arXiv subjects
Publications and source records attributed to Giacomo Mauro D'Ariano.
The operational axiomatization of quantum theory can be regarded as a set of six epistemological rules for falsifying propositions of the theory. In particular, the Purification postulate-the only one that is not shared with classical theory-allows falsification of random-sequences generators, a task unfeasible classically.
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, non-monogamous 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 characterisation theorem for the parallel composition rules of arbitrary theories, and specialise 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.
A composite quantum system has properties that are incompatible with every property of its parts. The existence of such global properties incompatible with all local properties constitutes what I call "mereological holism"--the distinctive holism of Quantum Theory. Mereological holism has the dramatic conceptual consequence of making untenable the usual understanding of the "quantum system" as being a "physical object", since composed objects have properties compatible with those of its parts. The notion of "property" can be extended in a unique way to the whole class of operational probabilistic theories (shortly OPTs), of which the most relevant cases are Quantum Theory and Classical Theory. Whereas Classical Theory is not mereologically holistic, we can now search for other OPTs that are so. Within the OPT framework the role of the "system" is that of an input-output connection between two objective events. In non holistic theories, such as Classical Theory, the system can still be regarded as an "object". On the contrary, in holistic theories interpreting "system" as "object" constitutes an hypostatization of a theoretical notion.
We explore definite theoretical assertions about consciousness, starting from a non-reductive psycho-informational solution of David Chalmers's 'hard problem', based on the hypothesis that a fundamental property of 'information' is its experience by the supporting 'system'. The kind of information involved in consciousness needs to be quantum for multiple reasons, including its intrinsic privacy and its power of building up thoughts by entangling qualia states. As a result we reach a quantum-information-based panpsychism, with classical physics supervening on quantum physics, quantum physics supervening on quantum information, and quantum information supervening on consciousness. We then argue that the internally experienced quantum state, since it corresponds to a definite experience-not to a random choice-must be pure, and we call it ontic, in contrast with the state predictable from the outside (i.e. the state describing the knowledge of the experience from the point of view of an external observer) which we call epistemic and is generally mixed. Purity of the ontic state requires an evolution that is purity preserving, namely a so-called 'atomic' quantum operation. The latter is generally probabilistic, and its particular outcome is interpreted as the free will, which is unpredictable even in principle since quantum probability cannot be interpreted as lack of knowledge. The same purity of state and evolution allows solving the 'combination problem' of panpsychism. Quantum state evolution accounts for a short-term buffer of experience and contains itself quantum-to-classical and classical-to-quantum information transfers. Long term memory, on the other hand, is classical, and needs memorization and recall processes that are quantum-to-classical and classical-to-quantum, respectively...
Any measurement is intended to provide information on a system, namely knowledge about its state. However, we learn from quantum theory that it is generally impossible to extract information without disturbing the state of the system or its correlations with other systems. In this paper we address the issue of the interplay between information and disturbance for a general operational probabilistic theory. The traditional notion of disturbance considers the fate of the system state after the measurement. However, the fact that the system state is left untouched ensures that also correlations are preserved only in the presence of local discriminability. Here we provide the definition of disturbance that is appropriate for a general theory. Moreover, since in a theory without causality information can be gathered also on the effect, we generalise the notion of no-information test. We then prove an equivalent condition for no-information without disturbance-atomicity of the identity-namely the impossibility of achieving the trivial evolution-the identity-as the coarse-graining of a set of non trivial ones. We prove a general theorem showing that information that can be retrieved without disturbance corresponds to perfectly repeatable and discriminating tests. Based on this, we prove a structure theorem for operational probabilistic theories, showing that the set of states of any system decomposes as a direct sum of perfectly discriminable sets, and such decomposition is preserved under system composition. As a consequence, a theory is such that any information can be extracted without disturbance only if all its systems are classical. Finally, we show via concrete examples that no-information without disturbance is independent of both local discriminability and purification.
