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Quantum private comparison (QPC) represents a cryptographic approach that enables two parties to determine whether their confidential data are equivalent, without disclosing the actual values. Most existing QPC protocols utilizing single photons or Bell states are considered highly feasible, but they suffer from inefficiency. To address this issue, we present a novel QPC protocol that capitalizes on the entanglement property of Bell states and local operations to meet the requirements of efficiency. In the proposed protocol, two participants with private inputs perform local operations on shared Bell states received from a semi-honest third party (STP). Afterward, the modified qubits are returned to the STP, who can then determine the equality of the private inputs and relay the results to the participants. A simulation on the IBM Quantum Cloud Platform confirmed the feasibility of our protocol, and a security analysis further demonstrated that the STP and both participants were unable to learn anything about the individual private inputs. In comparison to other QPC protocols, our proposed solution offers superior performance in terms of efficiency.

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The paper considers the possibility of implementing a quantum entanglement distribution in the cell microtubule. It has been shown that a quantum entanglement distribution proposed in the paper determines the process of quantum state teleportation through microtubule tryptophan chain. The work shows that the system of tryptophans in a microtubule essentially is a quantum network that consists of: spatially spaced nodes - tryptophans, quantum communication channels connecting tryptophans and qubits transmitted through these communication channels. The connection between the process of quantum teleportation in living nature and its classical analogue is discussed. The quantum protocol established in the work determines the possible principle of quantum information transmission in biosystems and also in the similar nanostructures.

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INTRODUCTION: There has been accumulating interest in the application of biofield therapy as complementary and alternative medicine (CAM) to treat various diseases. The practices include reiki, qigong, blessing, prayer, distant healing, known as biofield therapies. This paper aims to state scientific knowledge on preclinical and clinical studies to validate its potential use as an alternative medicine in the clinic. It also provides a more in-depth context for understanding the potential role of quantum entanglement in the effect of biofield energy therapy. CONTENT: A comprehensive literature search was performed using the different databases (PubMed, Scopus, Medline, etc.). The published English articles relevant to the scope of this review were considered. The review gathered 45 papers that were considered suitable for the purpose. Based on the results of these papers, it was concluded that biofield energy therapy was effective in treating different disease symptoms in preclinical and clinical studies. SUMMARY: Biofield therapies offer therapeutic benefits for different human health disorders, and can be used as alternative medicine in clinics for the medically pluralistic world due to the growing interest in CAM worldwide. OUTLOOK: The effects of the biofield energy therapies are observed due to the healer's quantum thinking, and transmission of the quantum energy to the subject leads to the healing that occurs spiritually through instantaneous communication at the quantum level via quantum entanglement.

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Single-layer transition-metal dichalcogenides provide an unique intrinsic entanglement between the spin/valley/orbital degrees of freedom and the polarization of scattered photons. This scenario gives rise to the well-assessed optical dichroism observed by using both steady and time-resolved probes. In this paper, we provide compact analytical modeling of the onset of a finite Faraday/Kerr optical rotation upon shining with circularly polarized light. We identify different optical features displaying optical rotation at different characteristic energies, and we describe in an analytical framework the time-dependence of their intensities as a consequence of the main spin-conserving and spin-flip processes.

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The cell is both synchronic and diachronic, based on ontogeny and phylogeny, respectively. As experimental evidence for this holism, absent gravitational force, differentiated lung and bone cells devolve, losing their phenotypes, losing their evolutionary status, reverting to their nonlocal status. Thus, when evolution is seen as serial homeostasis, it is homologous with Quantum Entanglement as the nonlocal means of maintaining homeostatic balance between particles. This monadic perspective on consciousness is one-hundred and eighty degrees out of synch with the conventional way of thinking about consciousness as a diad, or mind and brain. There have been many attempts to explain consciousness, virtually all of them based on the brain as mind. The working hypothesis is that consciousness is a holism constituted by the unicell, the lipid cell membrane forming a barrier between inside and outside of the cell's environment as a topology. Conceptually, both the unicell and 'two hands clapping' are holisms, but because the cell is constituted by the ambiguity of negative entropy, and 'one hand clapping' requires two hands, they are both pseudo-holisms, constantly striving to be whole again. In the case of the cell, it is incomplete in the sense that there are factors in the ever-changing environment that can homeostatically complete it. That process results in biochemical modification of specific DNA codes in the egg or sperm so that the offspring is able to adapt in subsequent generations epigenetically. The opportunity to trace the evolution of the breath from humans to fish opens up to the further revelation of the interplay between evolution and geological change, tracing it back to invertebrates, sponges, and ultimately to unicellular organisms. And therein is evidence that the Cosmos itself 'breathes', providing the ultimate celestial fundament for this trail of holisms.

