Quantifying the ergotropy (also known as available energy), namely the maximal amount of energy that can be extracted from a thermally isolated system, is a central problem in quantum thermodynamics. Notably, the same problem has been long studied for classical systems as well, e.g., in plasma physics and astrophysics, where the basic principles for its solution are known for the case of collisionless fluids. Here we provide the general analytical expression of ergotropy of classical systems valid regardless of their size and the type of interparticle interactions, and show that it emerges as the classical limit of the quantum expression of ergotropy, for quantum systems that are classically ergodic. We thus establish a unified theory of classical and quantum ergotropy, whose applicability ranges from atomic to galactic scale. Such unified theory is indispensable for studying the genuine quantum signatures of ergotropy: We show that the celebrated decomposition of quantum ergotropy into coherent ant inchoherent parts survives in the classical regime, indicating that coherences do not necessarily reveal quantumness. The unified theory also allows to port tools and methods across the classical-quantum boundary to unlock the solution of standing problems. We apply this to swiftly solve the open problem of ergotropy extraction in the classical regime.

Optical clocks based on atoms and ions probe relativistic effects with unprecedented sensitivity. They resolve time dilation due to atom motion or different positions in the gravitational potential through frequency shifts. However, all measurements of time dilation so far can be explained effectively as the result of dynamics with respect to a classical proper time parameter. Here we show that atomic clocks can probe effects where a classical description of the proper time dynamics is insufficient as superpositions of proper time emerge. We apply a Hamiltonian formalism to derive time dilation effects in harmonically trapped clock atoms and show how second-order Doppler shifts due to the vacuum energy, squeezing, and quantum corrections to the dynamics arise. We also demonstrate that time-dilation-induced entanglement between motion and clock evolution can become observable in state-of-the-art clocks when the motion of the atoms is strongly squeezed, realizing proper time interferometry. Our results show that experiments with trapped ion clocks are within reach of probing relativistic evolution of clocks for which a quantum description of proper time becomes necessary.

Consciousness presents a structural puzzle: a unified, context-sensitive, globally integrated mode of experience emerging from distributed neural dynamics. While classical neuroscience has mapped synaptic, oscillatory, and network-level mechanisms with increasing precision, debate persists as to whether classical formalisms fully capture the integrative and contextual features of conscious processing. This review examines whether quantum principles offer explanatory leverage in two distinct senses: as formal mathematical frameworks for modeling contextual cognition, and as mechanistic hypotheses proposing biologically instantiated non-classical states. We surveyed empirical and theoretical developments spanning zero-quantum-coherence in MRI signals, entanglement-structured learning paradigms, quantum-inspired computational models, and proposed neural substrates, including microtubules, nuclear spins, and photonic architectures. Although certain findings have been interpreted as consistent with a non-classical structure, no study to date has demonstrated entanglement, long-lived coherence, or collapse dynamics in neural tissue under operational criteria comparable to those used in controlled quantum systems. Replication remains limited, biological entanglement witnesses are not yet established, and nonlinear classical dynamics can reproduce many putative quantum signatures. Accordingly, the decisive question is not whether the brain is quantum, but whether its dynamics exceed the explanatory reach of rigorously defined classical models. Progress hinges on replication, adversarial scrutiny, and operational criteria precise enough to discriminate genuine non-classical correlations from classical complexity. Whether quantum mechanisms ultimately prove necessary or refined classical models remain sufficient, this inquiry compels a deeper understanding of integration, contextuality, and the physical constraints shaping conscious experience.

An arbitrated quantum signature scheme based on entanglement swapping and hash functions

Quantum signature protocols often rely on quantum states to carry signature information directly. However, they need SWAP tests, which require numerous copies to ensure accuracy and security, resulting in high implementation costs. This study proposes an arbitrated quantum signature protocol that incorporates classical information with entanglement swapping. Quantum states are converted into classical information immediately after measurement. The protocol does not rely on SWAP tests, avoids long-term storage of quantum signatures, and employs exclusive-OR operations and hash functions to process signature data. By leveraging a third-party arbitrator, it enables reliable identity verification of the signer and verifier, thereby guaranteeing unforgeability and nonrepudiation.