It is almost universally believed that in quantum theory the two following statements hold: 1) all transformations are achieved by a unitary interaction followed by a von Neumann measurement; 2) all mixed states are marginals of pure entangled states. I name this doctrine the dogma of purification ontology. The source of the dogma is the original von Neumann axiomatisation of the theory, which largely relies on the Schroedinger equation as a postulate, which holds in a nonrelativistic context, and whose operator version holds only in free quantum field theory, but no longer in the interacting theory. In the present paper I prove that both ontologies of unitarity and state purity are unfalsifiable, even in principle, and therefore axiomatically spurious. I propose instead a minimal four-postulate axiomatisation: 1) associate a Hilbert space HA to each system A; 2) compose two systems by the tensor product rule HAB = HAxHB; 3) associate a transformation from system A to B to a quantum operation, i.e. to a completely positive trace-non-increasing map between the trace-class operators of A and B; 4) (Born rule) evaluate all joint probabilities through that of a special type of quantum operation: the state preparation. I then conclude that quantum paradoxes-such as the Schroedinger-cat's, and, most relevantly, the information paradox-are originated only by the dogma of purification ontology, and they are no longer paradoxes of the theory in the minimal formulation. For the same reason, most interpretations of the theory (e.g. many-world, relational, Darwinism, transactional, von Neumann-Wigner, time-symmetric, ...) interpret the same dogma, not the strict theory stripped of the spurious postulates.
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---under the hypothesis of $n$-local discriminability---no mixed state admits of a purification. Our results hold also in the general case where the sets of states fail to be convex.
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.
A quantum walk describes the discrete unitary evolution of a quantum particle on a discrete graph. Some quantum walks, referred to as the Weyl and Dirac quantum walks, provide a description of the free evolution of relativistic quantum fields in a regime where the wave-vectors involved in the particle state are small. The clash between the intrinsic discreteness of quantum walks and the symmetries of special relativity can be resolved by rethinking the notion of a change of inertial reference frame. We give here a definition of the latter that avoids a pre-defined space-time geometry, in terms of a change of values of the constants of motion that leaves the walk operator unchanged. Starting from the family of 1+1 dimensional Dirac quantum walks with all possible values of the mass parameter, we introduce a unique walk encompassing the latter as an extra degree of freedom, and we derive its group of changes of inertial frames. This symmetry group contains a non linear realization of $SO^+(2,1) \ltimes \mathbb{R}^3$; since one of the two space-like dimensions does not correspond to an actual spatial degree of freedom but rather the mass, we interpret it as a 2+1 dimensional de-Sitter group. This group group contains also a non-linear realisation of the proper orthochronous Poincaré group $SO^+(1,1) \ltimes \mathbb{R}^2$ in 1+1 dimension, as the ones considered within the framework of doubly special relativity, which recovers the usual relativistic symmetry of the Dirac Equation in the limit of small wave-vectors and masses. Surprisingly, if one considers the Dirac walk with a fixed value of the mass parameter, the group of allowed changes of reference frame does not have a consistent interpretation in the relativistic limit of small wave-vectors.
Causality never gained the status of a "law" or "principle" in physics. Some recent literature even popularized the false idea that causality is a notion that should be banned from theory. Such misconception relies on an alleged universality of reversibility of laws of physics, based either on determinism of classical theory, or on the multiverse interpretation of quantum theory, in both cases motivated by mere interpretational requirements for realism of the theory. Here, I will show that a properly defined unambiguous notion of causality is a theorem of quantum theory, which is also a falsifiable proposition of the theory. Such causality notion appeared in the literature within the framework of operational probabilistic theories. It is a genuinely theoretical notion, corresponding to establish a definite partial order among events, in the same way as we do by using the future causal cone on Minkowski space. The causality notion is logically completely independent of the misidentified concept of "determinism", and, being a consequence of quantum theory, is ubiquitous in physics. In addition, as classical theory can be regarded as a restriction of quantum theory, causality holds also in the classical case, although the determinism of the theory trivializes it. I then conclude arguing that causality naturally establishes an arrow of time. This implies that the scenario of the "Block Universe" and the connected "Past Hypothesis" are incompatible with causality, and thus with quantum theory: they both are doomed to remain mere interpretations and, as such, not falsifiable, similar to the hypothesis of "super-determinism". This article is part of a discussion meeting issue "Foundations of quantum mechanics and their impact on contemporary society".
We study the solutions of the interacting Fermionic cellular automaton introduced in Ref. [Phys Rev A 97, 032132 (2018)]. The automaton is the analogue of the Thirring model with both space and time discrete. We present a derivation of the two-particles solutions of the automaton, which exploits the symmetries of the evolution operator. In the two-particles 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 even for vanishing coupling constant. As a complement to the analytical derivations we show numerical simulations of the interacting evolution.
