arXiv subjects

Fabio Costa

Publications and source records attributed to Fabio Costa.

At least 19 recordsLinked to original sources

arXiv2026

Indefinite Quantum Causality

In recent years, operational approaches to quantum foundations have been developed as a means of understanding the core principles and distinctive features of quantum theory. Such approaches typically view physical processes as sequences of operations, with earlier operations serving as causes of later effects. However, a growing literature is emerging on the possibility of relaxing this assumption and allowing for quantum indefiniteness in the causal order. This development stems from a variety of motivations, both fundamental and applied, including exploring the role of causality in quantum theory, the interplay between quantum theory and general relativity, and higher-order quantum computing. A prominent offshoot of this development is the emergence of indefinite causal order as a feasible resource for quantum information processing. This review provides an overview of the current state of the art in the field, covering the methodology underlying indefinite quantum causality within the so-called "process matrix formalism", outlining key results and experimental implementations, and discussing recent advances.

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arXiv2026

Causal Order Cannot Be An Observable

Recent developments in the formalisation of quantum causal structures have made it possible to test and compare hypotheses about causal structure empirically, rather than being a-priori assumptions. Such differences in causal structure may be leveraged to distinguish between the processes they belong to, akin to distinguishing between quantum states known to belong to different eigenspaces of an observable. So how far this analogy can be pushed? Can causal order be interpreted as a kind of observable? Can it be measured? To this end we construct a completely operational definition of observables in terms of `discrimination tasks'. This begins with some base set of classes (analogous to a quantum observable's eigenspaces) before we impose three conditions on how these classes relate under discrimination tasks. These conditions recover the properties of a standard observable, letting us apply this definition to non-state entities such as quantum processes, which naturally encode causal structure. These conditions can be described in plain language as (1) `members of any class are perfectly distinguishable from members of any other' (i.e. our classes are `sharp'), (2) `entities perfectly distinguishable pairwise are all perfectly distinguishable by a joint intervention', and (3) `if all members of a class are perfectly distinguishable from an entity, then the whole class is perfectly distinguishable from it jointly'. By analysing classes of quantum processes having strict causal orders, we find causal classes which are sharp but violate condition 2, and classes which violate condition 3. This implies that causal order cannot be an observable. We note cases in the literature which claim to prove the opposite, and discuss them. We find their analyses presume special circumstances equivalent to conditions (2) and (3), and so do not contradict our own findings.

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arXiv2026

Resource theory of coherence in continuous position basis from measurement-induced dephasing

We develop a resource-theoretic framework for quantum coherence directly in continuous basis, with emphasis on the position representation. Since position eigenstates are non-normalizable generalized eigenstates, the standard finite-dimensional dephasing map cannot be transferred directly to normal states. We therefore introduce a physically motivated dephasing channel based on random momentum kicks, equivalently described as the unconditional back-action of a finite-resolution position measurement. This yields a fixed-point notion of incoherence and a natural class of dephasing-covariant free operations. For physically relevant kernels, however, the fixed-point set contains no normal states, showing that continuous-basis coherence is tied to dephasing disturbance rather than to distance from a nonempty set of diagonal states. We study two quantifiers built from the channel action: a relative-entropy dephasing loss and a Hilbert-Schmidt dephasing loss. The former satisfies the main resource-theoretic properties under the free operations considered, while the latter is convex and experimentally transparent but fails monotonicity and strong monotonicity. We also formulate threshold witnesses for certifying coherence above a finite value and connect them, in a two-path setting, with interference visibility. Finally, we illustrate the framework with a Gaussian wavepacket evolving in a gravitational potential. The resulting theory provides a mathematically consistent and physically motivated treatment of coherence in continuous-variable systems.

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arXiv2025

Continuous operations on non-Markovian processes

Continuous measurements are central to quantum control and sensing, yet lack a model-independent operational description that can be applied to arbitrary non-Markovian processes without specifying a microscopic measurement model. Existing multi-time frameworks, such as process matrices, allow for an arbitrary sequence of operations to be applied on a general process, but are restricted to interventions at discrete times and cannot represent measurements of finite duration. We introduce a continuous-time extension of multi-time quantum processes based on process and operation functionals, which generalise the Feynman-Vernon influence functional and yield a continuous Born rule that cleanly separates processes from operations. This framework provides a consistent representation of non-Markovian dynamics under continuous monitoring and leads to natural definitions of causality and Markovianity in continuous time, opening the way to formalising quantum causal structures in the continuum. We illustrate the formalism by analysing continuous measurements in a generalised Caldeira-Leggett model, demonstrating its applicability to realistic non-Markovian scenarios.

