Giacomo D'Ariano | University of Pavia (original) (raw)

Papers by Giacomo D'Ariano

Research paper thumbnail of Extremal covariant quantum operations and POVM's

arXiv: Quantum Physics, 2003

We consider the convex sets of QO's (quantum operations) and POVM's (positive operator va... more We consider the convex sets of QO's (quantum operations) and POVM's (positive operator valued measures) which are covariant under a general finite-dimensional unitary representation of a group. We derive necessary and sufficient conditions for extremality, and give general bounds for ranks of the extremal POVM's and QO's. Results are illustrated on the basis of simple examples.

Research paper thumbnail of Quantum Theory is an Information Theory

Foundations of Physics, 2015

We derive quantum theory from purely informational principles. Five elementary axioms-causality, ... more We derive quantum theory from purely informational principles. Five elementary axioms-causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning-define a broad class of theories of information processing that can be regarded as standard. One postulate-purification-singles out quantum theory within this class.

Research paper thumbnail of A solvable model for a system of Coulomb particles in R 2 with homotopically nontrivial phase space

... Page 6. 186 C. AGNES, C. BLTZANO, G. D'ARIANO and M. ICASETTI ... The hypergeometrie... more ... Page 6. 186 C. AGNES, C. BLTZANO, G. D'ARIANO and M. ICASETTI ... The hypergeometrie function in (15) is in fact a complete elliptic integral of the first kind, namely K([solt), which for ISol-~ 1-behaves like a logarithmic function: [ln4--ln(1-[So[t)+ ]. Thus ~(s0) develops an ...

Research paper thumbnail of Classicality without local discriminability: Decoupling entanglement and complementarity

Physical Review A

An operational probabilistic theory where all systems are classical, and all pure states of compo... more An operational probabilistic theory where all systems are classical, and all pure states of composite systems are entangled, is constructed. The theory is endowed with a rule for composing an arbitrary number of systems, and with a nontrivial set of transformations. Hence, we demonstrate that the presence of entanglement is independent of the existence of incompatible measurements. We then study a variety of phenomena occurring in the theory, some of them contradicting both classical and quantum theories, including cloning, entanglement swapping, dense coding, additivity of classical capacities, nonmonogamous entanglement, hypersignaling. We also prove the existence, in the theory, of a universal processor. The theory is causal and satisfies the no-restriction hypothesis. At the same time, it violates a number of information-theoretic principles enjoyed by quantum theory, most notably, local discriminability, purity of parallel composition of states, and purification. Moreover, we introduce an exhaustive procedure to construct generic operational probabilistic theories, and a sufficient set of conditions to verify their consistency. In addition, we prove a characterization theorem for the parallel composition rules of arbitrary theories, and specialize it to the case of bilocal-tomographic theories. We conclude pointing out some open problems. In particular, on the basis of the fact that every separable state of the theory is a statistical mixture of entangled states, we formulate a no-go conjecture for the existence of a local-realistic ontological model.

Research paper thumbnail of Classical theories with entanglement

Physical Review A

We investigate operational probabilistic theories where the pure states of every system are the v... more We investigate operational probabilistic theories where the pure states of every system are the vertices of a simplex. A special case of such theories is that of classical theories, i.e. simplicial theories whose pure states are jointly perfectly discriminable. The usual Classical Theory satisfies also local discriminability. However, simplicial theories-including the classical ones-can violate local discriminability, thus admitting of entangled states. First, we prove sufficient conditions for the presence of entangled states in arbitrary probabilistic theories. Then, we prove that simplicial theories are necessarily causal, and this represents a no-go theorem for conceiving non-causal classical theories. We then provide necessary and sufficient conditions for simplicial theories to exhibit entanglement, and classify their system-composition rules. We conclude proving that, in simplicial theories, an operational formulation of the superposition principle cannot be satisfied, and that no mixed state admits of a purification. Our results hold also in the general case where the sets of states fail to be convex.

