The Bennett-Brassard cryptographic scheme (BB84) needs two bases, at least one of them linearly polarized. The problem is that linear polarization formulated in terms of helicities is not a relativistically covariant notion: State which is linearly polarized in one reference frame becomes depolarized in another one. We show that a relativistically moving receiver of information should define linear polarization with respect to projection of Pauli-Lubanski's vector in a principal null direction of the Lorentz transformation which defines the motion, and not with respect to the helicity basis. Such qubits do not depolarize. PACS numbers: PACS numbers: 03.67.Dd, 03.65.UdIn non-relativistic quantum mechanics a generic state of a free particle with spin takes the form where spin and momentum degrees of freedom are non-entangled, i.e.This is the reason why it is possible to base the concept of a non-relativistic qubit on a 2-dimensional Hilbert space.In particular, observables asociated with spin are always of the form A⊗1, where 1 = d 3 p|p p| is the identity in momentum space and A stands for a spin operator. The formula Tr ρ(A ⊗ 1) = Tr r ρ r A. allows to define states of qubits in terms of 2 × 2 reduced density matrices.In relativistic quantum mechanics a generic state satisfiesThe origin of this property is very deeply rooted in the structure of unitary representations of the Poincaré group. A qubit which in one reference frame takes the form (1) will be seen in a form (2) by another observer. A Poincaré transformation necessarily involves multiplication by p-dependent SU (2) matrices, a fact making the form (1) non-covariant. Definitions of qubits in terms of reduced density matrices with traced-out momenta are no longer justified. This is why quantum information theory based on such a formal notion of qubit [1,2,3,4] is in danger of internal physical inconsistency. Constructing nonzero-spin unitary representations of the Poincaré group we always encounter certain spinor structure. The simplest representation corresponds to mass m and spin 1/2. Whenever we write the state in a form (2) we implicitly choose a 'spin quantization axis' and spin is here associated with the second Casimir invariant of the group, W a W a , where W a is the Pauli-Lubanski (PL) vector.The most popular choice of quantization axis corresponds to a timelike direction t a = (1, 0, 0, 0). The resulting spin operator t a W a is proportional to the helicity (in order to obtain directly the helicity one should choose t a = (1/|p|, 0, 0, 0)). In application to quantum cryptography we need several different yes-no observables and helicity eigenstates are not sufficient. Natural candidates for such yes-no observables are projectors on linear combinations of opposite helicities, i.e. linear polarizations. The problem with linear polarizations defined in terms of helicities is that different momentum components undergo different SU (2) transformations. In the photon case the SU (2) transformations are diagonal and multiply opposite helicities by phas...

The 1996 Brune {\it et al.} experiment on vacuum Rabi oscillation is analyzed by means of alternative models of atom-reservoir interaction. Agreement with experimental Rabi oscillation data can be obtained if one defines jump operators in the dressed-state basis, and takes into account thermal fluctuations between dressed states belonging to the same manifold. Such low-frequency transitions could be ignored in a closed cavity, but the cavity employed in the experiment was open, which justifies our assumption. The cavity quality factor corresponding to the data is $Q=3.31\cdot 10^{10}$, whereas $Q$ reported in the experiment was $Q=7\cdot 10^7$. The rate of decoherence arising from opening of the cavity can be of the same order as an analogous correction coming from finite time resolution $\Delta t$ (formally equivalent to collisional decoherence). Peres-Horodecki separability criterion shows that the rate at which the atom-field state approaches a separable state is controlled by fluctuations between dressed states from the same manifold, and not by the rate of transitions towards the ground state. In consequence, improving the $Q$ factor we do not improve the coherence properties of the cavity.Comment: typo in eq. (60) corrected; (older comments: 14 figures (1 added), value of Q improved, a section on the Peres-Horodecki test of separability added, various small improvements; v3 includes discussion of finite time resolution, v4 includes microscopic derivation of the master equation

The paper continues the analysis of vacuum Rabi oscillations we started in Part I [Phys. Rev. A 79, 033836 (2009)]. Here we concentrate on experimental consequences for cavity QED of two different classes of representations of harmonic oscillator Lie algebras. The zero-temperature master equation, derived in Part I for irreducible representations of the algebra, is reformulated in a reducible representation that models electromagnetic fields by a gas of harmonic oscillator wave packets. The representation is known to introduce automatic regularizations that in irreducible representations would have to be justified by ad hoc arguments. Predictions based on this representation are characterized in thermodynamic limit by a single parameter ς, responsible for collapses and revivals of Rabi oscillations in exact vacuum. Collapses and revivals disappear in the limit ς → ∞. Observation of a finite ς would mean that cavity quantum fields are described by a non-Wightmanian theory, where vacuum states are zero-temperature Bose-Einstein condensates of a N -particle bosonic oscillator gas and, thus, are non-unique. The data collected in the experiment of Brune et al. [Phys. Rev. Lett. 76, 1800(1996] are consistent with any ς > 400.