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arXiv2025

Quantum metasurfaces as probes of vacuum particle content

The quantum vacuum of the electromagnetic field is inherently entangled across distinct spatial sub-regions, resulting in entangled particle content across these sub-regions. However accessing this particle content in a controlled laboratory experiment has remained out of experimental reach. Here, we analyse the feasibility of witnessing such vacuum effects with highly non-perturbative boundary condition changes with a quantum metasurface made from a two-dimensional sub-wavelength atomic array. The array response to light is tunable between transmissive and reflective states by a control atom that is excited to a Rydberg state. We find that vacuum photon content from non-perturbative changes of the boundary conditions and therefore distinct spatial sub-regions of the vacuum causes subtle frequency shifts and analyse the accessibility to sub-wavelength atom array platforms. This novel approach to probing vacuum particle content leverages the unique ability to generate coherent dynamics in superpositions of transmissive and reflective states of the array reflectivity, providing a quantum-enhanced platform for observing vacuum particle creation driven by highly non-perturbative changes in the boundary conditions of the electromagnetic vacuum.

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arXiv2024

Hamiltonian characterisation of multi-time processes with classical memory

A central problem in open quantum systems is the characterization of non-Markovian processes, where an environment retains the memory of its interaction with the system. A key distinction is whether or not this memory can be simulated classically, as this can lead to efficient modelling and noise mitigation. Powerful tools have been developed recently within the process matrix formalism, a framework that conveniently characterizes all multi-time correlations through a sequence of measurements. This leads to a detailed classification of classical and quantum-memory processes and provides operational procedures to distinguish between them. However, these results leave open the question of what type of system-environment interactions lead to classical memory. More generally, process-matrix methods lack a direct connection to joint system-environment evolution, a cornerstone of open-system modelling. In this work, we characterize Hamiltonian and circuit-based models of system-environment interactions leading to classical memory. We show that general time-dependent Hamiltonians with product eigenstates, and where the environment's eigenstates form a time-independent, orthonormal basis, always produce a particular type of classical memory: probabilistic mixtures of unitary processes. Equivalently, these Hamiltonians are characterized as commuting with a complete set of observables on the environment. Additionally, we show that the most general type of classical memory processes can be generated by a quantum circuit in which the system and environment interact through a specific class of controlled unitaries. Our results establish the first strong link between process-matrix methods and traditional Hamiltonian-based approaches to open quantum systems.

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arXiv2024

Quantum state tomography on closed timelike curves using weak measurements

Any given prescription of quantum time travel necessarily endows a Hilbert space to the chronology-violating (CV) system on the closed timelike curve (CTC). However, under the two foremost models, Deutsch's prescription (D-CTCs) and postselected teleportation (P-CTCs), the CV system is treated very differently: D-CTCs assign a definite form to the state on this system, while P-CTCs do not. To further explore this distinction, we present a methodology by which an operational notion of state may be assigned to their respective CV systems. This is accomplished via a conjunction of state tomography and weak measurements, with the latter being essential in leaving any notions of self-consistency intact. With this technique, we are able to verify the predictions of D-CTCs and, perhaps more significantly, operationally assign a state to the system on the P-CTC. We show that, for any given combination of chronology-respecting input and unitary interaction, it is always possible to recover the unique state on the P-CTC, and we provide a few specific examples in the context of select archetypal temporal paradoxes. We also demonstrate how this state may be derived from analysis of the P-CTC prescription itself, and we explore how it compares to its counterpart in the CV state predicted by D-CTCs.

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arXiv2024

Measuring two temperatures using a single thermometer

We consider the question: Is it possible to measure two temperatures simultaneously using a single thermometer? Under common circumstances, where the thermometer can interact with only one bath at a time and the interaction leads to complete thermalization, this is clearly impossible because the final state of the thermometer would be independent of the temperature of the first bath. In this work, we show that this task can indeed be accomplished with the assistance of quantum control. In particular, we consider a composite particle with multiple quantum degrees of freedom (DoF) as a temperature sensor, where one of the DoF -- termed as internal DoF -- is susceptible to the local temperature, thereby functioning as a thermometer, whereas another DoF -- termed external DoF -- is quantum-controlled. We leverage the entanglement between the aforementioned DoF in a composite particle for two-temperature thermometry by preparing the external DoF in a quantum superposition, exposing the internal DoF to two local temperatures. We show that such a particle used in a Mach-Zehnder type interferometer, or a quantum switch -- which allows quantum control over the order of application of quantum channels -- can be used to estimate two temperatures simultaneously, thus affirming our main proposition. For each of these setups, we obtain the variance in the estimated temperatures through the multi-parameter Cram\'er-Rao bound, and compare their performances based on the range of total variance of the two temperatures estimated. On benchmarking all the setups based on the total variance of the estimated temperatures, we find that a quantum switch with a qudit probe outperforms other setups. On restricting our probe to be a qubit, we find that quantum switch performs equally well as a Mach-Zehnder type interferometer.