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To estimate the degree of quantum entanglement of random pure states, it is crucial to understand the statistical behavior of entanglement indicators such as the von Neumann entropy, quantum purity, and entanglement capacity. These entanglement metrics are functions of the spectrum of density matrices, and their statistical behavior over different generic state ensembles have been intensively studied in the literature. As an alternative metric, in this work, we study the sum of the square root spectrum of density matrices, which is relevant to negativity and fidelity in quantum information processing. In particular, we derive the finite-size mean and variance formulas of the sum of the square root spectrum over the Bures-Hall ensemble, extending known results obtained recently over the Hilbert-Schmidt ensemble.

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Quantum Entanglement has been hypothesized to mediate non-local consciousness, underlying which, empirically, is the force of gravity. Upon further reflection, the case can be made for 'the breath' as the physiologic trait that binds all of these properties together, offering further opportunity for hypothesis testing experimentation. Humans have inexplicably made extraordinary intellectual and technical advances within a relatively very short period of time, referred to as the 'great leap forward'. It would be of great value if we could identify how and why we have evolved so rapidly. There is a holotropism that begins with the Big Bang that is centered on the homeostatic control of energy, perpetually referencing the First Principles of Physiology. "The Breath" is how and why our physiology has managed to perpetuate our species, and perhaps why the lung has been 'over-engineered' in order to facilitate the role of breathing in consciousness.

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The cell-cell signaling mechanisms that are the basis for all of physiology have been used to trace evolution back to the unicellular state, and beyond, to the "First Principles of Physiology". And since our physiology derives from the Cosmos based on Symbiogenesis, it has been hypothesized that the cell behaves like a functional Mobius Strip, having no 'inside or outside' cell membrane surface - it is continuous with the Cosmos, its history being codified from Quantum Entanglement to Newtonian Mechanics, affording the cell consciousness and unconsciousness/subconsciousness as a continuum for the first time. Similarly, Klein and Maimon have concluded that their 'Soft Logic' mathematics also constitutes a Mobius Strip, using both a real number axis, combined with a zero axis, numerically representing cognition. This is congruent with the cell as 'two-tiered' consciousness, the first tier being the real-time interface between the cell membrane and its environment; the second tier constituting integrated physiology, referencing the consciousness of the Cosmos. Thus, there is coherence between physiology, consciousness and mathematics for the first time.

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The future quantum internet will leverage existing communication infrastructures, including deployed optical fibre networks, to enable novel applications that outperform current information technology. In this scenario, we perform a feasibility study of quantum communications over an industrial 224 km submarine optical fibre link deployed between Southport in the United Kingdom (UK) and Portrane in the Republic of Ireland (IE). With a characterisation of phase drift, polarisation stability and the arrival time of entangled photons, we demonstrate the suitability of the link to enable international UK-IE quantum communications for the first time.

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We review methods that allow one to detect and characterize quantum correlations in many-body systems, with a special focus on approaches which are scalable. Namely, those applicable to systems with many degrees of freedom, without requiring a number of measurements or computational resources to analyze the data that scale exponentially with the system size. We begin with introducing the concepts of quantum entanglement, Einstein-Podolsky-Rosen steering, and Bell nonlocality in the bipartite scenario, to then present their multipartite generalization. We review recent progress on characterizing these quantum correlations from partial information on the system state, such as through data-driven methods or witnesses based on low-order moments of collective observables. We then review state-of-the-art experiments that demonstrate the preparation, manipulation and detection of highly-entangled many-body systems. For each platform (e.g. atoms, ions, photons, superconducting circuits) we illustrate the available toolbox for state preparation and measurement, emphasizing the challenges that each system poses. To conclude, we present a list of timely open problems in the field.