Research paper thumbnail of Quantum Information and Foundations

Entropy

The new era of quantum foundations, fed by the quantum information theory experience and opened i... more The new era of quantum foundations, fed by the quantum information theory experience and opened in the early 2000s by a series of memorable papers [...]

Research paper thumbnail of Chirality from quantum walks without a quantum coin

Physical Review A

Quantum walks (QWs) describe the evolution of quantum systems on graphs. An intrinsic degree of f... more Quantum walks (QWs) describe the evolution of quantum systems on graphs. An intrinsic degree of freedom-called the coin and represented by a finite-dimensional Hilbert space-is associated to each node. Scalar quantum walks are QWs with a one-dimensional coin. We propose a general strategy allowing one to construct scalar QWs on a broad variety of graphs, which admit embedding in Eulidean spaces, thus having a direct geometric interpretation. After reviewing the technique that allows one to regroup cells of nodes into new nodes, transforming finite spatial blocks into internal degrees of freedom, we prove that no QW with a two-dimensional coin can be derived from an isotropic scalar QW in this way. Finally we show that the Weyl and Dirac QWs can be derived from scalar QWs in spaces of dimension up to three, via our construction.

Research paper thumbnail of Solutions of a Two-Particle Interacting Quantum Walk

Entropy

We study the solutions of an interacting Fermionic cellular automaton which is the analogue of th... more We study the solutions of an interacting Fermionic cellular automaton which is the analogue of the Thirring model with both space and time discrete. We present a derivation of the two-particle solutions of the automaton recently in the literature, which exploits the symmetries of the evolution operator. In the two-particle sector, the evolution operator is given by the sequence of two steps, the first one corresponding to a unitary interaction activated by two-particle excitation at the same site, and the second one to two independent one-dimensional Dirac quantum walks. The interaction step can be regarded as the discrete-time version of the interacting term of some Hamiltonian integrable system, such as the Hubbard or the Thirring model. The present automaton exhibits scattering solutions with nontrivial momentum transfer, jumping between different regions of the Brillouin zone that can be interpreted as Fermion-doubled particles, in stark contrast with the customary momentum-exchange of the one-dimensional Hamiltonian systems. A further difference compared to the Hamiltonian model is that there exist bound states for every value of the total momentum and of the coupling constant. Even in the special case of vanishing coupling, the walk manifests bound states, for finitely many isolated values of the total momentum. As a complement to the analytical derivations we show numerical simulations of the interacting evolution.

Research paper thumbnail of Teoria Fisica e Sua Realificazione. Caso DI Studio: La Causalità

Istituto Lombardo - Accademia di Scienze e Lettere - Incontri di Studio

I will discuss realism of classical and quantum theories, assessing the untenability of the objec... more I will discuss realism of classical and quantum theories, assessing the untenability of the object ontology, and proposing its substitution with the notion of system used in operational theories, notion that represents a theoretical connection between two events. Within operational theories the distinction between theory and objective reality is well defined: the theory provides the mathematical description of systems and events, and predicts the joint probability of the events; objective reality is identified with the collection of events that actually occurred. I then analyse some cases of realification of the theory – namely the fallacy of identifying theory with reality. In particular, the cases of the notion of causality and causal connection between events are analysed, emphasising their purely theoretical nature, contrarily to the widespread connotation of objectivity. I re-establish the role of causality in physics as a theorem of quantum theory, and hence also of classical ...

Research paper thumbnail of Isotropic quantum walks on lattices and the Weyl equation

Physical Review A

We present a thorough classification of the isotropic quantum walks on lattices of dimension d = ... more We present a thorough classification of the isotropic quantum walks on lattices of dimension d = 1,2,3 with a coin system of dimension s = 2. For d = 3 there exist two isotropic walks, namely, the Weyl quantum walks presented in the work of D'Ariano and Perinotti [G. M. D'Ariano and P. Perinotti, Phys. Rev. A 90, 062106 (2014)], resulting in the derivation of the Weyl equation from informational principles. The present analysis, via a crucial use of isotropy, is significantly shorter and avoids a superfluous technical assumption, making the result completely general.