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arXiv2024

A de Finetti theorem for quantum causal structures

What does it mean for a causal structure to be `unknown'? Can we even talk about `repetitions' of an experiment without prior knowledge of causal relations? And under what conditions can we say that a set of processes with arbitrary, possibly indefinite, causal structure are independent and identically distributed? Similar questions for classical probabilities, quantum states, and quantum channels are beautifully answered by so-called "de Finetti theorems", which connect a simple and easy-to-justify condition -- symmetry under exchange -- with a very particular multipartite structure: a mixture of identical states/channels. Here we extend the result to processes with arbitrary causal structure, including indefinite causal order and multi-time, non-Markovian processes applicable to noisy quantum devices. The result also implies a new class of de Finetti theorems for quantum states subject to a large class of linear constraints, which can be of independent interest.

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arXiv2023

Multi-time quantum process tomography on a superconducting qubit

Current quantum technologies are at the cusp of becoming useful, but still face formidable obstacles such as noise. Noise severely limits the ability to scale quantum devices to the point that they would offer an advantage over classical devices. To understand the sources of noise it is necessary to fully characterise the quantum processes occurring across many time steps; only this would reveal any time-correlated noise called non-Markovian. Previous efforts have attempted such a characterisation but obtained only a limited reconstruction of such multi-time processes. In this work, we fully characterise a multi-time quantum process on superconducting hardware using in-house and cloud-based quantum processors. We achieve this by employing sequential measure-and-prepare operations combined with post-processing. Employing a recently developed formalism for multi-time processes, we detect general multi-time correlated noise. We also detect quantum correlated noise which demonstrates that part of the noise originates from quantum sources, such as physically nearby qubits on the chip.

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arXiv2023

Reassessing thermodynamic advantage from indefinite causal order

Indefinite causal order is a key feature involved in the study of quantum higher order transformations. Recently, intense research has been focused on possible advantages related to the lack of definite causal order of quantum processes. Quite often the quantum switch is claimed to provide advantages in information-theoretic and thermodynamic tasks. We address here the question whether indefinite causal order is a resource for quantum thermodynamics. Inspired by previous results in the literature, we show that indefinite causal order is not necessary for the reported increase in free energy and ergotropy. More specifically, we show that a simple causally ordered process, which replaces the system's state with a new one before the final measurement, outperforms the quantum switch in all thermodynamic tasks considered so far. We further show that a similar advantage can be also achieved without completely discarding system, if we allow for non-Markovian interactions between the system and an environment. We extend the analysis to more extreme examples of indefinite causal order, showing that they do not provide an advantage either. Finally, we discuss a possible way to study the advantages that may arise from indefinite causal order in a general scenario.

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arXiv2022

Background Independence and Quantum Causal Structure

One of the key ways in which quantum mechanics differs from relativity is that it requires a fixed background reference frame for spacetime. In fact, this appears to be one of the main conceptual obstacles to uniting the two theories. Additionally, a combination of the two theories is expected to yield non-classical, or "indefinite", causal structures. In this paper, we present a background-independent formulation of the process matrix formalism - a form of quantum mechanics that allows for indefinite causal structure - while retaining operationally well-defined measurement statistics. We do this by postulating an arbitrary probability distribution of measurement outcomes across discrete "chunks" of spacetime, which we think of as physical laboratories, and then requiring that this distribution be invariant under any permutation of laboratories. We find (a) that one still obtains nontrivial, indefinite causal structures with background independence, (b) that we lose the idea of local operations in distinct laboratories, but can recover it by encoding a reference frame into the physical states of our system, and (c) that permutation invariance imposes surprising symmetry constraints that, although formally similar to a superselection rule, cannot be interpreted as such.

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arXiv2022

Constraining the number of fundamental quantum degrees of freedom using gravity

We consider the effect of gravity on extended quantum systems (EQS) in the low energy regime. We model the gravitational effect due to a nearby source mass as a redshift in the internal Hamiltonian of the EQS. Due to the dependence of the energy spectrum of the EQS on the position of the massive particle (via the redshift) at zero temperature, our model predicts gravitational decoherence of the massive particle in the position basis. We show that the decoherence effect is multiplicative, in the sense that the increase in number of EQS gravitationally interacting with a single massive particle leads to an increase in its decoherence. If the considered model of gravitational redshift holds alongside the linearity of quantum mechanics (as an appropriate limit of an accepted theory for coupling quantum matter with gravity) to allow for a spatial superposition of the source mass, we propose that the same methodology can be applied to continuous fields, which are essentially EQS. This could provide an upper limit on the number of undiscovered fields by observing coherent superpositions of masses, e.g., in a matter wave interferometer. Besides, by taking a spin chain as a toy model of an EQS, we analyse the dependence of the new effect on relevant system parameters and identify the number of independent spin chains that can cause a detectable effect.

