arXiv subjects

Borivoje Dakić

Publications and source records attributed to Borivoje Dakić.

At least 19 recordsLinked to original sources

arXiv2026

Entanglement without Quantum Mechanics: Operational Constraints on the Quantum Signature

Quantum entanglement is defined as nonseparability of density operators, yet experimental phase-space statistics alone cannot distinguish classical from quantum sources, so classical data can be used to violate en- tanglement inequalities. Imposing uncertainty bounds, or full tomography, can map the same data onto positive, entangled density operators, yielding a hybrid regime in which classical and quantum models coincide. Thus, certifying genuine quantum entanglement requires additional tests, such as Wigner negativity, incompatibility beyond phase-space measurements, or nonlinear dynamics.

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arXiv2026

Reply to the Comment on "The Axiom of Choice and the No-Signalling Principle"

We clarify the meaning of a probabilistic no-signalling strategy in Ref [Proc. R. Soc. A 481, 20240601]. For every fixed input, the deterministic strategy constructed using the Axiom of Choice can indeed be represented by a Dirac probability distribution over the outputs. The relevant distinction arises when one considers the complete process from input to output, with the input itself sampled according to a probability distribution. In this case, the input and output spaces must be measurable and the dependence of the conditional output distribution on the input must also be measurable. Equivalently, the conditional distributions must form a Markov kernel. The Axiom-of-Choice strategy fails precisely this measurability requirement.

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arXiv2026

Classical and quantum mechanics across representations: an operational reading of the Wigner Weyl correspondence

The physical content of a theory is not intrinsically tied to any single mathematical formalism. Both classical and quantum mechanics admit equivalent representations, notably in phase space and in Hilbert space, related by the Wigner-Weyl correspondence. While this correspondence has long been studied in mathematical physics, its foundational and operational implications are often left implicit. Here we give a systematic account of what changes, and what does not, when classical and quantum theories are expressed in each other's native language. This representational viewpoint separates artifacts (such as the appearance of non-positivity or negativity under certain maps) from robust structural distinctions that persist across representations, in particular noncommutativity and its $\hbar$-dependent $\star$-deformation of the classical algebra. We develop the comparison at the level of states, kinematics, and dynamics, and extend it to measurement by formulating both outcome statistics and state-update rules within the same framework.

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arXiv2026

Gravitational Entanglement in Optomechanics: Distinguishing Classical and Quantum Models

Observation of gravitationally induced quantum entanglement is often interpreted as a direct evidence of non-classical gravity. While the form and the degree of non-classicality have been rigorously studied from a foundational perspective, classical models reproducing experimental signatures of such entanglement remain underexplored. Motivated by the experimental simplicity, nearly all existing optomechanical approaches assume Gaussian initial states, and due to the weakness of gravity the quantum Newtonian potential is truncated at the second order. However, this regime admits a classical description in terms of the Wigner-Weyl representation, including features typically associated with quantum entanglement. A clear distinction between classical and quantum predictions emerges only beyond this setting. We comprehensively analyze the possibilities and provide operational witnesses for detection of non-classicality via Wigner negativity, and detection of non-quantumness via negativity of the Weyl operator. Our results demonstrate that the experimental requirements on certifying gravitational entanglement are more stringent than previously anticipated.

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arXiv2026

The classical limit of quantum mechanics through coarse-grained measurements

Understanding how classical physics emerges from quantum mechanics remains a central problem in the foundations of physics. Here we derive a classical limit from finite-resolution measurements, modeled by continuous coarse-grained POVMs. When the resolved phase-space area is large compared with Planck's constant, the accessible statistics of any quantum state admit an effective classical description: coarse-grained observables become approximately jointly measurable and the induced probability density is positive. We derive the exact evolution equation for this density and show that, in the strong coarse-graining regime, its non-Liouville corrections are suppressed up to an Ehrenfest time, resulting in classical Hamiltonian flow generated by a Hamiltonian smoothed over the measurement cell. When the Hamiltonian varies negligibly across such a cell, the smoothed Hamiltonian reduces to the classical Hamiltonian whose quantization produced the quantum dynamics, thereby closing the quantization--classical-limit loop. Repeated finite-resolution measurements then generate stochastic records confined, with high probability, to tubes around classical trajectories. Our results provide a unified operational framework for the quantum-to-classical transition in microscopic and macroscopic systems, and establish the consistency of the quantization--classical-limit cycle.

