arXiv subjects

Giacomo Mauro D'Ariano

Publications and source records attributed to Giacomo Mauro D'Ariano.

At least 55 records · Page 3Linked to original sources

arXiv2013

The Dirac Quantum Cellular Automaton in one dimension: Zitterbewegung and scattering from potential

We study the dynamical behaviour of the quantum cellular automaton of Refs. [1, 2], which reproduces the Dirac dynamics in the limit of small wavevectors and masses. We present analytical evaluations along with computer simulations, showing how the automaton exhibits typical Dirac dynamical features, as the Zitterbewegung and the scattering behaviour from potential that gives rise to the so-called Klein paradox. The motivation is to show concretely how pure processing of quantum information can lead to particle mechanics as an emergent feature, an issue that has been the focus of solid-state, optical and atomic-physics quantum simulator.

quant-ph↗

arXiv2012

Universality of Computation in Real Quantum Theory

Recently de La Torre et al. [1] reconstructed Quantum Theory from its local structure on the basis of local discriminability and the existence of a one-parameter group of bipartite transformations containing an entangling gate. This result relies on universality of an entangling gate for quantum computation. Here we prove universality of C-NOT with local gates for Real Quantum Theory (RQT), showing that such universality would not be sufficient for the result, whereas local discriminability and the qubit structure play a crucial role. For reversible computation, generally an extra rebit is needed for RQT. As a byproduct we also provide a short proof of universality of C-NOT for CQT.

quant-ph↗

arXiv2012

The Dirac Quantum Automaton: a preview

Quantum Information and the new informational paradigm are entering the domain of quantum field theory and gravity, suggesting the quantum automata framework. The quantum automaton is the minimal-assumption extension to the Planck and ultrarelativistic scales of quantum field theory. It can describe localized states and measurements, which are unmanageable by quantum field theory. The automaton theory is a very promising framework for quantum gravity, since it is quantum ab-initio, with relativistic covariance as emergent and not assumed a priori, it is free from all the problems arising from the continuum, it doesn't suffer violations of causality, and has no divergences. It is the natural scenario to accommodate the quantum holographic principle. Lorentz covariance and all other symmetries are violated in the ultrarelativistic Planckian regime, but are perfectly recovered at the Fermi-scale. In the present report, after briefly reviewing the fundamental principles at the basis of the quantum cellular automata extension of quantum field theory, I will present a preview of recent results on the Fermi scale limit [1] and on the Dirac automaton in two space-dimensions [2]. The automaton in three dimensions is under way.

quant-ph↗

arXiv2012

Emergence of Space-Time from Topologically Homogeneous Causal Networks

We study the emergence of Minkowski space-time from a causal network. Differently from previous approaches, we require the network to be topologically homogeneous, so that the metric is derived from pure event-counting. Emergence from events has an operational motivation in requiring that every physical quantity---including space-time---be defined through precise measurement procedures. Topological homogeneity is a requirement for having space-time metric emergent from the pure topology of causal connections, whereas physically homogeneity corresponds to the universality of the physical law. We analyze in detail the case of 1+1 dimensions. If we consider the causal connections as an exchange of classical information, we can establish coordinate systems via an Einsteinian protocol, and this leads to a digital version of the Lorentz transformations. In a computational analogy, the foliation construction can be regarded as the synchronization with a global clock of the calls to independent subroutines (corresponding to the causally independent events) in a parallel distributed computation. Thus the Lorentz time-dilation emerges as an increased density of leaves within a single tic-tac of a clock, whereas space-contraction results from the corresponding decrease of density of events per leaf. The operational procedure of building up the coordinate system introduces an in-principle indistinguishability between neighboring events, resulting in a network that is coarse-grained, the thickness of the event being a function of the observer's clock.

gr-qc↗

arXiv2012

Quantum computation with programmable connections between gates

A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e. g. in achieving the programmability of permutations of N different unitary channels with 1 use instead of N uses per channel. For this task, a new elemental resource is needed, the "quantum switch", which can be programmed to switch the order of two channels with a single use of each one.

