arXiv subjects

Valerio Scarani

Publications and source records attributed to Valerio Scarani.

At least 19 recordsLinked to original sources

arXiv2026

Exact and approximate conditions of tabletop reversibility: when is Petz recovery cost-free?

Channels $\mathcal{N}$ that describe open quantum dynamics are inherently irreversible: it is impossible to undo their effect completely, but one can study partial recovery of the information. The Petz recovery map $\hat{\mathcal{N}}_γ^{(\texttt{P})}$ is a systematic construction that depends only on $\mathcal{N}$ and on a reference state $γ$, which will be recovered exactly. If the real input state was different from $γ$, the recovery is partial, with a guarantee of near-optimality. Generically, an implementation of the Petz recovery map would look very different from the implementation of the channel. It is natural to study under which conditions the two maps require similar or even identical resources. The noisy forward channel $\mathcal{N}$ is called ``tabletop time-reversible'' for a given $γ$ when the corresponding Petz recovery map is realizable in such a way. First, we study the exact tabletop reversibility (TTR) conditions. We show in particular that a time-sensitive control of an ancilla system is needed. Second, we present the approximate TTR conditions, which do not require such a time-sensitive control. Third, we derive Lindbladian TTR conditions under a random-time collision model.

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arXiv2026

Quantum Belief Characterization: A Multi-Shot Notion of Equivalence

A recent formulation of quantum belief showed that quantum retrodiction depends not only on the reduced density operator of the system of interest, but also on correlations with a hidden reference system, which leads to the notion of quantum belief equivalence. In this paper we formulate a multi-shot problem, where the extended posterior obtained after one update is used again as the prior for the next update. We first define a formal notion of $n$-shot equivalence and derive several propositions for arbitrary extended beliefs. We then argue that the agent must also specify why the data obtained in different rounds concern the same underlying object. Through the quantum de Finetti representation, this narrows the one-copy belief to a special class: candidate-state ensemble belief. In that sector, we show that two beliefs are $n$-shot equivalent if and only if their $(n+1)$-th moments are equal. We also give a physical interpretation of this moment condition and illustrate it through the equivalence between Haar priors and projective-design priors at bounded update depth.

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arXiv2026

Trading energy for coherence in mode discrimination

Energy is arguably the main resource in classical physics; coherence is the prototypical quantum resource. In this paper, we study the interplay between these two resources in the task of optimal mode discrimination. This task, motivated by cryptography and metrology, consists of finding in which mode a signal has been encoded, for a given finite set of possible modes. After recalling that the task can be cast as a semi-definite program, we solve completely the case of two-mode discrimination under a hard energy constraint $n\leq N$. Specifically, we identify the region of modes overlap, for which the maximal energy state (the Fock state with N excitations) is the best choice for discrimination. For other overlaps, having access to coherence leads to better discrimination.

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arXiv2026

Tsirelson's nonclassicality witness under dissipative dynamics

A dynamics-based test, originally proposed by Tsirelson for the harmonic oscillator, provides a method for certifying quantumness under the assumption of a known Hamiltonian. These tests, however, are typically proposed for isolated systems, an assumption that breaks down in experimental implementation. In this paper, we extend the protocol to the harmonic oscillator coupled to standard models of dissipation: thermal relaxation, pure dephasing, and the Caldeira--Leggett model. Using the Moyal-Wigner formalism of quantum mechanics in phase space, we show that the introduction of dissipation requires a dissipation-dependent shift of the classical bound, and provide the threshold under which the nonclassicality witness retains its validity.

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arXiv2026

Experimental certification of multipartite Bell correlations using only few-body symmetric correlations

Certifying Bell correlations in increasingly larger multipartite quantum systems is challenging because conventional Bell inequalities rely on many-body correlations, which become experimentally demanding to estimate as system size grows. Here we demonstrate that multipartite Bell correlations can be certified using few-body permutation-invariant (PI) correlations with a fixed maximal correlation order. We experimentally test few-body PI Bell correlation witnesses tailored for six- and eight-photon postselected Dicke states. The addition of a few four-body correlators is found to significantly enhance the noise tolerance compared with previously studied two-body witnesses: for instance, for six qubits, the selected witness tolerates a white-noise fraction of $p_c\approx0.301$, compared with $p_c\approx0.048$ for the best two-body PI inequality with the same two settings per party. For six and eight photons respectively, we observe violations of the witness bounds by $32$ and $8.9$ standard deviations, arising from postselected polarisation states with fidelities of $0.933(4)$ and $0.916(11)$ to the corresponding half-excitation Dicke states. The witnesses for the six- and eight-photon cases use the same symmetric two- and four-body correlators, just with different coefficients. These results demonstrate an experimentally accessible approach for certifying multipartite Bell correlations in larger systems without requiring full-body correlation measurements.

