arXiv subjects

Paolo Perinotti

Publications and source records attributed to Paolo Perinotti.

At least 19 recordsLinked to original sources

arXiv2026

Fermions are fundamentally more nonlocal than Bosons

Bell's theorem shows that entangled quantum particles can exhibit correlations that classical particles cannot reproduce without an additional nonlocal resource, such as communication. In this sense, quantum particles are fundamentally more nonlocal than classical ones, and entanglement becomes unavoidable in physics. Here we prove the analogous result within quantum theory itself: indistinguishable fermions transmitted through a quantum network can generate correlations that distinguishable particles or indistinguishable bosons cannot reproduce without additional communication. In the same sense, fermions are fundamentally more nonlocal than bosons or distinguishable particles, motivating fermionic anticommutation and indistinguishability as unavoidable operational resources. Our result further implies that fermions can strictly surpass all qubit-based protocols for certain distributed computing tasks, demonstrating that a complete understanding of information processing requires going beyond qubits to fermionic information carriers - febits.

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arXiv2026

Higher-order transformations of bidirectional quantum processes

Bidirectional devices are devices for which the roles of the input and output ports can be exchanged. Mathematically, these devices are described by bistochastic quantum channels, namely completely positive linear maps that are both trace-preserving and identity-preserving. Recently, it has been shown that bidirectional quantum devices can, in principle, be used in ways that are incompatible with a definite input-output direction, giving rise to a new phenomenon called input-output indefiniteness. Here we characterize the most general forms of input-output indefiniteness, associated with a hierarchy of higher-order transformations built from transformations of bistochastic quantum channels. Some levels of the hierarchy correspond to transformations that combine bistochastic channels in a definite causal order, while generally using each channel in an indefinite input-output direction. For other levels of the hierarchy, the indefiniteness can involve both the local input-output direction of each process and the global causal order among the processes. On the foundational side, the hierarchy of higher-order transformations characterized here can be regarded as the largest set of physical processes compatible with a time-symmetric variant of quantum theory, where the possible state transformations are restricted to bistochastic channels.

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arXiv2025

Renormalisation of Fermionic Cellular Automata

We present an exact renormalisation scheme for fermionic cellular automata on hypercubic lattices. By grouping neighbouring cells into tiles and selecting subspaces within them, multiple evolution steps on the original system correspond to a single step of an effective automaton acting on the subspaces. We derive a necessary and sufficient condition for renormalisability and fully characterise the renormalisation flow for two-cell tiles and two time steps of nearest-neighbour fermionic automata on a chain of spinless modes, identifying all fixed points.

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arXiv2025

Quantum complementarity

We propose an operational definition of complementarity, pinning down the concept originally introduced by Bohr. Two properties of a system are considered complementary if they cannot be simultaneously well defined. We further show that, within quantum theory, this notion is equivalent to the incompatibility of operations -- that is, their inability to be performed simultaneously.

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arXiv2025

Classification of qubit cellular automata on hypercubic lattices

We classify quantum cellular automata whose cells are qubits, on hypercubic lattices $\mathbb Z^s$, with the von Neumann neighborhood scheme, in terms of realizability as finite-depth quantum circuits. We show the most general structure of such automata and use its characterisation to simulate a few steps of evolution and evaluate the rate of entanglement production between one cell and its surroundings.

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arXiv2025

Renormalisation of Quantum Cellular Automata

We study a coarse-graining procedure for quantum cellular automata on hypercubic lattices that consists in grouping neighboring cells into tiles and selecting a subspace within each tile. This is done in such a way that multiple evolution steps applied to this subspace can be viewed as a single evolution step of a new quantum cellular automaton, whose cells are the subspaces themselves. We derive a necessary and sufficient condition for renormalizability and use it to investigate the renormalization flow of cellular automata on a line, where the cells are qubits and the tiles are composed of two neighboring cells. The problem is exhaustively solved, and the fixed points of the renormalization flow are highlighted.

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arXiv2025

Disentangling signalling and causal influence

The causal effects activated by a quantum interaction are studied, modelling the last one as a bipartite unitary channel. The two parties, say Alice and Bob, can use the channel to exchange messages -- i.e. to signal. On the other hand, the most general form of causal influence includes also the possibility for Alice, via a local operation on her system, to modify Bob's correlations and viceversa. The presence or absence of these two effects are equivalent, but when they both occur, they can differ in their magnitude. We study the properties of two functions that quantify the amount of signalling and causal influence conveyed by an arbitrary unitary channel. The functions are proved to be continuous and monotonically increasing with respect to the tensor product of channels. Monotonicity is instead disproved in the case of sequential composition. Signalling and causal influence are analytically computed for the quantum SWAP and CNOT gates, in the single use scenario, in the $n$-parallel uses scenario, and in the asymptotic regime. A finite gap is found between signalling and causal influence for the quantum CNOT, thus proving the existence of extra causal effects that cannot be explained in terms of communication only. However, the gap disappears in the asymptotic limit of an infinite number of parallel uses, leaving room for asymptotic equivalence between signalling and causal influence.

