Quantum entangled fractional Fourier transform based on the IWOP technique

In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform.The core function of the coordinate-momentum exchange operators in the addition law of fractional Fourier transform was analyzed too.In this paper,the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators(IWOP)are used to establish the entanglement fractional Fourier transform theory to the extent of quantum.A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.

Quantum entangled connectivity and functional connectivity of human brain

Quantum process may conduce to brain function.Particularly,it was proposed that the Posner molecules,Cag(PO4)6,can serve as neural qubits,which can maintain quantum entanglement between phosphorus nuclei for quite a long time.We study the process from entangled Posner molecules to the synchronized activities of brain.A diffusion model of Posner molecules with appropriate boundary conditions and the mean first arriving time of Posner molecules from one area of brain to another are obtained.We establish linkages between the quantum entangled connectivity of brain and the remaining time of entangled Posner molecules before decoherence.Based on these results,we find direct correlations between entangled Posner molecules and the functional connectivity of human brain.Furthermore,we discover that the quantum entangled connectivity depends on age.

Broadband multi-channel quantum noise suppression and phase-sensitive modulation based on entangled beam

We present a theoretical scheme for broadband multi-channel quantum noise suppression and phase-sensitive modulation of continuous variables in a coupled resonant system with quantum entanglement properties.The effects of different coupling strengths,pumping power in suppressing quantum noise and controlling the width of quantum interference channels are analyzed carefully.Furthermore,quantum noise suppression at quadrature amplitude is obtained with phase-sensitive modulation.It shows that the entanglement strength of the output field and the quantum noise suppression effect can be enhanced significantly by a strong pumping filed due to interaction of pumping light with the nonlinear crystal.The full width at half maxima(FWHM)of the noise curve at the resonant peak(△=0 MHz)is broadened up to 2.17 times compared to the single cavity.In the strong coupling resonant system,the FWHM at △=0 MHz(△=±3.1 MHz)is also broadened up to 1.27(3.53)times compared to the weak coupling resonant system case.The multi-channel quantum interference creates an electromagnetically induced transparent-like line shape,which can be used to improve the transmission efficiency and stability of wave packets in quantum information processing and quantum memory.

Single-photon scattering and quantum entanglement of two giant atoms with azimuthal angle differences in a waveguide system

We theoretically investigate coherent scattering of single photons and quantum entanglement of two giant atoms with azimuthal angle differences in a waveguide system.Using the real-space Hamiltonian,analytical expressions are derived for the transport spectra scattered by these two giant atoms with four azimuthal angles.Fano-like resonance can be exhibited in the scattering spectra by adjusting the azimuthal angle difference.High concurrence of the entangled state for two atoms can be implemented in a wide angle-difference range,and the entanglement of the atomic states can be switched on/off by modulating the additional azimuthal angle differences from the giant atoms.This suggests a novel handle to effectively control the single-photon scattering and quantum entanglement.

Detecting the quantum phase transition from the perspective of quantum information in the Aubry–André model

We investigate the effectiveness of entropic uncertainty, entanglement and steering in discerning quantum phase transitions(QPTs). Specifically, we observe significant fluctuations in entropic uncertainty as the driving parameter traverses the phase transition point. It is observed that the entropic uncertainty, entanglement and quantum steering, based on the electron distribution probability, can serve as indicators for detecting QPTs. Notably, we reveal an intriguing anticorrelation relationship between entropic uncertainty and entanglement in the Aubry–André model. Moreover, we explore the feasibility of detecting a QPT when the period parameter is a rational number. These observations open up new and efficient avenues for probing QPTs.

Structural Foundation and Geometry of the Material Singularity (and Its Quantum Entanglement)

In this paper we develop and study, as the second part of one more general development, the energy transmutation equation for the material singularity, previously obtained through the symmetrisation of a wave packet, that is, we develop the correlation between the terms of this equation, which accounts for the formation of matter from a previous vibrational state, and the different possible energy species. These energetic species are ascribed, in a simplified form, to the equation E¯ω=E¯k+E¯f, which allows us, through its associated phase factor, to gain an insight into the wave character of the kinetic energy and thus to attain the basis of the matter-wave, and all sorts of related phenomenologies, including that concerning quantum entanglement. The formation of the matter was previously identified as an energetic process, analogous to the kinetic one, in which finally the inertial mass is consolidated as a mass in a different phase, now, in addition, the mass of the material singularity is identified as a volumetric density of waves of toroidal geometry created in the process of singularisation or energy transfer between species, which makes it possible to establish the real relation or correspondence between the corpuscular and photonic energy equation (E=mc2=hν), i.e. to explain through m the intimate sense of the first equivalence, which explains what νis in the second one.