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arXiv2026

Tomographic Limits of the Petz Recovery Map

The Petz recovery map is considered one of the key candidates for the quantum analogue of Bayesian inference and Jeffrey's conditionalization. Since, there seems to be a natural connection between Bayesian inference and the notion of state tomography, it is natural to ask if the Petz recovery can be used for this latter task. In this paper, we discuss such recent results on iterated Petz recovery and relate them to Bayesian approaches to quantum state tomography. We highlight the limitations of direct Petz iteration and show how an extended Petz construction, by lifting the inference problem to a classical distribution over candidate quantum states, recovers the structure of Bayesian and maximum likelihood tomography. This provides perspective on the modifications or nuances required for a Petz approach to quantum retrodiction to perform quantum state tomography.

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arXiv2026

Cluster-State Witnesses of Finite-Speed Hidden Influences

Bell experiments rule out local common-cause explanations of quantum correlations, yet they do not exclude hidden influences that travel faster than light while still having a finite speed in a preferred frame. Multipartite spacetime arrangements turn this possibility into a constraint: two late parties that are outside each other's hidden-influence cones must remain Bell-local once the earlier events are fixed. Here, we formulate this constraint as a projected-polytope separation problem for cluster-state correlations, using only marginal data containing at most one late party. From linear cluster states, we construct a four-qubit witness with the bound $S_4\le 6$ and quantum value $4+2\sqrt2$, and a five-qubit witness with $S_5\le 10$ and quantum value $6+4\sqrt2$. We certify that the exposed faces are facets of the corresponding projected hidden-influence polytopes. These results identify linear-cluster graph states as certifiable and experimentally friendly resources for finite-speed hidden-influence tests.

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arXiv2026

A quantum entropy production operator

We introduce a fully quantum notion of entropy production based on the non-commutative extension of the classical log-ratio between forward and reverse processes. Given a pair of quantum objects associated with the forward and reverse descriptions, we define a Hermitian entropy-production operator whose expectation value is non-negative and equal to the Belavkin--Staszewski relative entropy. The operator satisfies exact integral and detailed fluctuation theorems without requiring commutativity. We then specialize this construction to the case in which the forward process is described by a single quantum channel and the reverse process is defined inferentially, through Bayesian retrodiction relative to a prior state, with the Petz transpose map as the Bayesian inverse. In this setting, the relevant quantities can be evaluated explicitly, leading to a number of natural structural and physical properties. The framework recovers the classical formula in the commutative limit, yields explicit expressions for the average entropy production, and clarifies where the fully quantum case departs from standard thermodynamic expectations.

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arXiv2026

Information causality beyond the random access code model

Information causality (IC) was one of the first principles that have been invoked to bound the set of quantum correlations. For some families of correlations, this principle recovers exactly the boundary of the quantum set; for others, there is still a gap. We close some of these gaps using a new quantifier for IC, based on the notion of ``redundant information''. This progress was made possible by the recognition that the principle of IC can be captured without referring to the success criterion of random access codes. We give strong numerical evidence that the new definition is still obeyed by quantum correlations in the same scenario.

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arXiv2026

Proposal for creating spatial superposition of a large mass in a RF trap

Engineering coherent spatial superpositions of levitated large masses is an ongoing challenge. Borrowing from recent experimental work, we consider a charged mass of hundreds of nanometers size (``nanoparticle'') co-trapped with an ion in a Paul trap, and propose a scheme to manipulate its spatial state through the Coulomb interaction with the ion. We focus on the achievable delocalisation, only sketching the other challenges of the protocol (initial cooling, preservation of coherence for long-enough times, and detection). We prove that our scheme can displace coherently the nanoparticle by a few nanometers, and give an estimate of the allowed noise. Though smaller than the nanoparticle's size, the nanoparticle displacement is much larger than the wavefunction of the trap's ground state. Thus the co-trapping scheme is in principle able to demonstrate the delocalisation of a charged nanoparticle if the required noise isolation can be realised.

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arXiv2026

Proper and improper mixed states serve as different prior beliefs for quantum state retrodiction

A mixed quantum state can be taken as capturing an unspecified form of ignorance; or as describing the lack of knowledge about the true pure state of the system ("proper mixture"); or as arising from entanglement with another system that has been disregarded ("improper mixture"). These different views yield identical density matrices and therefore identical predictions for future measurements. But when used as prior beliefs for inferring the past state from later observations ("retrodiction"), they lead to different updated beliefs. This is a purely quantum feature of Bayesian agency. Based on this observation, we establish a framework for retrodicting on any quantum belief and we prove a necessary and sufficient condition for the equivalence of beliefs. We also illustrate how these differences have operational consequences in quantum state recovery.

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arXiv2026

Unifying Quantum Smoothing Theories with Extended Retrodiction

Estimating the state of an open quantum system monitored over time requires incorporating information from past measurements (filtering) and, for improved accuracy, also from future measurements (smoothing). While classical smoothing is well understood within a Bayesian framework, its quantum generalization has been challenging, leading to distinct and seemingly incompatible approaches. In this work, we demonstrate that quantum state smoothing hinges on a uniquely quantum feature: the fundamental dependence of retrodiction on prior correlations. We introduce auxiliary systems into the prior belief to capture correlations formed during preparation and evolution and develop a comprehensive framework for quantum state smoothing based on extended Bayesian retrodiction. This framework identifies all previous approaches as different choices of the extended prior, and naturally extends it to other choices that have not been considered before. We also give an information-theoretic characterization of the choices of prior, in terms of the average entropy of the smoothed states. Our results establish quantum state smoothing as a fundamentally retrodictive process just like classical smoothing, with proper quantum features clearly identified.

