Entanglement witnesses for a class of bipartite states of n x n qubits

We characterize the positive maps detecting the entangled bipartite states of n x n qubits that are diagonal with respect to the orthonormal basis constructed by tensor products of Pauli matrices acting on the totally symmetric state. We then discuss the case n=2 for a class of states completely determined by the geometric patterns of subsets of a 16 point lattice.Comment: 25 page

Direct CP-violation as a test of quantum mechanics

Direct CP-violating effects in the neutral kaon system result in violations of certain Bell-like inequalities. The new experimental results on the determination of the phenomenological parameter epsilon' allow to dismiss a large class of ``hidden variable'' alternatives to quantum mechanics.Comment: 15 pages, Te

On deciding whether a Boolean function is constant or not

We study the probability of making an error if, by querying an oracle a fixed number of times, we declare constant a randomly chosen n-bit Boolean function. We compare the classical and the quantum case, and we determine for how many oracle-queries k and for how many bits n one querying procedure is more efficient than the other.Comment: 8 pages, Latex, 5 figures; accepted for publication on International Journal of Quantum Informatio

Translation Invariant States on Twisted Algebras on a Lattice

We construct an algebra with twisted commutation relations and equip it with the shift. For appropriate irregularity of the non-local commutation relations we prove that the tracial state is the only translation-invariant state

On Some Hamiltonian Models of Brownian Motion

The Langevin and Fokker-Planck structures of two phase-space gaussian Markov processes are investigated in terms of their algebraic properties

The Classical Limit of a Class of Quantum Dynamical Semigroups

The Ghirardi-Rimini-Weber (G.R.W.-) model is studied in the limit ħ → 0 and it is shown that a weak-coupling limit is needed in order to retain its dissipative character at the phase-space level. As a byproduct, solutions of the corresponding Chapman-Kolmogorov differential equation, with linear Liouville term, are provided explicitly

Non-markovian mesoscopic dissipative dynamics of open quantum spin chains

We study the dissipative dynamics of $N$ quantum spins with Lindblad generator consisting of operators scaling as fluctuations, namely with the inverse square-root of $N$. In the large $N$ limit, the microscopic dissipative time-evolution converges to a non-Markovian unitary dynamics on strictly local operators, while at the mesoscopic level of fluctuations it gives rise to a dissipative non-Markovian dynamics. The mesoscopic time-evolution is Gaussian and exhibits either a stable or an unstable asymptotic character; furthermore, the mesoscopic dynamics builds correlations among fluctuations that survive in time even when the original microscopic dynamics is unable to correlate local observables.Comment: 18 page

PULP-HD: Accelerating Brain-Inspired High-Dimensional Computing on a Parallel Ultra-Low Power Platform

Computing with high-dimensional (HD) vectors, also referred to as $\textit{hypervectors}$, is a brain-inspired alternative to computing with scalars. Key properties of HD computing include a well-defined set of arithmetic operations on hypervectors, generality, scalability, robustness, fast learning, and ubiquitous parallel operations. HD computing is about manipulating and comparing large patterns-binary hypervectors with 10,000 dimensions-making its efficient realization on minimalistic ultra-low-power platforms challenging. This paper describes HD computing's acceleration and its optimization of memory accesses and operations on a silicon prototype of the PULPv3 4-core platform (1.5mm$^2$, 2mW), surpassing the state-of-the-art classification accuracy (on average 92.4%) with simultaneous 3.7$\times$ end-to-end speed-up and 2$\times$ energy saving compared to its single-core execution. We further explore the scalability of our accelerator by increasing the number of inputs and classification window on a new generation of the PULP architecture featuring bit-manipulation instruction extensions and larger number of 8 cores. These together enable a near ideal speed-up of 18.4$\times$ compared to the single-core PULPv3