On entanglement and Lorentz transformations

We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as viewed from two inertial frames moving with constant velocity with respect to each other. Though the finite dimensional matrices describing the Lorentz transformations are non-unitary, each single particle state of the entangled pair undergoes an effective, momentum dependent, local unitary rotation, thereby preserving the entanglement fidelity of the bipartite state. The details of how these unitary transformations are manifested are explicitly worked out for the Bell states comprised of massive spin 1/2 particles and massless photon polarizations. The relevance of this work to non-inertial frames is briefly discussed.

Topographic plasticity in primary visual cortex is mediated by local corticocortical connections

The placement of monocular laser lesions in the adult cat retina produces a lesion projection zone (LPZ) in primary visual cortex (V1) in which the majority of neurons have a normally located receptive field (RF) for stimulation of the intact eye and an ectopically located RF ( displaced to intact retina at the edge of the lesion) for stimulation of the lesioned eye. Animals that had such lesions for 14 - 85 d were studied under halothane and nitrous oxide anesthesia with conventional neurophysiological recording techniques and stimulation of moving light bars. Previous work suggested that a candidate source of input, which could account for the development of the ectopic RFs, was long-range horizontal connections within V1. The critical contribution of such input was examined by placing a pipette containing the neurotoxin kainic acid at a site in the normal V1 visual representation that overlapped with the ectopic RF recorded at a site within the LPZ. Continuation of well defined responses to stimulation of the intact eye served as a control against direct effects of the kainic acid at the LPZ recording site. In six of seven cases examined, kainic acid deactivation of neurons at the injection site blocked responsiveness to lesioned-eye stimulation at the ectopic RF for the LPZ recording site. We therefore conclude that long-range horizontal projections contribute to the dominant input underlying the capacity for retinal lesion-induced plasticity in V1.

Communicating continuous quantum variables between different Lorentz frames

We show how to communicate Heisenberg-limited continuous (quantum) variables between Alice and Bob in the case where they occupy two inertial reference frames that differ by an unknown Lorentz boost. There are two effects that need to be overcome: the Doppler shift and the absence of synchronized clocks. Furthermore, we show how Alice and Bob can share Doppler-invariant entanglement, and we demonstrate that the protocol is robust under photon loss.

Lorentz invariant intrinsic decoherence

We present a Lorentz invariant extension of a previous model for intrinsic decoherence (Milburn 1991 Phys. Rev. A 44 5401). The extension uses unital semigroup representations of space and time translations rather than the more usual unitary representation, and does the least violence to physically important invariance principles. Physical consequences include a modification of the uncertainty principle and a modification of field dispersion relations, similar to modifications suggested by quantum gravity and string theory, but without sacrificing Lorentz invariance. Some observational signatures are discussed.