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arXiv2026

Reconstruction of Quantum Fields: CCR, CAR and Transfields

One of the traditional ways of introducing bosons and fermions is through creation-annihilation algebras. Historically, these have been associated with emission and absorption processes at the quantum level and are characteristic of the language of second quantization. In this work, we formulate the transition from first to second quantization by taking quotients of the state spaces of distinguishable particles, so that the resulting equivalence classes identify states that contain no information capable of distinguishing between particles, thereby generalising the usual symmetrisation procedure. Assuming that the resulting indistinguishable-particle space (i) admits an ordered basis compatible with how an observer may label the accessible modes, (ii) is invariant under unitary transformations of those modes, and (iii) supports particle counting as a mode-wise local operation, we derive a new class of creation-annihilation algebras. These algebras reproduce the partition functions of transtatistics, the maximal generalisations of bosons and fermions consistent with these operational principles.

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arXiv2026

Acquisition of delocalized information via classical and quantum carriers

We investigate the information-theoretic power of spatial superposition by analyzing tasks in which infor- mation is locally encoded at multiple distant sites and must be acquired by a single information carrier, such as a particle. Within an operational framework, we systematically compare the statistical correlations that can be generated in such tasks using classical particles, quantum particles in spatial superposition, and more general "second-order interference" resources. We bound classical strategies via convex polytopes and present a study of their symmetry, demonstrating that the vertices are inherently connected to K-juntas as defined in the classical theory of Boolean functions, while their facet inequalities are in one-to-one correspondence with oracle games. We then analyze the violation of the "fingerprinting inequality" achievable by the use of one quantum particle, and we study the dependence of this violation on the dimension d of the particle's internal degree of freedom. In particular, we show that the case of d = 2 can achieve a higher violation of the inequality than the previously investigated case of d = 1. We also provide analytic and numerical evidence that this violation cannot be further increased for larger d > 2. Finally, we find that both quantum and any other (generalized) second-order interference models exhibit the same asymptotic scaling in violating the fingerprinting inequality. Our results thereby further articulate quantum interference and spatial superposition as a resource for information processing.

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arXiv2026

Post-processing optimization and optimal bounds for non-adaptive shadow tomography

Informationally overcomplete POVMs are known to outperform minimally complete measurements in many tomography and estimation tasks, and they also leave a purely classical freedom in shadow tomography: the same observable admits infinitely many unbiased linear reconstructions from identical measurement data. We formulate the choice of reconstruction coefficients as a convex minimax problem and give an algorithm with guaranteed convergence that returns the tightest state-independent variance bound achievable by post-processing for a fixed POVM and observable. Numerical examples show that the resulting estimators can dramatically reduce sampling complexity relative to standard (canonical) reconstructions, and can even improve the qualitative scaling with system size for structured noncommuting targets.

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arXiv2025

Testing Single Photon Entanglement using Self-Referential Measurements

Entanglement does not always require one particle per party. It was predicted some thirty years ago that a single photon traversing a beam splitter could violate a Bell inequality. Although initially debated, single-photon nonlocality was eventually demonstrated via homodyne measurements. Here, we present an alternate realisation that avoids the complexity of homodyne measurements and potential loopholes in their implementation. We violate a Bell inequality by performing joint measurements on two copies of the same single-photon entangled state, where one photon acts as a phase reference for the other, making it self-referential. We observe CHSH parameters of $2.71\pm 0.09$ and $2.23\pm 0.07$, depending on the joint measurements implemented. This offers a new perspective on single-photon nonlocality and a more accessible experimental route, potentially applicable to general mode-entangled states in diverse platforms.