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The quantum entanglement entropy of the electrons in a one-dimensional hydrogen molecule is quantified locally using an appropriate partitioning of the two-dimensional configuration space. Both the global and the local entanglement entropy exhibit a monotonic increase when increasing the inter-nuclear distance, while the local entropy remains peaked in the middle between the nuclei with its width decreasing. Our findings show that at the inter-nuclear distance where a stable hydrogen molecule is formed, the quantum entropy shows no peculiarity thus indicating that the entropy and the energy measures display different sensitivity with respect to the interaction between the two identical electrons involved. One possible explanation is that the calculation of the quantum entropy does not account explicitly for the distance between the nuclei, which contrasts to the total energy calculation where the energy minimum depends decisively on that distance. The numerically exact and the time-dependent quantum Monte Carlo calculations show close results.

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In this study, the security implications of utilizing the concept of entanglement in time in the quantum representation of a blockchain data structure are investigated. The analysis reveals that the fundamental idea underlying this representation relies on an uncertain interpretation of experimental results. A different perspective is provided by adopting the Copenhagen interpretation, which explains the observed correlations in the experiment without invoking the concept of entanglement in time. According to this interpretation, the qubits responsible for these correlations are not entangled, posing a challenge to the security foundation of the data structure. The study incorporates theoretical analysis, numerical simulations, and experiments using real quantum hardware. By employing a dedicated circuit for detecting genuine entanglement, the existence of entanglement in the process of generating a quantum blockchain is conclusively excluded.

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Cluster molecular magnets prove their potential for applications in quantum technologies, encouraging studies of quantum entanglement in spin systems. In the paper we discuss quantum entanglement properties of pentamer cluster composed of spins S=1/2 forming a tetrahedron with additional spin in its center, with geometry reproducing the smallest nonplanar graph. We model the system with isotropic Heisenberg Hamiltonian including external magnetic field and use exact diagonalization approach to explore the ground-state phase diagram and thermodynamic properties within canonical ensemble formalism. We focus the interest on two-spin entanglement quantified by Wootters concurrence. For ground state, we find two states with total cluster spin equal to 3/2 exhibiting entanglement, occurring preferably for antiferromagnetic interactions. For finite temperatures, we predict the presence of magnetic-field-induced entanglement as well as temperature-induced entanglement.

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We review the mathematical speed limits on quantum information processing in many-body systems. After the proof of the Lieb-Robinson Theorem in 1972, the past two decades have seen substantial developments in its application to other questions, such as the simulatability of quantum systems on classical or quantum computers, the generation of entanglement, and even the properties of ground states of gapped systems. Moreover, Lieb-Robinson bounds have been extended in non-trivial ways, to demonstrate speed limits in systems with power-law interactions or interacting bosons, and even to prove notions of locality that arise in cartoon models for quantum gravity with all-to-all interactions. We overview the progress which has occurred, highlight the most promising results and techniques, and discuss some central outstanding questions which remain open. To help bring newcomers to the field up to speed, we provide self-contained proofs of the field's most essential results.

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Since two quantum states that are local unitary (LU) equivalent have the same amount of entanglement, it is meaningful to find a practical method to determine the LU equivalence of given quantum states. In this paper, we present a valid process to find the unitary tensor product decomposition for an arbitrary unitary matrix. Then, by using this process, the conditions for determining the local unitary equivalence of quantum states are obtained. A numerical verification is carried out, which shows the practicability of our protocol. We also present a property of LU invariants by using the universality of quantum gates which can be used to construct the complete set of LU invariants.

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The existence of universal quantum computers has been theoretically well established. However, building up a real quantum computer system not only relies on the theory of universality, but also needs methods to satisfy requirements on other features, such as programmability, modularity, scalability, etc. To this end, here we study the recently proposed model of quantum von Neumann architecture by putting it in a practical and broader setting, namely, the hierarchical design of a computer system. We analyze the structures of quantum CPU and quantum control units and draw their connections with computational advantages. We also point out that a recent demonstration of our model would require less than 20 qubits.