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arXiv2026

Experimental Tabletop Petz recovery of a photonic qubit

The quantum information lost in open evolutions cannot be fully recovered, but partial recovery is possible. The Petz recovery map guarantees almost optimal recovery, notably if the chosen reference state is close to the real one. This map has been widely used in theoretical studies, but has been the object of only a handful of experimental realisations, typically under a single fixed noise model. In this work, we describe and implement the Petz recovery map for a versatile class of qubit channels with tunable decoherence and dissipation. The setup we realize is also the first experimental example of ``tabletop reversibility'': for a good range of choices of the reference state, the Petz recovery map can be implemented with the same devices as the forward dissipative evolution, whose effect it is partially undoing. Our results demonstrate that the Petz recovery map can be resource-efficiently realized without requiring complex ancillary resources, providing a feasible pathway for mitigating information loss in quantum systems.

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arXiv2026

The Petz recovery map for optical losses

Optical systems are a main platform for quantum information processing. A main challenge is information loss due to scattering in unmonitored modes. These losses are modeled as state-independent beam-splitter interactions, with a thermal state (for all practical purposes, the vacuum) in the second input port. The perfect correction of these Gaussian lossy channels with Gaussian operations alone is known to be impossible. In this work, we investigate the Petz recovery map as an approximate recovery. For single mode losses and Gaussian reference states, the Petz map is found to use either a beam-splitter or a state-independent amplifier, depending on the parameters. Then we study the recovery performance on several examples, showing that it is near-optimal among the considered class of protocols. We also obtain more specific comparisons: Petz is always better than just re-preparing the reference state; but it is worse than doing nothing if the reference state is far from the true state. Finally, we extend our study to losses on two modes, and compare the global Petz map to the local implementation on each mode separately.

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arXiv2026

Three sins against physics by an exaggerated quantum information perspective

I point out three ways in which the perspective of quantum information may lead to distorted claims about physics: forgetting that light does not need to be quantised to show coherence; ignoring the generators of unitary evolutions; and approaching the discovery of nature as a fight against an adversary.

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arXiv2026

Kochen-Specker nonlocal hidden variables must include time-ordering to allow for measurement independence of several agents

We consider an ontology, in which contextual nonlocal hidden variables are stored as pre-existing possibilities in a repository outside space-time; and in which the context can be chosen ``freely'' (measurement independence) by each agent, both in spacelike and timelike configurations. We show that, in Bell-type experiments involving several agents, for this ontology to be consistent, the context must include not only the measurements that can be performed, but also the time ordering of the choices of different agents.

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arXiv2026

Sub-Bath Cooling in Bosonic Systems: Gaussian Constraints and Non-Gaussian Enhancements

Cooling quantum systems with finite resources is a central task in quantum technologies and has been extensively explored in discrete-variable settings. As continuous-variable (CV) platforms play an increasingly important role in quantum information processing, it becomes crucial to understand the fundamental limitations of cooling bosonic systems. In this work, we develop a general framework for cooling CV systems, identifying both the constraints imposed by Gaussianity and the advantages enabled by non-Gaussian interactions. We derive a reachable bound on the cooling performance of Gaussian operations that applies to arbitrary cooling architectures. By optimizing over all protocols saturating this bound, we further identify the most efficient scheme, which minimizes dissipated energy for a given number of ancilla modes. Beyond Gaussian operations, we show that $p$-excitation exchange exploits non-Gaussian resources to achieve a $p$-fold enhancement of the cooling limit. Our results establish the fundamental limits of CV heat-bath algorithmic cooling and reveal the crucial role of non-Gaussianity in surpassing Gaussian cooling barriers.

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arXiv2025

All three-angle variants of Tsirelson's precession protocol, and improved bounds for wedge integrals of Wigner functions

Tsirelson's precession protocol is a nonclassicality witness that can be defined for both discrete and continuous variable systems. Its original version involves measuring a precessing observable, like the quadrature of a harmonic oscillator or a component of angular momentum, along three equally-spaced angles. In this work, we characterise all three-angle variants of this protocol. For continuous variables, we show that the maximum score $\mathbf{P}_3^\infty$ achievable by the quantum harmonic oscillator is the same for all such generalised protocols. We also derive markedly tighter bounds for $\mathbf{P}_3^\infty$, both rigorous and conjectured, which translate into improved bounds on the amount of negativity a Wigner function can have in certain wedge-shaped regions of phase space. For discrete variables, we show that changing the angles significantly improves the score for most spin systems. Like the original protocol, these generalised variants can detect non-Gaussian and genuine multipartite entanglement when applied on composite systems. Overall, this work broadens the scope of Tsirelson's original protocol, making it capable to detect the nonclassicality and entanglement of many more states.

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