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arXiv2025

Minimal operational theories: classical theories with quantum features

We introduce a class of probabilistic theories, termed Minimal Strongly Causal Operational Probabilistic Theories, where system dynamics are constrained to the minimal set of operations consistent with the set of states and permitting conditional tests. Specifically, the allowed instruments are limited to those derived from compositions of preparations, measurements, swap transformations, and conditional operations. We demonstrate that minimal theories with conditioning and a spanning set of non-separable states satisfy two quantum no-go theorems: no-information without disturbance and no-broadcasting. As a key example, we construct Minimal Strongly Causal Bilocal Classical Theory, a classical toy-theory that lacks incompatible measurements, preparation uncertainty relations, and is noncontextual (both Kochen-Specker and generalised), yet exhibits irreversibility of measurement disturbance, no-information without disturbance, and no-broadcasting. Therefore, the latter three properties cannot be understood $\textit{per se}$ as signatures of non-classicality. We further explore distinctions between a theory and its minimal strongly causal counterpart, showing that while the minimal strongly causal version of quantum theory diverges from full quantum theory, the same does not hold for classical theory. Additionally, we establish the pairwise independence of the properties of simpliciality, strong causality, and local discriminability.

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arXiv2025

Fermionic cellular automata in one dimension

We consider quantum cellular automata for one-dimensional chains of Fermionic modes and study their implementability as finite depth quantum circuits. Fermionic automata have been classified in terms of an index modulo circuits and the addition of ancillary systems. We strengthen this result removing the ancilla degrees of freedom in defining the equivalence classes. A complete characterization of nearest-neighbours automata is given. A class of Fermionic automata is found which cannot be expressed in terms of single mode and controlled-phase gates composed with shifts, as is the case for qubit cellular automata.

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arXiv2024

Effective dynamics from minimising dissipation

It is known that the same physical system can be described by different effective theories depending on the scale at which it is observed. In this work, we formulate a prescription for finding the unitary that best approximates the large scale dynamics of a quantum system evolving discretely in time, as it is the case for digital quantum simulators. We consider the situation in which the degrees of freedom of the system can be divided between an IR part that we can observe, and a UV part that we cannot observe. Following a principle of minimal dissipation, our goal is to find the unitary dynamics that best approximates the (generally non unitary) time evolution of the IR degrees of freedom. We first prove that when the IR and UV degrees of freedom are weakly coupled, the unitary that maximises the fidelity is given by a mean-field dynamics and the error is given by a sum of energy variances. We then apply our results to a one dimensional quantum walk, which is known to reproduce the Dirac equation in the small mass and momenta limit. We find that in this limit the effective IR dynamics is obtained by a mass redefinition.

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arXiv2024

The composition rule for quantum systems is not the only possible one

Quantum theory provides a significant example of two intermingling hallmarks of science: the ability to consistently combine physical systems and study them compositely, and the power to extract predictions in the form of correlations. A striking consequence of this facet is the violation of Bell inequalities, which has been experimentally demonstrated via Bell tests. The prediction of this phenomenon originates as quantum systems are prescribed to combine according to the composition postulate, i.e. the tensor-product rule. This rule has also an operationally salient formulation given in terms of discriminability of composite states via local measurements. However, both the theoretical and the empirical status of such a postulate have been repeatedly challenged, questioning its independence from other physical principles -- most notably from quantum postulates pertaining solely to single systems. Is the composition postulate the only viable way to combine quantum systems into a consistent physical theory? Here, this long-standing problem is resolved by answering in the negative. This is achieved by adopting an operational approach to physical theories and exhibiting a family of theories that differ from standard quantum theory in their system-composition rule. These theories have the same predictions as standard quantum theory as far as Bell-like correlation scenarios are concerned. Quantum theory is thus established to embody genuinely more than quantum correlations. As a result, foundational programmes based on single-system principles only, or on mere Bell-like correlations, are operationally incomplete. On the experimental side, ascertaining the independence of postulates is a fundamental step to adjudicate between quantum theory and alternative physical theories: hence, the composition postulate calls for experimental scrutiny independently of the other features of quantum theory.

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arXiv2024

A perturbative approach to the solution of the Thirring quantum cellular automaton

The Thirring Quantum Cellular Automaton (QCA) describes the discrete time dynamics of local fermionic modes that evolve according to one step of the Dirac cellular automaton followed by the most general on-site number-preserving interaction, and serves as the QCA counterpart of the Thirring model in quantum field theory. In this work, we develop perturbative techniques for the QCA path-sum approach, expanding both the number of interaction vertices and the mass parameter of the Thirring QCA. By classifying paths within the regimes of very light and very heavy particles, we computed the transition matrices in the two- and three-particle sectors to the first few orders. Our investigation into the properties of the Thirring QCA, addressing the combinatorial complexity of the problem, yielded some useful results applicable to the many-particle sector of any on-site number-preserving interactions in one spatial dimension.