Quantum entanglement and quantum nonlocality for N-photon entangled states

Quantum entanglement and quantum nonlocality of N-photon entangled states ｜ψNm） m Cm [cos γ｜N - m） 1 ｜m）2 ＋ e^iθm sinγ｜m）1｜N- m）2] and their superpositions are studied. We point out that the relative phase θm affects the quantum nonlocality but not the quantum entanglement for the state ｜ψNm）. We show that quantum nonlocality can be controlled and manipulated by adjusting the state parameters of ｜ψNm）, superposition coefficients, and the azimuthal angles of the Bell operator. We also show that the violation of the Bell inequality can reach its maximal value under certain conditions. It is found that quantum superpositions based on ｜ψNm） can increase the amount of entanglement, and give more ways to reach the maximal violation of the Bell inequality.

Cryptanalysis and improvement of a quantum secret sharing scheme based on χ-type entangled states

In the paper [2010 Chin. Phys. B 19 050306], Yang et al. put forward a novel three-party quantum secret sharing protocol of secure direct communication based on x-type entangled states, they claimed that the scheme is secure. However, in this paper, we study the security of the protocol and find that it is insecure. Applying intercept and resend attack, the agent Bob can obtain Alice＇s secret without the help from the other agent Charlie. In the end, we give our effective modification for its improvement.

Quantum nonlocality of generic family of four-qubit entangled pure states

We directly introduce a Bell-type inequality for four-qubit systems. Using the inequality we investigate quantum nonlocality of a generic family of states ｜Gabcd〉[Phys. Rev. A 65 052112（2002）] and several canonical four-qubit entangled states. It has been demonstrated that the inequality is maximally violated by the so called ＂four-qubit the maximally entangled state ｜Gm〉＂ and it is also violated by four-qubit W state and a special family of states ｜Gab00〉. Moreover, a useful entanglement-nonlocality relationship for the family of states ｜Gab00〉is derived. Finally, we present a scheme of preparation of the state ｜Gm〉with linear optics and cross-Kerr nonlinearities.

Quantum entanglement of an entangled coherent state: Role of particle losses

We analyze entanglement properties of entangled coherent state （ECS）, ｜α,0） 1,2 ＋｜0,α） 1,2, with and without photon losses. By separating the coherent state into ]a） = co｜0） ＋ √-Co2｜α）, we derive exact results of the logarithmic negativity EN, which quantifies the degree of entanglement between the two bosonic modes. Without particle losses, E~ = 1 for the NOON state; while for the ECS, E jr increases from 0 to 1 as ｜α｜-→∞. In the presence of photon losses, we find that the ECS with large enough photon number is more robust than that of the NOON state. An optimal ECS is obtained by maximizing E~ with respect to l a 12.

Efficient quantum secret sharing scheme with two-particle entangled states

This paper proposes a protocol for multi-party quantum secret sharing utilizing four non-orthogonal two-particle entangled states following some ideas in the schemes proposed by Liu et al. （2006 Chin. Phys. Lett. 23 3148） and Zhang et al. （2009 Chin. Phys. B 18 2149） respectively. The theoretical efficiency for qubits of the new protocol is improved from 50% to approaching 100%. All the entangled states can be used for generating the private key except those used for the eavesdropping check. The validity of a probable attack called opaque cheat attack to this kind of protocols is considered in the paper for the first time.

Quantum Interference by Entangled Trajectories

The quantum interference pattern in the double-slit experiment is qualitatively reproduced by using the entangled trajectory molecular dynamics method and compared with previous works. We compare entangled trajectory and classical trajectory with the same initial state in the phase space to show quantum effect in the evolution of trajectories. It is involved with breakdown in the statistical independence of the trajectories. Although our result does not agree well with exact quantum calculation in quantitatively with loss of part of interference pattern peaks, we can offer a reasonable explanation by analyzing quantum interference of two Gaussian wave packets in the phase space.

