Quantum Computation Violates Mirror Symmetry

Abstract

The CNOT gate is asymmetric with respect to parity. It requires interaction with the environment, and cannot be realized as an isolated quantum collision.An elastic collision between spinning particles might be viewed as a kind of logic gate, where the spin directions represent different bit values. Since each particle is a representation of the Poincaré group, characterized by mass, spin, and helicity, it is most natural to classify the various transitions in terms of helicity amplitudes. (1) This formalism provides a completely general description of quantum collisions involving spinning particles.For example, proton-proton scattering pp → pp is routinely analyzed in terms of five independent amplitudes. (1) Using a polarized beam, a polarized target, and polarized detectors, the cross section at a particular scattering angle is given by the square of the helicity amplitude for the polarizations selected. Measurements taken at many different angles could be converted into partial waves, but that is not necessary.Consider the general case AB → CD, where A = C and B = D. For particles with two possible spin states, there are a total of 16 helicity amplitudes. In Table 1, the amplitudes F 1 through F 6 are independent, while the other ten dependent amplitudes are related by mirror symmetry (parity), which flips all the helicities, and by time-reversal symmetry, which reverses the order of the initial and final states.

Quantum one-way permutation over the finite field of two elements

“…Otherwise, x 2 + x + 1 is entangled (or non-separable) because the probability of factoring it is not greater than 1 poly(x) . This multiplicative inverse polynomial distance between an entangled state and the separable set reduces the separability criterion in bidirectional quantum controlled schemes [35,36,37] to an NP-hard problem [42].…”