Research paper thumbnail of Quantum cellular automata and free quantum field theory

Research paper thumbnail of Thirring quantum cellular automaton

Physical Review A

We analytically diagonalize a discrete-time on-site interacting fermionic cellular automaton in t... more 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.

Research paper thumbnail of Critical behavior of the order parameter at antiferrodistortive transitions with cubic fluctuations

Physical Review B

The temperature dependence of the generalized order parameter, namely the rotation angle of the N... more The temperature dependence of the generalized order parameter, namely the rotation angle of the Nb06 octahedron, at the antiferrodistortive transition in the perovskite crystal NaNbO3, is derived through the high-resolution analysis of the second-order quadrupole shift of Na NMR spectra. The second-order character of the transition and the small value of the apparent critical exponent for the order parameter are critically discussed in the framework of a renormalization-group approach for a system with an effective Hamiltonian of cubic symmetry and an anisotropic dispersion in the static structure factor.

Research paper thumbnail of Tomographic measurement of the density matrix of the radiation field

Quantum and Semiclassical Optics: Journal of the European Optical Society Part B

Abstracr Recently a novel homodine tomographic technique has been proposed which allows us to det... more Abstracr Recently a novel homodine tomographic technique has been proposed which allows us to detect the density matrix experimentally in terms of averages on data. The method has been further exrended to a general matrix element (+l6lq) of the density operator 6, along with the possibility of using low-efficiency detectors. In this paper this technique is remusidered as a new genuine quantum measurement. Numerical resuits for measured probabilities are given. and the mechanism underlying the genesation of statistical m r s in the measured matrix is illusirated. It is shown that the data prQcessing of the novel technique can also be used as a new imaging algorithm for conventional tomography.

Research paper thumbnail of Time evolution of an anharmonic oscillator interacting with a squeezed bath

Quantum and Semiclassical Optics: Journal of the European Optical Society Part B

The evolution of a single mode of the electromagnetic field interacting with a squeezed bath in a... more The evolution of a single mode of the electromagnetic field interacting with a squeezed bath in a Kerr medium is considered. The solution of the corresponding master equation is given numerically. It is argued that the creation of a superposition state (Schrödinger's cat) is better achieved in presence of a squeezed reservoir than of a thermal one.

Research paper thumbnail of Reconstructing the density operator by using generalized field quadratures

Quantum and Semiclassical Optics: Journal of the European Optical Society Part B

The Wigner function for one and two-mode quantum systems is explicitely expressed in terms of the... more The Wigner function for one and two-mode quantum systems is explicitely expressed in terms of the marginal distribution for the generic linearly transformed quadratures. Then, also the density operator of those systems is written in terms of the marginal distribution of these quadratures. Some examples to apply this formalism, and a reduction to the usual optical homodyne tomography are considered.

Research paper thumbnail of Functional quantum computing: An optical approach

Physical Review A, 2016

Recent theoretical investigations treat quantum computations as functions, quantum processes whic... more Recent theoretical investigations treat quantum computations as functions, quantum processes which operate on other quantum processes, rather than circuits. Much attention has been given to the N − switch function which takes N black box quantum operators as input, coherently permutes their ordering, and applies the result to a target quantum state. This is something which cannot be equivalently done using a quantum circuit. Here, we propose an all-optical system design which implements coherent operator permutation for an arbitrary number of input operators.

Research paper thumbnail of Optimal covariant quantum networks

AIP Conference Proceedings, 2009

A sequential network of quantum operations is efficiently described by its quantum comb [1], a no... more A sequential network of quantum operations is efficiently described by its quantum comb [1], a non-negative operator with suitable normalization constraints. Here we analyze the case of networks enjoying symmetry with respect to the action of a given group of physical transformations, introducing the notion of covariant combs and testers, and proving the basic structure theorems for these objects. As an application, we discuss the optimal alignment of reference frames (without preestablished common references) with multiple rounds of quantum communication, showing that i) allowing an arbitrary amount of classical communication does not improve the alignment, and ii) a single round of quantum communication is sufficient.