Effects of quantum quench on entanglement dynamics in antiferromagnetic Ising model

We study the relationship between quench dynamics of entanglement and quantum phase transition in the antiferromagnetic Ising model with the Dzyaloshinskii–Moriya(DM)interaction by using the quantum renormalization-group method and the definition of negativity.Two types of quench protocols(i)adding the DM interaction suddenly and(ii)rotating the spins around x axis are considered to drive the dynamics of the system,respectively.By comparing the behaviors of entanglement in both types of quench protocols,the effects of quench on dynamics of entanglement are studied.It is found that there is the same characteristic time at which the negativity firstly reaches its maximum although the system shows different dynamical behaviors.Especially,the characteristic time can accurately reflect the quantum phase transition from antiferromagnetic to saturated chiral phases in the system.In addition,the correlation length exponent can be obtained by exploring the nonanalytic and scaling behaviors of the derivative of the characteristic time.

Entanglement and thermalization in the extended Bose–Hubbard model after a quantum quench: A correlation analysis

Exploring the role of entanglement in quantum nonequilibrium dynamics is important to understand the mechanism of thermalization in an isolated system. We study the relaxation dynamics in a one-dimensional extended Bose–Hubbard model after a global interaction quench by considering several observables: the local Boson numbers, the nonlocal entanglement entropy, and the momentum distribution functions. We calculate the thermalization fidelity for different quench parameters and different sizes of subsystems, and the results show that the degree of thermalization is affected by the distance from the integrable point and the size of the subsystem. We employ the Pearson coefficient as the measurement of the correlation between the entanglement entropy and thermalization fidelity, and a strong correlation is demonstrated for the quenched system.

Quantum Theory of Consciousness

Both consciousness and quantum phenomenon are subjective and indeterministic. In this paper, we propose consciousness is a quantum phenomenon. A quantum theory of consciousness (QTOC) is presented based on a new interpretation of quantum physics. We show that this QTOC can address the mind and body problem, the hard problem of consciousness. It also provides a physics foundation and mathematical formulation to study consciousness and neural network. We demonstrate how to apply it to develop and extend various models of consciousness. We show the predictions from this theory about the existence of a universal quantum vibrational field and the large-scale, nearly instantaneous synchrony of brainwaves among different parts of brain, body, people, and objects. The correlation between Schumann Resonances and some brainwaves is explained. Recent progress in quantum information theory, especially regarding quantum entanglement and quantum error correction code, is applied to study memory and shed new light in neuroscience.

Design and Implementation of Quantum Repeaters:Insights on Quantum Entanglement Purification

Quantum communication is a groundbreaking technology that is driving the future of information transmission and communication technologies to a new paradigm.It relies on quantum entanglement to facilitate the transmission of quantum states between parties.Quantum repeaters are crucial for facilitating long-distance quantum communication.These quantum devices act as intermediaries between adjacent communication channel segments within a fragmented quantum network,allowing for entanglement swapping between the channel segments.This entanglement swapping process establishes entanglement links between the endpoints of adjacent segments,gradually creating a continuous entanglement connection over the entire length of the transmission channel.The established quantum link can be utilized for secure and efficient quantum communication between distant sender and receiver nodes.This study focuses on quantum entanglement purification,a protocol aimed at maintaining high fidelity entangled states above the operational threshold of the communication channel.This study investigates the optimal stage for executing the purification protocol and applies optimization schemes to evaluate various purification protocols.We use IBM Qiskit for circuit implementation and simulation.The results offer valuable insights into future approaches to implementing practical quantum repeaters and shed light on existing and anticipated challenges.

