arXiv subjects

Luca Apadula

Publications and source records attributed to Luca Apadula.

9 recordsLinked to original sources

arXiv2026

Frame-Dependent Traces and the Third-Particle Paradox

The Paradox of the Third Particle arises when comparing subsystem descriptions across Quantum Reference Frame (QRF) perspectives. We isolate two distinct origins of the Paradox: the QRF covariance of the partial trace and the failure of the physical Hilbert space to inherit the kinematical tensor-product structure. We give an explicit counterexample to the Relational Trace (RT) resolution: an uncorrelated product state for which the RT statistical condition trivialises. We then introduce a new statistical consistency condition comparing subsystem discarding between external and internal QRFs, together with an associated frame-dependent map, the Perspective Relational Trace (PRT). We argue that our condition captures the operational content of the Paradox: rather than imposing consistency on the whole state space, we characterise exactly the states on which it holds in the Perspective-Neutral (PN) and Quantum-Information (QI) approaches. This separates three levels of description: a PN subsystem of a PN whole, where consistency fails on a characterised set that includes product states; a QI subsystem of a QI whole, where it holds for all states; and a QI subsystem obtained from a PN whole by kinematical partial trace, where the full weakly invariant algebra is recovered, yet consistency holds only on a proper subset. These results show that the PN approach can consistently describe only a closed, isolated system, while the QI approach can accommodate arbitrary subsystems. Tracing out a subsystem from a globally PN state yields a charge-superselected algebra, reproducing in a minimal QRF model the boundary-charge structure of edge modes. We understand the Paradox not as a genuine contradiction, but as the consequence of comparing inequivalent physical layers without tracking which information is externally and which internally accessible.

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arXiv2026

Frame perspectives for process matrices: from coordinate parametrization to spacetime representation

We study how to implement and transform frame perspectives for quantum processes in the process-matrix formalism. We argue that, for pure processes, the causal reference frames (CRF)and time-delocalized subsystems (TDS) formalisms should be understood as coordinate parametrizations of a single perspective-neutral higher-order object. A genuine perspective arises when one endows the process with additional frame data by choosing an operational foliation into circuit fragments (events). With this distinction, existing no-go results acquire a clear scope: they rule out unitary transformations that preserve time foliation, attempting to switch perspectives while keeping the fragment boundaries -- hence the global past/future partition -- fixed. Focusing on the quantum switch, we construct explicit maps that transform perspectives unitarily at the price of reshuffling the notions of past and future. We then show that unitary transformations between perspectives can also be achieved in a different way, namely by extending the process with subsystems that define quantum reference frames and provide a shared spatiotemporal scaffold. In this extended setting, complementary CRF/TDS perspectives become unitarily related while preserving global past and future. We discuss how this frame-perspectival approach informs the broader question of empirical realizability of abstract process matrices.

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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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arXiv2024

Identification is Pointless: Quantum Coordinates, Localisation of Events, and the Quantum Hole Argument

The study of quantum reference frames (QRFs) is motivated by the idea of taking into account the quantum properties of the reference frames used, explicitly or implicitly, in our description of physical systems. Like classical reference frames, QRFs can be used to define physical quantities relationally. Unlike their classical analogue, they relativise the notions of superposition and entanglement. Here, we explain this feature by examining how configurations or locations are identified across different branches in superposition. We show that, in the presence of symmetries, whether a system is in "the same" or "different" configurations across the branches depends on the choice of QRF. Hence, sameness and difference -- and thus superposition and entanglement -- lose their absolute meaning. We apply these ideas to the context of semi-classical spacetimes in superposition and use coincidences of four scalar fields to construct a comparison map between spacetime points in the different branches. This reveals that the localisation of an event is frame-dependent. We discuss the implications for indefinite causal order and the locality of interaction and conclude with a generalisation of Einstein's hole argument to the quantum context.

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arXiv2022

Quantum Reference Frames for Lorentz Symmetry

Since their first introduction, Quantum Reference Frame (QRF) transformations have been extensively discussed, generalising the covariance of physical laws to the quantum domain. Despite important progress, a formulation of QRF transformations for Lorentz symmetry is still lacking. The present work aims to fill this gap. We first introduce a reformulation of relativistic quantum mechanics independent of any notion of preferred temporal slicing. Based on this, we define transformations that switch between the perspectives of different relativistic QRFs. We introduce a notion of ''quantum Lorentz transformations'' and ''superposition of Lorentz boosts'', acting on the external degrees of freedom of a quantum particle. We analyse two effects, superposition of time dilations and superposition of length contractions, that arise only if the reference frames exhibit both relativistic and quantum-mechanical features. Finally, we discuss how the effects could be observed by measuring the wave-packet extensions from relativistic QRFs.

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arXiv2022

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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arXiv2020

Probing quantum coherence at a distance and Aharonov-Bohm non-locality

In a standard interferometry experiment, one measures the phase difference between two paths by recombining the two wave packets on a beam-splitter. However, it has been recently recognized that the phase can also be estimated via local measurements, by using an ancillary particle in a known superposition state. In this work, we further analyse these protocols for different types of particles (bosons or fermions, charged or uncharged), with a particular emphasis on the subtleties that arise when the phase is due to the coupling to an abelian gauge field. In that case, we show that the measurable quantities are spacetime loop integrals of the 4-vector potential, enclosed by two identical particles or by a particle-antiparticle pair. Furthermore, we generalize our considerations to scenarios involving an arbitrary number of parties performing local measurements on a general charged fermionic state. Finally, as a concrete application, we analyse a recent proposal by Marletto and Vedral (arXiv:1906.03440) involving the time-dependent Aharonov-Bohm effect.

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arXiv2020

Unruh effect for detectors in superposition of accelerations

The Unruh effect is the phenomenon that accelerated observers detect particles even when inertial observers experience the vacuum state. In particular, uniformly accelerated observers are predicted to measure thermal radiation that is proportional to the acceleration. Here we consider the Unruh effect for a detector that follows a quantum superposition of different accelerated trajectories in Minkowski spacetime. More precisely, we analyse the excitations of a pointlike multilevel particle detector coupled to a massless real scalar field and moving in the superposition of accelerated trajectories. We find that the state of the detector excitations is, in general, not a mere (convex) mixture of the thermal spectrum characteristics of the Unruh effect for each trajectory with well-defined acceleration separately. Rather, for certain trajectories and excitation levels, and upon the measurement of the trajectory state, the state of the detector excitations features in addition off-diagonal terms. The off-diagonal terms of these "superpositions of thermal states" are related to the distinguishability of the different possible states in which the field is left after its interaction with detector's internal degrees of the freedom.

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arXiv2019

Symmetries of the Dirac quantum walk and emergence of the de Sitter group

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.

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