quant-ph↗

arXiv2012

Experimental implementation of unambiguous quantum reading

We provide the optimal strategy for unambiguous quantum reading of optical memories, namely when perfect retrieving of information is achieved probabilistically, for the case where noise and loss are negligible. We describe the experimental quantum optical implementations, and provide experimental results for the single photon case.

quant-ph↗

arXiv2011

Physics as Quantum Information Processing: Quantum Fields as Quantum Automata

Can we reduce Quantum Field Theory (QFT) to a quantum computation? Can physics be simulated by a quantum computer? Do we believe that a quantum field is ultimately made of a numerable set of quantum systems that are unitarily interacting? A positive answer to these questions corresponds to substituting QFT with a theory of quantum cellular automata (QCA), and the present work is examining this hypothesis. These investigations are part of a large research program on a "quantum-digitalization" of physics, with Quantum Theory as a special theory of information, and Physics as emergent from the same quantum-information processing. A QCA-based QFT has tremendous potential advantages compared to QFT, being quantum "ab-initio" and free from the problems plaguing QFT due to the continuum hypothesis. Here I will show how dynamics emerges from the quantum processing, how the QCA can reproduce the Dirac-field phenomenology at large scales, and the kind of departures from QFT that that should be expected at a Planck-scale discreteness. I will introduce the notions of linear field quantum automaton and local-matrix quantum automaton, in terms of which I will provide the solution to the Feynman's problem about the possibility of simulating a Fermi field with a quantum computer.

quant-ph↗

arXiv2011

Memory cost of quantum protocols

In this paper we consider the problem of minimizing the ancillary systems required to realize an arbitrary strategy of a quantum protocol, with the assistance of classical memory. For this purpose we introduce the notion of memory cost of a strategy, which measures the resources required in terms of ancillary dimension. We provide a condition for the cost to be equal to a given value, and we use this result to evaluate the cost in some special cases. As an example we show that any covariant protocol for the cloning of a unitary transformation requires at most one ancillary qubit. We also prove that the memory cost has to be determined globally, and cannot be calculated by optimizing the resources independently at each step of the strategy.

quant-ph↗

arXiv2011

Quantum learning algorithms for quantum measurements

We study quantum learning algorithms for quantum measurements. The optimal learning algorithm is derived for arbitrary von Neumann measurements in the case of training with one or two examples. The analysis of the case of three examples reveals that, differently from the learning of unitary gates, the optimal algorithm for learning of quantum measurements cannot be parallelized, and requires quantum memories for the storage of information.

quant-ph↗

arXiv2011

Extremal quantum protocols

Generalized quantum instruments correspond to measurements where the input and output are either states or more generally quantum circuits. These measurements describe any quantum protocol including games, communications, and algorithms. The set of generalized quantum instruments with a given input and output structure is a convex set. Here we investigate the extremal points of this set for the case of finite dimensional quantum systems and generalized instruments with finitely many outcomes. We derive algebraic necessary and sufficient conditions for extremality.

quant-ph↗

arXiv2011

Tradeoff between energy and error in the discrimination of quantum-optical devices

We address the problem of energy-error tradeoff in the discrimination between two linear passive quantum optical devices with a single use. We provide an analytical derivation of the optimal strategy for beamsplitters and an iterative algorithm converging to the optimum in the general case. We then compare the optimal strategy with a simpler strategy using coherent input states and homodyne detection. It turns out that the former requires much less energy in order to achieve the same performances.

quant-ph↗

arXiv2011

Informational power of quantum measurements

We introduce the informational power of a quantum measurement as the maximum amount of classical information that the measurement can extract from any ensemble of quantum states. We prove the additivity by showing that the informational power corresponds to the classical capacity of a quantum-classical channel. We restate the problem of evaluating the informational power as the maximization of the accessible information of a suitable ensemble. We provide a numerical algorithm to find an optimal ensemble, and quantify the informational power.