Quantum Entanglement Could Be the Result of Leptons, Quarks and Photons Simultaneously Experiencing 4-D Space as (3 + 1)-D Spacetime

We propose that quantum entanglement occurs because the fundamental particles, such as electrons, quarks, and photons, simultaneously experience both the 4th real spatial dimension in R4 as well as the time dimension in (3 + 1)-D spacetime. Consequently, the entangled particles can never become separated in the 4th spatial dimension no matter how far they have moved apart in the other 3 spatial dimensions. Because the quark and lepton families represent specific different discrete symmetry binary subgroups of SU(2), we can establish that the quantum states of the fundamental particles are defined in 4 spatial dimensions, so there is then no need for a spacetime communication from one detector (or particle) to inform the other detector (or particle) of the physical state of the first detected entangled particle. A clever experiment needs to determine whether the fundamental particles actually experience a 4th spatial dimension, and if so, whether they experience the 4th spatial dimension as the time dimension simultaneously. Apparently, if a Casimir-like test reveals that virtual particles have a non-zero mass, there are claims that a 4th spatial dimension does not exist.

On Topics in Quantum Games

This work concentrates on simultaneous move non-cooperating quantum games. Part of it is evidently not new, but it is included for the sake self consistence, as it is devoted to introduction of the mathematical and physical grounds of the pertinent topics, and the way in which a simple classical game is modified to become a quantum game (a procedure referred to as a quantization of a classical game). The connection between game theory and information science is briefly stressed, and the role of quantum entanglement (that plays a central role in the theory of quantum games), is exposed. Armed with these tools, we investigate some basic concepts like the existence (or absence) of a pure strategy and mixed strategy Nash equilibrium and its relation with the degree of entanglement. The main results of this work are as follows: 1) Construction of a numerical algorithm based on the method of best response functions, designed to search for pure strategy Nash equilibrium in quantum games. The formalism is based on the discretization of a continuous variable into a mesh of points, and can be applied to quantum games that are built upon two-players two-strategies classical games, based on the method of best response functions. 2) Application of this algorithm to study the question of how the existence of pure strategy Nash equilibrium is related to the degree of entanglement (specified by a continuous parameter γ ). It is shown that when the classical game GC has a pure strategy Nash equilibrium that is not Pareto efficient, then the quantum game GQ with maximal entanglement (γ = π/2) has no pure strategy Nash equilibrium. By studying a non-symmetric prisoner dilemma game, it is found that there is a critical value 0γc such that for γγc there is a pure strategy Nash equilibrium and for γ≥γc there is no pure strategy Nash equilibrium. The behavior of the two payoffs as function of γ starts at that of the classical ones at (D, D) and approaches the cooperative classical ones at (C, C) (C = confess, D = don’t confess). 3) We then study Bayesian quantum games and show that under certain conditions, there is a pure strategy Nash equilibrium in such games even when entanglement is maximal. 4) We define the basic ingredients of a quantum game based on a two-player three strategies classical game. This requires the introduction of trits (instead of bits) and quantum trits (instead of quantum bits). It is proved that in this quantum game, there is no classical commensurability in the sense that the classical strategies are not obtained as a special case of the quantum strategies.

Anonymous voting for multi-dimensional CV quantum system

We investigate the design of anonymous voting protocols,CV-based binary-valued ballot and CV-based multi-valued ballot with continuous variables（CV） in a multi-dimensional quantum cryptosystem to ensure the security of voting procedure and data privacy.The quantum entangled states are employed in the continuous variable quantum system to carry the voting information and assist information transmission,which takes the advantage of the GHZ-like states in terms of improving the utilization of quantum states by decreasing the number of required quantum states.It provides a potential approach to achieve the efficient quantum anonymous voting with high transmission security,especially in large-scale votes.

Entangling two levitated charged nanospheres through Coulomb interaction

Limited by the thermal environment, the entanglement of a massive object is extremely difficult to generate. Based on a coherent scattering mechanism, we propose a scheme to generate the entanglement of two optically levitated nanospheres through the Coulomb interaction. Two nanospheres are charged and coupled to each other through the Coulomb interaction.In this manner, the entanglement of two nanospheres is induced either under a weak/strong optomechanical coupling regime or under an ultra-strong optomechanical coupling regime. The charges, radius and distance of the two nanospheres are taken into consideration to enhance the Coulomb interaction, thereby achieving a higher degree of entanglement in the absence of ground-state cooling. The corresponding maximum entanglement can be attained as the dynamics of the system approaches the boundary between the steady and the unsteady regimes. This provides a useful resource for both quantum-enhanced sensing and quantum information processing, as well as a new platform for studying many-body physics.