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Fenna-Mathews-Olson complexes participate in the photosynthetic process of Sulfur Green Bacteria. These biological subsystems exhibit quantum features which possibly are responsible for their high efficiency; the latter may comprise multipartite entanglement and the apparent tunnelling of the initial quantum state. At first, to study these aspects, a multidisciplinary approach including experimental biology, spectroscopy, physics, and math modelling is required. Then, a global computer modelling analysis is achieved in the computational biology domain. The current work implements the Hierarchical Equations of Motion to numerically solve the open quantum system problem regarding this complex. The time-evolved states obtained with this method are then analysed under several measures of entanglement, some of them already proposed in the literature. However, for the first time, the maximum overlap with respect to the closest separable state is employed. This authentic multipartite entanglement measure provides information on the correlations, not only based on the system bipartitions as in the usual analysis. Our study has led us to note a different view of FMO multipartite entanglement as tiny contributions to the global entanglement suggested by other more basic measurements. Additionally, in another related trend, the initial state, considered as a Förster Resonance Energy Transfer, is tracked using a novel approach, considering how it could be followed under the fidelity measure on all possible permutations of the FMO subsystems through its dynamical evolution by observing the tunnelling in the most probable locations. Both analyses demanded significant computational work, making for a clear example of the complexity required in computational biology.

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Quantum chaos has become a cornerstone of physics through its many applications. One trademark of quantum chaotic systems is the spread of local quantum information, which physicists call scrambling. In this work, we introduce a mathematical definition of scrambling and a resource theory to measure it. We also describe two applications of this theory. First, we use our resource theory to provide a bound on magic, a potential source of quantum computational advantage, which can be efficiently measured in experiment. Second, we also show that scrambling resources bound the success of Yoshida's black hole decoding protocol.

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Based on the classical dynamical entropy, the channel coding theorem is investigated. Attempts to extend the dynamical entropy to quantum systems have been made by several researchers In 1999, Kossakowski, Ohya and I introduced the quantum dynamical entropy (KOW entropy) for completely positive maps containing an automorphism describing the time evolution. Its formulation used transition expectations and lifting in the sense of Accardi and Ohya and was studied as a measure of the complexity of quantum mechanical systems. This KOW entropy allowed the extension of generalized AF (Alicki and Fannes) entropy and generalized AOW (Accardi, Ohya and Watanabe) entropy. In addition, the S-Mixing entropy and S-mixing mutual-entropy were formulated by Ohya in 1985. Compound states are an important tool for formulating mutual entropy, and the complexity was constructed by the generalized AOW entropy. In this paper, the complexity associated with the entangled compound states in the C* dynamical system based on the generalized AOW entropy based on the KOW entropy is investigated to lay the foundation for the proof of the theorem of channel coding for quantum systems. We show that the fundamental inequalities of the mutual entropy are satisfied when the initial state is transmitted over the channel changes with time.

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Quantum routers will provide for important functionality in emerging quantum networks, and the deployment of quantum routing in real networks will initially be realized on low-complexity (few-qubit) noisy quantum devices. A true working quantum router will represent a new application for quantum entanglement-the coherent superposition of multiple communication paths traversed by the same quantum signal. Most end-user benefits of this application are yet to be discovered, but a few important use-cases are now known. In this work, we investigate the deployment of quantum routing on low-complexity superconducting quantum devices. In such devices, we verify the quantum nature of the routing process as well as the preservation of the routed quantum signal. We also implement quantum random access memory, a key application of quantum routing, on these same devices. Our experiments then embed a five-qubit quantum error-correcting code within the router, outlining the pathway for error-corrected quantum routing. We detail the importance of the qubit-coupling map for a superconducting quantum device that hopes to act as a quantum router, and experimentally verify that optimizing the number of controlled-X gates decreases hardware errors that impact routing performance. Our results indicate that near-term realization of quantum routing using noisy superconducting quantum devices within real-world quantum networks is possible.