arXiv subjects
Publications and source records attributed to A. Bisio.
We analytically diagonalize a discrete-time on-site interacting fermionic cellular automaton in the two-particle sector. Important features of the solutions sensibly differ from those of analogous Hamiltonian models. In particular, we found a wider variety of scattering processes, we have bound states for every value of the total momentum, and there exist bound states also in the free case, where the coupling constant is null.
It is shown how a Doubly-Special Relativity model can emerge from a quantum cellular automaton description of the evolution of countably many interacting quantum systems. We consider a one-dimensional automaton that spawns the Dirac evolution in the relativistic limit of small wave-vectors and masses (in Planck units). The assumption of invariance of dispersion relations for boosted observers leads to a non-linear representation of the Lorentz group on the $(ω,k)$ space, with an additional invariant given by the wave-vector $k=π/2$. The space-time reconstructed from the $(ω,k)$ space is intrinsically quantum, and exhibits the phenomenon of relative locality.
A single-party strategy in a multi-round quantum protocol can be implemented by sequential networks of quantum operations connected by internal memories. Here provide the most efficient realization in terms of computational-space resources.
We address the problem of learning an unknown unitary transformation from a finite number of examples. The problem consists in finding the learning machine that optimally emulates the examples, thus reproducing the unknown unitary maximum fidelity. Learning a unitary is equivalent to storing it in the state of a quantum memory (the memory of the learning machine), and subsequently retrieving it. We prove that, whenever the unknown unitary is drawn from a group, the optimal strategy consists in a parallel call of the available uses followed by a "measure-and-rotate" retrieving. Differing from the case of quantum cloning, where the incoherent "measure-and-prepare" strategies are typically suboptimal, in the case of learning the "measure-and-rotate" strategy is optimal even when the learning machine is asked to reproduce a single copy of the unknown unitary. We finally address the problem of the optimal inversion of an unknown unitary evolution, showing also in this case the optimality of the "measure-and-rotate" strategies and applying our result to the optimal approximate realignment of reference frames for quantum communication.
We present the first complete optimization of quantum tomography, for states, POVMs, and various classes of transformations, for arbitrary prior ensemble and arbitrary representation, giving corresponding feasible experimental schemes.