derivative of f with respect to ' x as in Eq. ( 9). Here the integration by parts is valid if ' ( ', ') Integration by parts also requires [6] that both functions be continuously differentiable ( ).…”

“…The covariant form of Eq. ( 22) may be useful in quantum field theory, which was the original motivation [9] for my interest in this topic. '  r r Eq.…”