How does quantum chaos lead to rapid scrambling of information as well as systematic errors across a system when one introduces perturbations in the dynamics? What are its consequences for the reliability of quantum simulations and quantum information processing? We employ continuous measurement quantum tomography as a paradigm to study these questions. The measurement record is generated as a sequence of expectation values of a Hermitian observable evolving under repeated application of the Floquet map of the quantum kicked top. We construct a quantity to capture the scrambling of systematic errors, an out-of-time-ordered correlator (OTOC), which serves as a signature of chaos and quantifies the spread of errors. We show that the spread of errors, as quantified by the OTOC, is related to the operator Loschmidt echo, which is defined as the Hilbert-Schmidt inner product of the operators On, and O'n generated from repeated application of the Floquet map for ideal (unperturbed) dynamics and the true (perturbed) dynamics, respectively. This also gives us an operational interpretation of Loschmidt echo (LE) for operators by connecting it to the performance of quantum tomography. We show how our results demonstrate not only a link between LE and scrambling of errors different than previous studies, but also that such a link can have operational consequences in quantum information processing.

ABSTRACT We propose a novel quantum digital signature protocol that eliminates the need for a trusted third‐party, a common limitation in existing quantum signature schemes. While the concept of third‐party‐free quantum signatures has been discussed in earlier works, such as Gottesman and Chuang (2001), no concrete protocol with provable information‐theoretic security has been presented to date. Recent studies have explored computationally secure quantum signature schemes without trusted parties, but their security relies on assumptions about quantum computational hardness. In contrast, our protocol achieves information‐theoretic unforgeability based solely on the non‐cloning property of quantum states. It uses classical private keys and quantum public keys, and requires only single‐qubit operations. The scheme also satisfies key security properties, including asymmetry, undeniability, and expandability, making it suitable for implementation in near‐term quantum technologies.

Plants exhibit rapid, coordinated responses to environmental stimuli despite lacking a central nervous system, prompting interest in non-classical signaling mechanisms. Recent findings in quantum biology indicate that quantum coherence and entanglement, previously considered too ephemeral for the hot, humid biological medium, could be the basis for certain types of plant signal transduction. This review integrates present knowledge on plant signaling networks and describes theoretical frameworks in which quantum behavior could be involved. Theoretical models, including site-based Hamiltonians for exciton transport in photosynthetic complexes, spin-Hamiltonian models of radical-pair processes in cryptochromes, and quantum percolation theories of plasmodesmatal transport, are reviewed. These models propose that plants might utilize quantum correlations to increase signal fidelity, energy efficiency, and adaptive response between tissues. Experimental evidence for coherence in photosynthesis and cryptochrome-mediated magnetoreception supports these models. Quantum entanglement is proposed to improve long-distance communication and energy transfer in plants. Implications for practical applications range from quantum-informed crop breeding, precision farming, and efficient resource management. Future research directions, including experimental verification of quantum signatures in vivo, are outlined, with implications for bio-inspired quantum engineering in agriculture. Combining quantum mechanics and plant biology provides a paradigm-changing view of plant communication and opens new interdisciplinary horizons in fundamental science and agricultural innovations.

In classical mechanics, driven systems with dissipation often exhibit complex, fractal dynamics known as strange attractors. This paper addresses the fundamental question of how such structures manifest in the quantum realm. We investigate the quantum Duffing oscillator, a paradigmatic chaotic system, using the Caldirola-Kanai framework, where dissipation is integrated directly into a time-dependent Hamiltonian. By employing the Husimi distribution to represent the quantum state in phase space, we present the first visualization of a quantum strange attractor within this model. Our simulations demonstrate how an initially simple Gaussian wave packet is stretched, folded, and sculpted by the interplay of chaotic dynamics and energy loss, causing it to localize onto a structure that beautifully mirrors the classical attractor. This quantum "photograph" is inherently smoothed, blurring the infinitely fine fractal details of its classical counterpart as a direct consequence of the uncertainty principle. We supplement this analysis by examining the out-of-time-ordered correlator, which shows that stronger dissipation clarifies the exponential growth associated with the classical Lyapunov exponent, thereby confirming the model's semiclassical behavior. This work offers a compelling geometric perspective on open chaotic quantum systems and sheds new light on the quantum-classical transition.

Identifying quantum chaos in Floquet systems with mixed classical phase spaces requires robust experimentally accessible signatures. We investigate the time-averaged quantum Fisher information (QFI) and the fidelity out-of-time-ordered correlator (FOTOC) of continuous periodically driven systems. We uncover two distinct power-law scalings of the time-averaged QFI with respect to system size: the standard quantum limit and the Heisenberg limit. These scalings correspond to initial states localized in the regular and chaotic regions of the classical phase space, respectively. Remarkably, we show that the time-averaged FOTOC can accurately identify the transition from mixed phase space to fully chaotic sea (at a critical driving strength Bx≈5.3) as verified by the maximum Lyapunov exponent. The results suggest that both time-averaged QFI and FOTOC can be used as excellent quantum signatures for probing mixed phase-space structures and our adopted protocol for measuring the FOTOC eliminates the need for time-reversal operations. This work establishes a practical framework for investigating quantum chaos in Floquet systems, bridging theoretical insights with experimental applications.