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arXiv2025

Quantum theory at the macroscopic scale

The quantum description of the microscopic world is incompatible with the classical description of the macroscopic world, both mathematically and conceptually. Nevertheless, it is generally accepted that classical mechanics emerges from quantum mechanics in the macroscopic limit. In this letter, we challenge this perspective and demonstrate that the behavior of a macroscopic system can retain all aspects of the quantum formalism, in a way that is robust against decoherence, particle losses and coarse-grained (imprecise) measurements. This departure from the expected classical description of macroscopic systems is not merely mathematical but also conceptual, as we show by the explicit violation of a Bell inequality and a Leggett-Garg inequality.

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arXiv2025

Experimental Quantum State Certification by Actively Sampling Photonic Entangled States

Entangled quantum states are essential ingredients for many quantum technologies, but they must be validated before they are used. As a full characterization is prohibitively resource-intensive, recent work has focused on developing methods to efficiently extract a few parameters of interest, in a so-called verification framework. Most existing approaches are based on preparing an ensemble of nominally identical and independent (IID) quantum states, and then measuring each copy of the ensemble. However, this leaves no states left for the intended quantum tasks and the IID assumptions do not always hold experimentally. To overcome these challenges, we experimentally implement quantum state certification (QSC) proposed by Gocanin \textit{et al.}, which measures only a subset of the ensemble, certifying the fidelity of multiple copies of the remaining states. We use active optical switches to randomly sample from sources of two-photon Bell states and three-photon GHZ states, reporting statistically-sound fidelities in real time without destroying the entire ensemble. Additionally, our QSC protocol removes the assumption that the states are identically distributed (but still assumes independent copies), can achieve close $N^{-1}$ scaling, in the number of states measured $N$, and can be implemented in a device-independent manner. Altogether, these benefits make our QSC protocol suitable for benchmarking large-scale quantum computing devices and deployed quantum communication setups relying on entanglement in both standard and adversarial situations.

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arXiv2025

Experimental data re-uploading with provable enhanced learning capabilities

The last decades have seen the development of quantum machine learning, stemming from the intersection of quantum computing and machine learning. This field is particularly promising for the design of alternative quantum (or quantum inspired) computation paradigms that could require fewer resources with respect to standard ones, e.g. in terms of energy consumption. In this context, we present the implementation of a data re-uploading scheme on a photonic integrated processor, achieving high accuracies in several image classification tasks. We thoroughly investigate the capabilities of this apparently simple model, which relies on the evolution of one-qubit states, by providing an analytical proof that our implementation is a universal classifier and an effective learner, capable of generalizing to new, unknown data. Hence, our results not only demonstrate data re-uploading in a potentially resource-efficient optical implementation but also provide new theoretical insight into this algorithm, its trainability, and generalizability properties. This lays the groundwork for developing more resource-efficient machine learning algorithms, leveraging our scheme as a subroutine.

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arXiv2025

Experimental neuromorphic computing based on quantum memristor

Machine learning has recently developed novel approaches, mimicking the synapses of the human brain to achieve similarly efficient learning strategies. Such an approach retains the universality of standard methods, while attempting to circumvent their excessive requirements, which hinder their scalability. In this landscape, quantum (or quantum inspired) algorithms may bring enhancement. However, high-performing neural networks invariably display nonlinear behaviours, which poses a challenge to quantum platforms, given the intrinsically linear evolution of closed systems. We propose a strategy to enhance the nonlinearity achievable in this context, without resorting to entangling gates and report the first neuromorphic architecture based on a photonic quantum memristor. In detail, we show how the memristive feedback loop enhances the nonlinearity and hence the performance of the tested algorithms. We benchmark our model on four tasks, a nonlinear function and three time series prediction. In these cases, we highlight the essential role of the quantum memristive element and demonstrate the possibility of using it as a building block in more sophisticated networks.