I argue for a full mathematisation of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: "physics from no physics". Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either don't have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as "clock", "rigid rod ", "force", "inertial mass" (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the Sixth Hilbert's Problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory.
We present a thorough classification of the isotropic quantum walks on lattices of dimension $d=1,2,3$ for cell dimension $s=2$. For $d=3$ there exist two isotropic walks, namely the Weyl quantum walks presented in Ref. [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.
Quantum cellular automata and quantum walks provide a framework for the foundations of quantum field theory, since the equations of motion of free relativistic quantum fields can be derived as the small wave-vector limit of quantum automata and walks starting from very general principles. The intrinsic discreteness of this framework is reconciled with the continuous Lorentz symmetry by reformulating the notion of inertial reference frame in terms of the constants of motion of the quantum walk dynamics. In particular, among the symmetries of the quantum walk which recovers the Weyl equation--the so called Weyl walk--one finds a non linear realisation of the Poincaré group, which recovers the usual linear representation in the small wave-vector limit. In this paper we characterise the full symmetry group of the Weyl walk which is shown to be a non linear realization of a group which is the semidirect product of the Poincaré group and the group of dilations.
We consider the Weyl quantum walk in 3+1 dimensions, that is a discrete-time walk describing a particle with two internal degrees of freedom moving on a Cayley graph of the group $\mathbb Z^3$, that in an appropriate regime evolves according to Weyl's equation. The Weyl quantum walk was recently derived as the unique unitary evolution on a Cayley graph of $\mathbb Z^3$ that is homogeneous and isotropic. The general solution of the quantum walk evolution is provided here in the position representation, by the analytical expression of the propagator, i.e. transition amplitude from a node of the graph to another node in a finite number of steps. The quantum nature of the walk manifests itself in the interference of the paths on the graph joining the given nodes. The solution is based on the binary encoding of the admissible paths on the graph and on the semigroup structure of the walk transition matrices.
The present short review article illustrates the latest theoretical developments on quantum tomography, regarding general optimization methods for both data-processing and setup. The basic theoretical tool is the informationally complete measurement. The optimization theory for the setup is based on the new theoretical approach of quantum combs.
David Finkelstein was very fond of the new information-theoretic paradigm of physics advocated by John Archibald Wheeler and Richard Feynman. Only recently, however, the paradigm has concretely shown its full power, with the derivation of quantum theory (Chiribella et al., Phys. Rev. A 84:012311, 2011; D'Ariano et al., 2017) and of free quantum field theory (D'Ariano and Perinotti, Phys. Rev. A 90:062106, 2014; Bisio et al., Phys. Rev. A 88:032301, 2013; Bisio et al., Ann. Phys. 354:244, 2015; Bisio et al., Ann. Phys. 368:177, 2016) from informational principles. The paradigm has opened for the first time the possibility of avoiding physical primitives in the axioms of the physical theory, allowing a refoundation of the whole physics over logically solid grounds. In addition to such methodological value, the new information-theoretic derivation of quantum field theory is particularly interesting for establishing a theoretical framework for quantum gravity, with the idea of obtaining gravity itself as emergent from the quantum information processing, as also suggested by the role played by information in the holographic principle (Susskind, J. Math. Phys. 36:6377, 1995; Bousso, Rev. Mod. Phys. 74:825, 2002). In this paper I review how free quantum field theory is derived without using mechanical primitives, including space-time, special relativity, Hamiltonians, and quantization rules. The theory is simply provided by the simplest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the three following simple principles: homogeneity, locality, and isotropy. The inherent discrete nature of the informational derivation leads to an extension of quantum field theory in terms of a quantum cellular automata and quantum walks. A simple heuristic argument sets the scale to the Planck one, and the observed regime is that of small wavevectors ...
We introduce quantum walks on Cayley graphs of non-Abelian groups. We focus on the easiest case of virtually Abelian groups, and introduce a technique to reduce the quantum walk to an equivalent one on an Abelian group with coin system having larger dimension. We apply the technique in the case of two quantum walks on virtually Abelian groups with planar Cayley graphs, finding the exact solution.