Research paper thumbnail of Quantum cellular automaton theory of light

Annals of Physics, 2016

We present a quantum theory of light based on quantum cellular automata (QCA). This approach allo... more We present a quantum theory of light based on quantum cellular automata (QCA). This approach allows us to have a thorough quantum theory of free electrodynamics encompassing an hypothetical discrete Planck scale. The theory is particularly relevant because it provides predictions at the macroscopic scale that can be experimentally tested. We show how, in the limit of small wavevector k, the free Maxwell's equations emerge from two Weyl QCAs derived from informational principles in Ref. [1]. Within this framework the photon is introduced as a composite particle made of a pair of correlated massless Fermions, and the usual Bosonic statistics is recovered in the low photon density limit. We derive the main phenomenological features of the theory, consisting in dispersive propagation in vacuum, the occurrence of a small longitudinal polarization, and a saturation effect originated by the Fermionic nature of the photon. We then discuss whether these effects can be experimentally tested, and observe that only the dispersive effects are accessible with current technology, from observations of arrival times of pulses originated at cosmological distances.

Research paper thumbnail of Quantum from Principles

Fundamental Theories of Physics, 2015

ABSTRACT Quantum theory was discovered in an adventurous way, under the urge to solve puzzles-lik... more ABSTRACT Quantum theory was discovered in an adventurous way, under the urge to solve puzzles-like the spectrum of the blackbody radiation-that haunted the physics community at the beginning of the 20th century. It soon became clear, though, that quantum theory was not just a theory of specific physical systems, but rather a new language of universal applicability. Can this language be reconstructed from first principles? Can we arrive at it from logical reasoning, instead of ad hoc guesswork? A positive answer was provided in Refs. [1, 2], where we put forward six principles that identify quantum theory uniquely in a broad class of theories. We first defined a class of "theories of information", constructed as extensions of probability theory in which events can be connected into networks. In this framework, we formulated the six principles as rules governing the control and the accessibility of information. Directly from these rules, we reconstructed a number of quantum information features, and eventually, the whole Hilbert space framework. In short, our principles characterize quantum theory as the theory of information that allows for maximal control of randomness.

Research paper thumbnail of Extremal covariant quantum operations and POVM's

arXiv: Quantum Physics, 2003

We consider the convex sets of QO's (quantum operations) and POVM's (positive operator va... more We consider the convex sets of QO's (quantum operations) and POVM's (positive operator valued measures) which are covariant under a general finite-dimensional unitary representation of a group. We derive necessary and sufficient conditions for extremality, and give general bounds for ranks of the extremal POVM's and QO's. Results are illustrated on the basis of simple examples.

Research paper thumbnail of Quantum Theory is an Information Theory

Foundations of Physics, 2015

We derive quantum theory from purely informational principles. Five elementary axioms-causality, ... more We derive quantum theory from purely informational principles. Five elementary axioms-causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning-define a broad class of theories of information processing that can be regarded as standard. One postulate-purification-singles out quantum theory within this class.

Research paper thumbnail of A solvable model for a system of Coulomb particles in R 2 with homotopically nontrivial phase space

... Page 6. 186 C. AGNES, C. BLTZANO, G. D'ARIANO and M. ICASETTI ... The hypergeometrie... more ... Page 6. 186 C. AGNES, C. BLTZANO, G. D'ARIANO and M. ICASETTI ... The hypergeometrie function in (15) is in fact a complete elliptic integral of the first kind, namely K([solt), which for ISol-~ 1-behaves like a logarithmic function: [ln4--ln(1-[So[t)+ ]. Thus ~(s0) develops an ...