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arXiv2024

Which entropy for general physical theories?

We address the problem of quantifying the information content of a source for an arbitrary information theory, where the information content is defined in terms of the asymptotic achievable compression rate. The functions that solve this problem in classical and quantum theory are Shannon's and von Neumann's entropy, respectively. However, in a general information theory there are three different functions that extend the notion of entropy, and this opens the question as to whether any of them can universally play the role of the quantifier for the information content. Here we answer the question in the negative, by evaluating the information content as well as the various entropic functions in a toy theory called Bilocal Classical Theory.

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arXiv2024

A massless interacting Fermionic Cellular Automaton exhibiting bound states

We present a Fermionic Cellular Automaton model which describes massless Dirac fermion in 1+1 dimension coupled with local, number preserving interaction. The diagonalization of the two particle sector shows that specific values of the total momentum and of the coupling constant allows for the formation of bound states. Furthermore, we present a classification of the local number-preserving interactions that are invariant under the isotropy group of the cellular automaton which simulates the Weyl equation.

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arXiv2024

Measurement incompatibility is strictly stronger than disturbance

The core of Heisenberg's heuristic argument for the uncertainty principle, involving the famous $γ$-ray microscope $\textit{Gedankenexperiment}$, hinges upon the existence of measurements that irreversibly alter the state of the system on which they are acting, causing an irreducible disturbance on subsequent measurements. The argument was put forward to justify measurement incompatibility in quantum theory, namely, the existence of measurements that cannot be performed jointly$-$a feature that is now understood to be different from irreversibility of measurement disturbance, though related to it. In this article, on the one hand, we provide a compelling argument showing that measurement incompatibility is indeed a sufficient condition for irreversibility of measurement disturbance; while, on the other hand, we exhibit a toy theory, termed the minimal classical theory (MCT), that is a counterexample for the converse implication. This theory is classical, hence it does not have complementarity nor preparation uncertainty relations, and it is both Kochen-Specker and generalised noncontextual. However, MCT satisfies not only irreversibility of measurement disturbance, but also the properties of no-information without disturbance and no-broadcasting, implying that these cannot be understood $\textit{per se}$ as signatures of nonclassicality.

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arXiv2024

Causal influence versus signalling for interacting quantum channels

A causal relation between quantum agents, say Alice and Bob, is necessarily mediated by an interaction. Modelling the last one as a reversible quantum channel, an intervention of Alice can have causal influence on Bob's system, modifying correlations between Alice and Bob's systems. Causal influence between quantum systems necessarily allows for signalling. Here we prove a mismatch between causal influence and signalling via direct computation of the two quantities for the Cnot gate. Finally we show a continuity theorem for causal effects of unitary channels: a channel has small causal influence iff it allows for small signalling.

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arXiv2024

Photonic cellular automaton simulation of relativistic quantum fields: observation of Zitterbewegung

Quantum Cellular Automaton (QCA) is a model for universal quantum computation and a natural candidate for digital quantum simulation of relativistic quantum fields. Here we introduce the first photonic platform for implementing QCA-simulation of a free relativistic Dirac quantum field in 1+1 dimension, through a Dirac Quantum Cellular Automaton (DQCA). Encoding the field position degree of freedom in the Orbital Angular Momentum (OAM) of single photons, our state-of-the-art setup experimentally realizes 8 steps of a DQCA, with the possibility of having complete control over the input OAM state preparation and the output measurement making use of two spatial light modulators. Therefore, studying the distribution in the OAM space at each step, we were able to reproduce the time evolution of the free Dirac field observing, the Zitterbewegung, an oscillatory movement extremely difficult to see in real case experimental scenario that is a signature of the interference of particle and antiparticle states. The accordance between the expected and measured Zitterbewegung oscillations certifies the simulator performances, paving the way towards the application of photonic platforms to the simulation of more complex relativistic effects.

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arXiv2024

No-signalling constrains quantum computation with indefinite causal structure

Quantum processes with indefinite causal structure emerge when we wonder which are the most general evolutions, allowed by quantum theory, of a set of local systems which are not assumed to be in any particular causal order. These processes can be described within the framework of higher-order quantum theory which, starting from considering maps from quantum transformations to quantum transformations, recursively constructs a hierarchy of quantum maps of increasingly higher order. In this work, we develop a formalism for quantum computation with indefinite causal structures; namely, we characterize the computational structure of higher order quantum maps. Taking an axiomatic approach, the rules of this computation are identified as the most general compositions of higher order maps which are compatible with the mathematical structure of quantum theory. We provide a mathematical characterization of the admissible composition for arbitrary higher order quantum maps. We prove that these rules, which have a computational and information-theoretic nature, are determined by the more physical notion of the signalling relations between the quantum systems of the higher order quantum maps.

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