Fermions: Spin, Hidden Variables, Violation of Bell’s Inequality and Quantum Entanglement

Using real fields instead of complex ones, it was recently claimed, that all fermions are made of pairs of coupled fields (strings) with an internal tension related to mutual attraction forces, related to Planck’s constant. Quantum mechanics is described with real fields and real operators. Schrodinger and Dirac equations then are solved. The solution to Dirac equation gives four, real, 2-vectors solutions ψ1=(U1D1)ψ2=(U2D2)ψ3=(U3D3)ψ4=(U4D4)where (ψ1,ψ4) are coupled via linear combinations to yield spin-up and spin-down fermions. Likewise, (ψ2,ψ3) are coupled via linear combinations to represent spin-up and spin-down anti-fermions. For an incoming entangled pair of fermions, the combined solution is Ψin=c1ψ1+c4ψ4where c1and c4are some hidden variables. By applying a magnetic field in +Z and +x the theoretical results of a triple Stern-Gerlach experiment are predicted correctly. Then, by repeating Bell’s and Mermin Gedanken experiment with three magnetic filters σθ, at three different inclination angles θ, the violation of Bell’s inequality is proven. It is shown that all fermions are in a mixed state of spins and the ratio between spin-up to spin-down depends on the hidden variables.

Thermal entanglement in molecular spin rings

The thermal entanglement in the triangular molecular spin ring with Dzyaloshinskii-Moriya interaction is studied. The concurrences of arbitrary two spins of the triangular molecular spin ring for various cases are evaluated. The tendency of the concurrence with Dzyaloshinskii-Moriya interaction and temperature is analysed and discussed. We note that the concurrence arrives at its maximum in the regime with the large Dzyaloshinskii-Moriya interaction and low temperature, and gradually decreases to zero with the increase of temperature. The concurrence has different features for the ferromagnetic and antiferromagnetic cases. For completeness, we also numerically calculate the concurrence of spin rings with N 〉 3 spins and analyse their behaviours.

Teleportation and thermal entanglement in two-qubit Heisenberg X Y Z spin chain with the Dzyaloshinski-Moriya interaction and the inhomogeneous magnetic field

This paper studies the average fidelity of teleportation and thermal entanglement for a two-qubit Heisenberg XYZ chain in the presence of both an inhomogeneous magnetic field and a Dzyaloshinski-Moriya interaction. It shows that for a fixed Dz, the increase of bz will broaden the critical temperature at the cost of decreasing the thermal entanglement. And it can modulate the inhomogeneous magnetic field and the Dzyaloshinski-Moriya interaction for the average fidelity of teleportation to be optimal.

Entanglement and quantum phase transition in alternating XY spin chain with next-nearest neighbouring interactions

By using the method of density-matrix renormalization-group to solve the different spin spin correlation functions, the nearest-neighbouring entanglement （NNE） and the next-nearest-neighbouring entanglement （NNNE） of one-dimensional alternating Heisenberg XY spin chain are investigated in the presence of alternating the-nearestneighbouring interaction of exchange couplings, external magnetic fields and the next-nearest neighbouring interaction. For a dimerised ferromagnetic spin chain, the NNNE appears only above a critical dimerized interaction, meanwhile, the dimerized interaction a effects a quantum phase transition point and improves the NNNE to a large extent. We also study the effect of ferromagnetic or antiferromagnetic next-nearest neighbouring （NNN） interaction on the dynamics of NNE and NNNE. The ferromagnetic NNN interaction increases and shrinks the NNE below and above a critical frustrated interaction respectively, while the antiferromagnetic NNN interaction always reduces the NNE. The antiferromagnetic NNN interaction results in a large value of NNNE compared with the case where the NNN interaction is ferromagnetic.

Values of Siva’s Constant “<i>K</i>” for All Fundamental Forces—A Review on Spin, Threshold Time and Quantum Entanglement

Siva’s constant “K” has been explained in brief. Its numerical values have been calculated for each fundamental force of nature. Spin of quantum mechanics has been interpreted in terms of Sivas constant “K”. Thus limitation to velocity of light and interrelation between relativity and quantum mechanics has been explained in a novel and profound way. Involvement of “physics of consciousness” in synchronizing relativity and quantum mechanics has been emphasized. Concept of “bio force” as fifth fundamental force in addition to other four fundamental forces, strong, weak, electromagnetic and gravitational forces also has been emphasized. Consciousness has been explained as entanglement between bio force particle named as “jeeton” and gravitational force particle “graviton”. Thus frequency mediated consciousness has been explained.

Multipartite entanglement concentration of electron-spin states with CNOT gates

We propose a different entanglement concentration protocol （ECP） for nonlocal N-electron systems in a partially entangled Bell-type pure state using the CNOT gates and the projection measurements on an additional electron. For each nonlocal N-electron system, Alice first entangles it with the additional electron, and then she projects the additional electron onto an orthogonal basis for dividing the N-electron systems into two groups. In the first group, the N parties obtain a subset of N-electron systems in a maximally entangled state directly. In the second group, they obtain some less-entangled N-electron systems, which are the resource for the entanglement concentration in the next round. By iterating the entanglement concentration process several times, the present ECP has the maximal success probability, which is the theoretical limit of an ECP, equal to the entanglement of the partially entangled state, and higher than the others. This ECP may be useful in quantum computers based on electron-spin systems in the future.