Blockchain systems built on classical cryptography face immediate risks from large-scale quantum computers, while purely quantum-based blockchains often rely on a single Private Key Generator (PKG) and incur heavy resource overheads. To overcome these issues, this paper proposes a hybrid quantum and post-quantum blockchain approach that removes single points of trust by using Distributed Key Generation and a dual-layer signature mechanism. This method integrates quantum digital signatures, rooted in the Fully Flipped Permutation problem, with classical post-quantum (lattice-based) cryptography, enabling users to switch between quantum and classical signatures according to security requirements and channel conditions. Delegated Proof-of-Stake with node behavior and Borda count has been incorporated to manage consensus, ensuring that witness nodes are regularly re-elected and malicious actors are penalized by distributing secret shares among multiple rotating witnesses. We eliminate the central vulnerability of a sole PKG while maintaining rigorous resistance to collusions. Our analytical model indicates that a fraction of transactions can use quantum signatures without system-wide bottlenecks, while the remaining transactions follow classical PQC paths with throughput approaching classical baselines under our modeling assumptions. Consequently, this hybrid method offers higher scalability, robust collusion resistance, and long-term security even under quantum-capable adversaries. This paper presents extensive theoretical analyses, probability models, and algorithmic complexities, demonstrating that our design provides resilient infrastructure that meets the key performance and security requirements of next-generation blockchain systems.

There is a growing interest in investigating top-quark systems using tools from quantum information theory. A key peculiarity of the top quark is that it decays before hadronization or spin decorrelation occurs, thereby preserving its spin information. This unique property enables direct access to spin correlations, making the top quark an ideal candidate for probing fundamental quantum correlations in high-energy physics processes. A wide range of concepts from quantum information theory, such as entanglement, Bell nonlocality, quantum steering, quantum discord, and fidelity, have been investigated in this context. Several of these measures have been employed as diagnostic tools to test the Standard Model and to search for possible signatures of physics beyond. However, the (NAQC) has remained largely unexplored in this context. In this work, we present a detailed investigation of the NAQC in top quark pair production. We employ two complementary NAQC measures based on the l 1 norm and the relative entropy of coherence. We also study the effect of angular averaging on these measures and assess the sensitivity of current LHC spin-correlation measurements to NAQC. Our findings reveal rich coherence structures and highlight NAQC as potentially a novel and complementary quantum signature in high-energy physics systems.

The luminescence properties of semiconductors are key to the development of photonics. In recent years, the targeted semiconductor materials have shifted from narrow-bandgap to wide- and ultra-wide-bandgap ones, which means spanning the domains of operation for devices beyond those possible with conventional semiconductors in the fields of high-power devices and deep-ultraviolet photodetectors. Furthermore, materials nanostructures with one or more dimensions at the nanoscale drive additional novelties in their optical properties, boosting innovative features. The next step in advanced materials necessarily goes through the quantum - photonic link, in which electromagnetic waves and electronic quantum states display all possible degrees of freedom. To achieve effective advances in this field, both innovative research in materials science and the development of suitable strategies to assess the quantum signatures in the material systems under study are required. This work reviews the fascinating light emission and confinement in wide and ultra-wide bandgap semiconducting oxides of technological interest in nanostructured form, focusing on their luminescence and the key role they can play in future quantum photonic technologies, such as single photon sources and quantum sensing. Finally, an outlook on future avenues in research isoutlined.

Transport across model junctions built by using atomic tip or lateral techniques can generate exotic quantum signatures. However, so far, a viable industrial pathway for atom-driven electronics has been lacking. Here, we demonstrate that a commercialized device platform can help to fill this nanotechnological gap. According to conducting tip atomic force microscopy, inserting C atoms into an ultrathin MgO layer generates nanotransport paths. Across microscale magnetic tunnel junctions, resonant tunneling causes large magnetoresistance peaks that we attribute to spin accumulation onto a C nanodot that the channels transport. We ascribe the concurrent presence of a spectrally localized, nonlinear current noise and a persistent memory effect to the charging of a 'gating' C nanodot, adjacent to the 'transport' C nanodot. This nanoscale dual-dot description of quantum transport across spin states within a microscale magnetic tunnel junction should stimulate further research toward maturing spintronics into a viable quantum technological track.