Research paper thumbnail of Classicality without local discriminability: Decoupling entanglement and complementarity

Physical Review A

An operational probabilistic theory where all systems are classical, and all pure states of compo... more An operational probabilistic theory where all systems are classical, and all pure states of composite systems are entangled, is constructed. The theory is endowed with a rule for composing an arbitrary number of systems, and with a nontrivial set of transformations. Hence, we demonstrate that the presence of entanglement is independent of the existence of incompatible measurements. We then study a variety of phenomena occurring in the theory, some of them contradicting both classical and quantum theories, including cloning, entanglement swapping, dense coding, additivity of classical capacities, nonmonogamous entanglement, hypersignaling. We also prove the existence, in the theory, of a universal processor. The theory is causal and satisfies the no-restriction hypothesis. At the same time, it violates a number of information-theoretic principles enjoyed by quantum theory, most notably, local discriminability, purity of parallel composition of states, and purification. Moreover, we introduce an exhaustive procedure to construct generic operational probabilistic theories, and a sufficient set of conditions to verify their consistency. In addition, we prove a characterization theorem for the parallel composition rules of arbitrary theories, and specialize it to the case of bilocal-tomographic theories. We conclude pointing out some open problems. In particular, on the basis of the fact that every separable state of the theory is a statistical mixture of entangled states, we formulate a no-go conjecture for the existence of a local-realistic ontological model.

Research paper thumbnail of Classical theories with entanglement

Physical Review A

We investigate operational probabilistic theories where the pure states of every system are the v... more We investigate operational probabilistic theories where the pure states of every system are the vertices of a simplex. A special case of such theories is that of classical theories, i.e. simplicial theories whose pure states are jointly perfectly discriminable. The usual Classical Theory satisfies also local discriminability. However, simplicial theories-including the classical ones-can violate local discriminability, thus admitting of entangled states. First, we prove sufficient conditions for the presence of entangled states in arbitrary probabilistic theories. Then, we prove that simplicial theories are necessarily causal, and this represents a no-go theorem for conceiving non-causal classical theories. We then provide necessary and sufficient conditions for simplicial theories to exhibit entanglement, and classify their system-composition rules. We conclude proving that, in simplicial theories, an operational formulation of the superposition principle cannot be satisfied, and that no mixed state admits of a purification. Our results hold also in the general case where the sets of states fail to be convex.

Research paper thumbnail of Quantum Information and Foundations

Entropy

The new era of quantum foundations, fed by the quantum information theory experience and opened i... more The new era of quantum foundations, fed by the quantum information theory experience and opened in the early 2000s by a series of memorable papers [...]

Research paper thumbnail of Chirality from quantum walks without a quantum coin

Physical Review A

Quantum walks (QWs) describe the evolution of quantum systems on graphs. An intrinsic degree of f... more Quantum walks (QWs) describe the evolution of quantum systems on graphs. An intrinsic degree of freedom-called the coin and represented by a finite-dimensional Hilbert space-is associated to each node. Scalar quantum walks are QWs with a one-dimensional coin. We propose a general strategy allowing one to construct scalar QWs on a broad variety of graphs, which admit embedding in Eulidean spaces, thus having a direct geometric interpretation. After reviewing the technique that allows one to regroup cells of nodes into new nodes, transforming finite spatial blocks into internal degrees of freedom, we prove that no QW with a two-dimensional coin can be derived from an isotropic scalar QW in this way. Finally we show that the Weyl and Dirac QWs can be derived from scalar QWs in spaces of dimension up to three, via our construction.

Research paper thumbnail of Solutions of a Two-Particle Interacting Quantum Walk

Entropy

We study the solutions of an interacting Fermionic cellular automaton which is the analogue of th... more We study the solutions of an interacting Fermionic cellular automaton which is the analogue of the Thirring model with both space and time discrete. We present a derivation of the two-particle solutions of the automaton recently in the literature, which exploits the symmetries of the evolution operator. In the two-particle sector, the evolution operator is given by the sequence of two steps, the first one corresponding to a unitary interaction activated by two-particle excitation at the same site, and the second one to two independent one-dimensional Dirac quantum walks. The interaction step can be regarded as the discrete-time version of the interacting term of some Hamiltonian integrable system, such as the Hubbard or the Thirring model. The present automaton exhibits scattering solutions with nontrivial momentum transfer, jumping between different regions of the Brillouin zone that can be interpreted as Fermion-doubled particles, in stark contrast with the customary momentum-exchange of the one-dimensional Hamiltonian systems. A further difference compared to the Hamiltonian model is that there exist bound states for every value of the total momentum and of the coupling constant. Even in the special case of vanishing coupling, the walk manifests bound states, for finitely many isolated values of the total momentum. As a complement to the analytical derivations we show numerical simulations of the interacting evolution.