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arXiv2025

Robust and Indestructible Macroscopic Entanglement

In this letter we investigate the possibility of observing macroscopic entanglement, considering realistic factors such as decoherence, particle losses, and measurements of limited precision (coarse-grained collective measurements). This forms the foundation for an operational definition of robust macroscopic entanglement. We also propose an even more resilient concept of macroscopic entanglement, allowing the parties to randomly select their portion of the shared system. Through a straightforward example, we demonstrate that achieving this is feasible using a simple class of quantum states. Our result opens a path for generalizing notions of quantum entanglement, such as a genuine multipartite entanglement in the macroscopic domain.

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arXiv2024

Optimising quantum tomography via shadow inversion

In quantum information theory, the accurate estimation of observables is pivotal for quantum information processing, playing a crucial role in compute and communication protocols. This work introduces a novel technique for estimating such objects, leveraging an underutilised resource in the inversion map of classical shadows that greatly refines the estimation cost of target observables without incurring any additional overhead. A generalised framework for computing and optimising additional degrees of freedom in the homogeneous space of the shadow inversion is given that may be adapted to a variety of near-term problems. In the special case of local measurement strategies we show feasible optimisation leading to an exponential separation in sample complexity versus the standard approach and in an exceptional case we give non-trivial examples of optimised post-processing for local measurements, achieving the same efficiency as the global Cliffords shadows.

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arXiv2024

Reconstruction of Quantum Particle Statistics: Bosons, Fermions, and Transtatistics

Identical quantum particles exhibit only two types of statistics: bosonic and fermionic. Theoretically, this restriction is commonly established through the symmetrization postulate or (anti)commutation constraints imposed on the algebra of creation and annihilation operators. The physical motivation for these axioms remains poorly understood, leading to various generalizations by modifying the mathematical formalism in somewhat arbitrary ways. In this work, we take an opposing route and classify quantum particle statistics based on operationally well-motivated assumptions. Specifically, we consider that a) the standard (complex) unitary dynamics defines the set of single-particle transformations, and b) phase transformations act locally in the space of multi-particle systems. We develop a complete characterization, which includes bosons and fermions as basic statistics with minimal symmetry. Interestingly, we have discovered whole families of novel statistics (dubbed transtatistics) accompanied by hidden symmetries, generic degeneracy of ground states, and spontaneous symmetry breaking -- effects that are (typically) absent in ordinary statistics.

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arXiv2024

Quantum coherence in networks

From a quantum information perspective, verifying quantum coherence in a quantum experiment typically requires adjusting measurement settings or changing inputs. A paradigmatic example is that of a double-slit experiment, where observing the interference pattern on the screen in a series of experimental settings where one, the other, and both slits are open unambiguously proves quantum coherence. Here we show that this is not necessary by verifying quantum coherence in a network scenario without the need for inputs. We show that there exist probability distributions for joint outcomes of three parties in a triangular network with independent sources that cannot be replicated using classical resources. Furthermore, we generalize our results to $n$-party networks and show that the discrepancy between correlations in classical and quantum networks increases with the number of parties. To this end, we derive nonlinear inequalities that are satisfied by classical correlations and find quantum states that violate them.

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arXiv2024

Direct and Efficient Detection of Quantum Superposition

One of the most striking quantum phenomena is superposition, where one particle simultaneously inhabits different states. Most methods to verify coherent superposition are indirect, in that they require the distinct states to be recombined. Here, we adapt an XOR game, in which separated parties measure different parts of a superposed particle, and use it to verify superpositions with \textit{local measurements} and a second independent particle. We then turn this game into a resource-efficient verification scheme, obtaining a confidence that the particle is superposed which approaches unity exponentially fast. We demonstrate our scheme using a single photon, obtaining a 99\% confidence that the particle is superposed with only 37 copies. Our work shows the utility of XOR games to verify quantum resources, allowing us to efficiently detect quantum superposition without reinterfering the superposed states.

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