quant-ph↗

arXiv2011

Quantum error correction with degenerate codes for correlated noise

We introduce a quantum packing bound on the minimal resources required by nondegenerate error correction codes for any kind of noise. We prove that degenerate codes can outperform nondegenerate ones in the presence of correlated noise, by exhibiting examples where the quantum packing bound is violated.

quant-ph↗

arXiv2011

Cloning of a quantum measurement

We analyze quantum algorithms for cloning of a quantum measurement. Our aim is to mimic two uses of a device performing an unknown von Neumann measurement with a single use of the device. When the unknown device has to be used before the bipartite state to be measured is available we talk about 1 -> 2 learning of the measurement, otherwise the task is called 1 -> 2 cloning of a measurement. We perform the optimization for both learning and cloning for arbitrary dimension of the Hilbert space. For 1 -> 2 cloning we also propose a simple quantum network that realizes the optimal strategy.

quant-ph↗

arXiv2010

Physics as quantum information processing

The experience from Quantum Information has lead us to look at Quantum Theory (QT) and the whole Physics from a different angle. The information-theoretical paradigm---"It from Bit'---prophesied by John Archibald Wheeler is relentlessly advancing. Recently it has been shown that QT is derivable from pure informational principles. The possibility that there is only QT at the foundations of Physics has been then considered, with space-time, Relativity, quantization rules and Quantum Field Theory (QFT) emerging from a quantum-information processing. The resulting theory is a discrete version of QFT with automatic relativistic invariance, and without fields, Hamiltonian, and quantization rules. In this paper I review some recent advances on these lines. In particular: i) How space-time and relativistic covariance emerge from the quantum computation; ii) The derivation of the Dirac equation as free information flow, without imposing Lorentz covariance; iii) the information-theoretical meaning of inertial mass and Planck constant; iv) An observable consequence of the theory: a mass-dependent refraction index of vacuum. I will then conclude with two possible routes to Quantum Gravity.

quant-ph↗

arXiv2010

Physics as Information Processing

I review some recent advances in foundational research at Pavia QUIT group. The general idea is that there is only Quantum Theory without quantization rules, and the whole Physics---including space-time and relativity--is emergent from the quantum-information processing. And since Quantum Theory itself is axiomatized solely on informational principles, the whole Physics must be reformulated in information-theoretical terms: this is the "It from Bit of J. A. Wheeler. The review is divided into four parts: a) the informational axiomatization of Quantum Theory; b) how space-time and relativistic covariance emerge from quantum computation; c) what is the information-theoretical meaning of inertial mass and of $\hbar$, and how the quantum field emerges; d) an observational consequence of the new quantum field theory: a mass-dependent refraction index of vacuum. I will conclude with the research lines that will follow in the immediate future.

quant-ph↗

arXiv2010

The Quantum Field as a Quantum Computer

It is supposed that at very small scales a quantum field is an infinite homogeneous quantum computer. On a quantum computer the information cannot propagate faster than $c=a/τ$, $a$ and $τ$ being the minimum space and time distances between gates, respectively. It is shown that the information flow satisfies a Dirac equation, with speed $v=ζc$ and $ζ=ζ(m)$ mass-dependent. For $a/τ=c$ the speed of light $ζ^{-1}$ is a vacuum refraction index increasing monotonically from $ζ^{-1}(0)=1$ to $ζ^{-1}(M)=\infty$, $M$ being the Planck mass for $2a$ the Planck length.

quant-ph↗

arXiv2010

Information - Disturbance Tradeoff in the Estimation of a Unitary Transformation

We address the problem of the information-disturbance trade-off associated to the estimation of a quantum transformation, and show how the extraction of information about the a black box causes a perturbation of the corresponding input-output evolution. In the case of a black box performing a unitary transformation, randomly distributed according to the invariant measure, we give a complete solution of the problem, deriving the optimal trade-off curve and presenting an explicit construction of the optimal quantum network.

quant-ph↗