Research paper thumbnail of Teoria Fisica e Sua Realificazione. Caso DI Studio: La Causalità

Istituto Lombardo - Accademia di Scienze e Lettere - Incontri di Studio

I will discuss realism of classical and quantum theories, assessing the untenability of the objec... more I will discuss realism of classical and quantum theories, assessing the untenability of the object ontology, and proposing its substitution with the notion of system used in operational theories, notion that represents a theoretical connection between two events. Within operational theories the distinction between theory and objective reality is well defined: the theory provides the mathematical description of systems and events, and predicts the joint probability of the events; objective reality is identified with the collection of events that actually occurred. I then analyse some cases of realification of the theory – namely the fallacy of identifying theory with reality. In particular, the cases of the notion of causality and causal connection between events are analysed, emphasising their purely theoretical nature, contrarily to the widespread connotation of objectivity. I re-establish the role of causality in physics as a theorem of quantum theory, and hence also of classical ...

Research paper thumbnail of Isotropic quantum walks on lattices and the Weyl equation

Physical Review A

We present a thorough classification of the isotropic quantum walks on lattices of dimension d = ... more We present a thorough classification of the isotropic quantum walks on lattices of dimension d = 1,2,3 with a coin system of dimension s = 2. For d = 3 there exist two isotropic walks, namely, the Weyl quantum walks presented in the work of D'Ariano and Perinotti [G. M. D'Ariano and P. Perinotti, Phys. Rev. A 90, 062106 (2014)], resulting in the derivation of the Weyl equation from informational principles. The present analysis, via a crucial use of isotropy, is significantly shorter and avoids a superfluous technical assumption, making the result completely general.

Research paper thumbnail of Quantum cellular automata and free quantum field theory

Research paper thumbnail of Thirring quantum cellular automaton

Physical Review A

We analytically diagonalize a discrete-time on-site interacting fermionic cellular automaton in t... more 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.

Research paper thumbnail of Critical behavior of the order parameter at antiferrodistortive transitions with cubic fluctuations

Physical Review B

The temperature dependence of the generalized order parameter, namely the rotation angle of the N... more The temperature dependence of the generalized order parameter, namely the rotation angle of the Nb06 octahedron, at the antiferrodistortive transition in the perovskite crystal NaNbO3, is derived through the high-resolution analysis of the second-order quadrupole shift of Na NMR spectra. The second-order character of the transition and the small value of the apparent critical exponent for the order parameter are critically discussed in the framework of a renormalization-group approach for a system with an effective Hamiltonian of cubic symmetry and an anisotropic dispersion in the static structure factor.

Research paper thumbnail of Tomographic measurement of the density matrix of the radiation field

Quantum and Semiclassical Optics: Journal of the European Optical Society Part B

Abstracr Recently a novel homodine tomographic technique has been proposed which allows us to det... more Abstracr Recently a novel homodine tomographic technique has been proposed which allows us to detect the density matrix experimentally in terms of averages on data. The method has been further exrended to a general matrix element (+l6lq) of the density operator 6, along with the possibility of using low-efficiency detectors. In this paper this technique is remusidered as a new genuine quantum measurement. Numerical resuits for measured probabilities are given. and the mechanism underlying the genesation of statistical m r s in the measured matrix is illusirated. It is shown that the data prQcessing of the novel technique can also be used as a new imaging algorithm for conventional tomography.

Research paper thumbnail of Time evolution of an anharmonic oscillator interacting with a squeezed bath

Quantum and Semiclassical Optics: Journal of the European Optical Society Part B

The evolution of a single mode of the electromagnetic field interacting with a squeezed bath in a... more The evolution of a single mode of the electromagnetic field interacting with a squeezed bath in a Kerr medium is considered. The solution of the corresponding master equation is given numerically. It is argued that the creation of a superposition state (Schrödinger's cat) is better achieved in presence of a squeezed reservoir than of a thermal one.