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arXiv2022

Billiard-ball paradox for a quantum wave packet

Past studies of the billiard-ball paradox, a problem involving an object that travels back in time along a closed timelike curve (CTC), typically concern themselves with entirely classical histories, whereby any trajectorial effects associated with quantum mechanics cannot manifest. Here we develop a quantum version of the paradox, wherein a (semiclassical) wave packet evolves through a region containing a wormhole time machine. This is accomplished by mapping all relevant paths on to a quantum circuit, in which the distinction of the various paths is facilitated by representing the billiard particle with a clock state. For this model, we find that Deutsch's prescription (D-CTCs) provides self-consistent solutions in the form of a mixed state composed of terms which represent every possible configuration of the particle's evolution through the circuit. In the equivalent circuit picture (ECP), this reduces to a binomial distribution in the number of loops of time machine. The postselected teleportation prescription (P-CTCs) on the other hand predicts a pure-state solution in which the loop counts have binomial coefficient weights. We then discuss the model in the continuum limit, with a particular focus on the various methods one may employ in order to guarantee convergence in the average number of clock evolutions. Specifically, for D-CTCs, we find that it is necessary to regularise the theory's parameters, while P-CTCs alternatively require more contrived modification.

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arXiv2022

Mass-energy equivalence in gravitationally bound quantum states of the neutron

Gravitationally bound neutrons have become an important tool in the experimental searches for new physics, such as modifications to Newton's force or candidates for dark matter particles. Here we include the relativistic effects of mass-energy equivalence into the model of gravitationally bound neutrons. Specifically, we investigate a correction in a gravitationally bound neutron's Hamiltonian due to the presence of an external magnetic field. We show that the neutron's additional weight due to mass-energy equivalence will cause a small shift in the neutron's eigenenergies and eigenstates, and examine how this relativistic correction would affect experiments with trapped neutrons. We further consider the ultimate precision in estimating the relativistic correction to the precession frequency and find that, at short times, a joint measurement of both the spin and motional degrees of freedom provides a metrological enhancement as compared to a measurement of the spin alone.

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arXiv2022

Indefinite temporal order without gravity

According to the general theory of relativity, time can flow at different rates depending on the configuration of massive objects, affecting the temporal order of events. Recent research has shown that, combined with quantum theory, this gravitational effect can result in events with an indefinite temporal order, which can be tested through the violation of Bell-type inequalities. According to Einstein, we shall assume physical equivalence of a uniform gravitational field and a corresponding acceleration of a reference system. Here we construct a non-gravitational scenario where accelerating particles interacting with optical cavities result in a violation of the temporal Bell inequalities analogous to the gravitational case. However, we find that the inequalities can also be violated by time-like events, exposing an ambiguity in their use as a theory-independent test of indefinite temporal order.

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arXiv2022

A no-go theorem for superpositions of causal orders

The causal order of events need not be fixed: whether a bus arrives before or after another at a certain stop can depend on other variables -- like traffic. Coherent quantum control of causal order is possible too and is a useful resource for several tasks. However, quantum control implies that a controlling system carries the which-order information -- if the control is traced out, the order of events remains in a probabilistic mixture. Can the order of two events be in a pure superposition, uncorrelated with any other system? Here we show that this is not possible for a broad class of processes: a pure superposition of any pair of Markovian, unitary processes with equal local dimensions and different causal orders is not a valid process, namely it results in non-normalised probabilities when probed with certain operations. The result imposes constraints on novel resources for quantum information processing and on possible processes in a theory of quantum gravity.

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arXiv2021

Operational models of temperature superpositions

A quantum system and a thermal bath can reach thermal equilibrium through an interaction, whereupon the system acquires the same temperature as the bath. But how does a delocalised quantum system thermalise with a bath whose local temperature varies, as, for example, in the Tolman effect? Here we formulate two scenarios in which the notion of a ``superposition of temperatures'' may arise. First: a probe interacting with two different baths dependent on the state of another quantum system (control). Second: a probe interacting with a single bath whose purified state is a superposition of states corresponding to different temperatures. We show that the two scenarios are fundamentally different and can be operationally distinguished. Moreover, we show that the probe does not in general thermalise even when the involved temperatures are equal, and that the final probe state is sensitive to the specific realisation of the thermalising channels. Our models may be applied to scenarios involving joint quantum, gravitational, and thermodynamic phenomena, and explain some recent results found in quantum intereference of relativistic probes thermalising with Unruh or Hawking radiation. Finally, we show that our results are reproduced in partial and pre-thermalisation processes, and thus our approach and conclusions hold beyond the idealised scenarios, where thermalisation is incomplete.

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