To probe the limits of dynamic thermalization, we numerically investigate the stability of exceptional periodic classical trajectories in chaotic many-spin systems and explore a possible connection between these trajectories and exceptional nonthermal quantum eigenstates known as "quantum many-body scars." The systems considered are chaotic spin chains with short-range interactions, both classical and quantum. On the classical side, the chosen periodic trajectories are such that all spins instantaneously point in the same direction, which evolves as a function of time. We find that the largest Lyapunov exponents characterizing the stability of these trajectories have surprisingly strong and nontrivial dependencies on the interaction constants and chain lengths. In particular, we identify rather long spin chains, where the above periodic trajectories are Lyapunov stable on many-body energy shells overwhelmingly dominated by chaotic motion. We show that the above phenomenology can be quantitatively described by connecting Lyapunov instabilities of translationally invariant periodic trajectories to irreducible representations of the translational symmetry group with well-defined wave vectors. We also find that instabilities around periodic trajectories in modestly large spin chains develop into a transient nearly quasiperiodic nonergodic regime. In some cases, the lifetime of this regime is extremely long, which we interpret as a manifestation of Arnold diffusion in the vicinity of integrable dynamics. On the quantum side, we numerically investigate the dynamics of quantum states starting with all spins initially pointing in the same direction: These are the quantum counterparts of the initial conditions for the above periodic classical trajectories. Our investigation reveals the existence of quantum many-body scars for numerically accessible finite chains of spins-3/2 and higher. No evidence of quantum scars was observed for spin-1/2 chains, while spin-1 chains were found to be transitional in this respect. The dynamic thermalization process dominated by quantum scars is shown to exhibit a slowdown in comparison with generic thermalization at the same energy. Finally, we identify quantum signatures of the proximity to a classical separatrix of the periodic motion.

A simplified arbitrated quantum signature protocol without entanglement: Design premise and security analysis

Transmission through potential barriers is a fundamental problem in quantum mechanics. While semiclassical methods can approximate certain aspects of transmission, they fail to capture the intrinsically quantum interference associated with Wigner-function negativity. We numerically study the transmission of displaced Fock states through an inverted-oscillator barrier, with and without a Kerr nonlinearity that offers a potential route to experimental realization. These states allow only an approximate classical description since their characteristic Wigner-function negativity is absent in phase space. The semiclassical simulation reproduces the overall transmission, but deviates from exact results and fails to capture short-time plateaus that arise when regions of Wigner-function negativity cross the barrier. With the Kerr nonlinearity, reflections from nonlinear boundaries drive interference into classically forbidden regions, an effect that is inaccessible to semiclassical approaches. We find that these interference effects do not alter the maximum transmission probability, which is bounded by the initial positive-energy fraction and therefore already encoded in the phase-space structure of the Fock states. Because Fock states cannot be faithfully represented within classical phase space, the transmission through a barrier reveals the fundamental limitations of semiclassical approaches.

The Earth’s geomagnetic field (GMF) is a fundamental environmental signal for plants, with its perception rooted in quantum biology. Specifically, the radical pair mechanism (RPM) explains how this weak force influences electron spin states in metabolic pathways, providing a framework for its profound biological impact. Research shows that a hypomagnetic field (hMF) directly reduces the production of reactive oxygen species (ROS), creating a quantum signature in plants. This is a counterintuitive finding, as it suggests the plant perceives less oxidative stress and, in response, downregulates its antioxidant defenses. This multi-level effect, from a quantum trigger to molecular and metabolic changes, ultimately affects the plant’s growth and phenotype. This review suggests a possible link between the GMF and plant health, identifying the GMF as a potential physiological modulator. Manipulating the magnetic field could therefore be a novel strategy for improving crop resilience and growth. However, the fact that some effects cannot be fully explained by the RPM suggests other quantum mechanisms are involved, paving the way for future research into these undiscovered processes and their potential inheritance across generations.

Abstract The quantum signature of the innermost stable circular orbit (ISCO), a region of profound importance in black hole astrophysics, is investigated. An atom is modeled as an Unruh–DeWitt detector coupled to a massless scalar field in the Boulware vacuum, and the excitation rate is calculated for a detector following a circular geodesic at the ISCO of a Schwarzschild black hole. In stark contrast to the continuous thermal spectra associated with static or infalling observers, the analysis reveals a unique, non‐thermal excitation spectrum characterized by a discrete “frequency comb” of sharp, resonant peaks. The locations of these peaks are determined by the orbital frequency at the ISCO, while their intensity increases dramatically as the orbit approaches this final stability boundary. This distinct spectral signature offers a novel theoretical probe of the quantum vacuum in a strong‐field gravitational regime and provides a clear distinction between the quantum phenomena experienced by observers on different trajectories. The findings have potential implications for interpreting the emission spectra from accretion disks and open new avenues for exploring the connection between quantum mechanics and gravity.

Quantum signature with formal security proof