Research paper thumbnail of Reconstructing the density operator by using generalized field quadratures

Quantum and Semiclassical Optics: Journal of the European Optical Society Part B

The Wigner function for one and two-mode quantum systems is explicitely expressed in terms of the... more The Wigner function for one and two-mode quantum systems is explicitely expressed in terms of the marginal distribution for the generic linearly transformed quadratures. Then, also the density operator of those systems is written in terms of the marginal distribution of these quadratures. Some examples to apply this formalism, and a reduction to the usual optical homodyne tomography are considered.

Research paper thumbnail of Functional quantum computing: An optical approach

Physical Review A, 2016

Recent theoretical investigations treat quantum computations as functions, quantum processes whic... more Recent theoretical investigations treat quantum computations as functions, quantum processes which operate on other quantum processes, rather than circuits. Much attention has been given to the N − switch function which takes N black box quantum operators as input, coherently permutes their ordering, and applies the result to a target quantum state. This is something which cannot be equivalently done using a quantum circuit. Here, we propose an all-optical system design which implements coherent operator permutation for an arbitrary number of input operators.

Research paper thumbnail of Optimal covariant quantum networks

AIP Conference Proceedings, 2009

A sequential network of quantum operations is efficiently described by its quantum comb [1], a no... more A sequential network of quantum operations is efficiently described by its quantum comb [1], a non-negative operator with suitable normalization constraints. Here we analyze the case of networks enjoying symmetry with respect to the action of a given group of physical transformations, introducing the notion of covariant combs and testers, and proving the basic structure theorems for these objects. As an application, we discuss the optimal alignment of reference frames (without preestablished common references) with multiple rounds of quantum communication, showing that i) allowing an arbitrary amount of classical communication does not improve the alignment, and ii) a single round of quantum communication is sufficient.

Research paper thumbnail of Quantum cellular automaton theory of light

Annals of Physics, 2016

We present a quantum theory of light based on quantum cellular automata (QCA). This approach allo... more We present a quantum theory of light based on quantum cellular automata (QCA). This approach allows us to have a thorough quantum theory of free electrodynamics encompassing an hypothetical discrete Planck scale. The theory is particularly relevant because it provides predictions at the macroscopic scale that can be experimentally tested. We show how, in the limit of small wavevector k, the free Maxwell's equations emerge from two Weyl QCAs derived from informational principles in Ref. [1]. Within this framework the photon is introduced as a composite particle made of a pair of correlated massless Fermions, and the usual Bosonic statistics is recovered in the low photon density limit. We derive the main phenomenological features of the theory, consisting in dispersive propagation in vacuum, the occurrence of a small longitudinal polarization, and a saturation effect originated by the Fermionic nature of the photon. We then discuss whether these effects can be experimentally tested, and observe that only the dispersive effects are accessible with current technology, from observations of arrival times of pulses originated at cosmological distances.

Research paper thumbnail of Quantum from Principles

Fundamental Theories of Physics, 2015

ABSTRACT Quantum theory was discovered in an adventurous way, under the urge to solve puzzles-lik... more ABSTRACT Quantum theory was discovered in an adventurous way, under the urge to solve puzzles-like the spectrum of the blackbody radiation-that haunted the physics community at the beginning of the 20th century. It soon became clear, though, that quantum theory was not just a theory of specific physical systems, but rather a new language of universal applicability. Can this language be reconstructed from first principles? Can we arrive at it from logical reasoning, instead of ad hoc guesswork? A positive answer was provided in Refs. [1, 2], where we put forward six principles that identify quantum theory uniquely in a broad class of theories. We first defined a class of "theories of information", constructed as extensions of probability theory in which events can be connected into networks. In this framework, we formulated the six principles as rules governing the control and the accessibility of information. Directly from these rules, we reconstructed a number of quantum information features, and eventually, the whole Hilbert space framework. In short, our principles characterize quantum theory as the theory of information that allows for maximal control of randomness.