Enhancing von Neumann entropy by chaos in spin–orbit entanglement

For a quantum system with multiple degrees of freedom or subspaces, loss of coherence in a certain subspace is intimately related to the enhancement of entanglement between this subspace and another one. We investigate intra-particle entanglement in two-dimensional mesoscopic systems, where an electron has both spin and orbital degrees of freedom and the interaction between them is enabled by Rashba type of spin-orbit coupling. The geometric shape of the scattering region can be adjusted to produce a continuous spectrum of classical dynamics with different degree of chaos. Focusing on the spin degree of freedom in the weak spin-orbit coupling regime, we find that classical chaos can significantly enhance spin-orbit entanglement at the expense of spin coherence. Our finding that classical chaos can be beneficial to intra-particle entanglement may have potential applications such as enhancing the bandwidth of quantum communications.

Scaling of entanglement entropy for spin chain with Dzyaloshinskii-Moriya interaction

This paper investigates the entanglement in an XX-type spin chain with Dzyaloshinskii--Moriya interaction under an external magnetic field. The von Neumann entropy of entanglement between two blocks for the ground state of the system is evaluated. It analyses and discusses the scaling behaviour of the entanglement entropy.

Entanglement control in one-dimensional s=1/2 random XY spin chain

The entanglement in one-dimensional random XY spin systems where the impurities of exchange couplings and the external magnetic fields are considered as random variables is investigated by solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynamics near particular locations of the system is also studied when the exchange couplings （or the external magnetic fields） satisfy three different distributions （the Gaussian distribution, double-Gaussian distribution, and bimodal distribution）. We find that the entanglement can be controlled by varying the strength of external magnetic field and the distributions of impurities. Moreover, the entanglement of some nearest-neighbouring qubits can be increased for certain parameter values of the three different distributions.

Decoherence-free spin entanglement generation and purification in nanowire double quantum dots

We propose a deterministic generation and purification of decoherence-free spin entangled states with singlet-triplet spins in nanowire double quantum dots via resonator-assisted charge manipulation and measurement techniques. Each spin qubit corresponds to two electrons in a double quantum dot in the nanowire, with the singlet and one of the triplets as the decoherence-free qubit states. The logical qubits are immunized against the dominant source of decoherence- dephasing--while the influences of additional errors are shown by numerical simulations. We analyse the performance and stability of all required operations and emphasize that all techniques are feasible in current experimental conditions.

Enhancement of next-nearest-neighbouring entanglement in quantum Ising spin chain

Using the method of the Jordan-Wigner transformation for solving different spin-spin correlation functions, we have investigated the generation of next-nearest-neighbouring entanglement in a one-dimensional quantum Ising spin chain with the Gaussian distribution impurities of exchange couplings and external magnetic fields taken into account. The maximal value of entanglement between the next-nearest-neighbouring qubits in the transverse Ising model was analysed in detail by varying the effectively controlled parameters such as interchange coupling, magnetic field and the system impurity. For such systems, where both exchange couplings and external magnetic field disorder appear, we show that it is possible to achieve next-nearest-neighbouring entanglement better than the previously discussed pure Ising spin chain case. We also show that the Gaussian distribution impurity can induce next-nearest-neighbouring entanglement, which can be used as a means to characterize quantum phase transition.

Macroscopic inequivalent entanglement witness in Heisenberg spin chain

Motivated by the wise idea of entanglement witness （EW）, we present an inequivalent entanglement witness （IEEW） that can analogously classify certain eigenstates entangled in inequivalent ways under stochastic local operations and classical communication （SLOCC） in the Heisenberg spin chain. Since the IEEW is the absolute value of magnetization （M） that is a macroscopically measurable quantity, our conclusions provide a macroscopic method to detect inequivalent entanglement between microscopic spins, on the one hand, and clearly show that inequivalent entanglement can yield different macroscopic effects, on the other hand.

Entanglement and Fidelity of a Spin Ladder with Dzyaloshinsky-Moriya Interaction

The spin ladder with Dzyaloshinsky-Moriya interaction is investigated by using the quantum renormalization-group method.The entanglement and fidelity are periodic functions of the time and oscillate between zero and one.The oscillation period decreases with either the interaction in the spin ladder or the Dzyaloshinsky-Moriya interaction increasing.When the system relates to the environment,both entanglement and fidelity oscillate with a damping rate related to intrinsic decoherence rate,the interaction in the spin ladder,and the Dzyaloshinsky-Moriya interaction.

Entanglement Resonance of End Spins in Different Spin Chains

The entanglement resonance in anisotropic spin-1/2 Heisenberg chains of different couplings is investigated when the nearest neighbor coupling is periodically modulated with external magnetic field. When the modulation frequency equals twice of the magnetic field, the entanglement resonance is larger than that at other modulation frequencies and decreases as the number of spins in the chain increases. When the modulation frequency equals the magnetic field, the entanglement resonance can be reduced to a quite low value by varying the coupling along z axis.

Robust Entanglement for Multiple Trapped Ions in Thermal Motion

A robust scheme is proposed for producing maximally entangled states for many trapped ions in thermal motion. In the scheme the ions are simultaneously illuminated by two standing-wave laser fields. During the operation the phases of the lasers are inverted, which not only cancels the vibration-dependent parts in the evolution operator, but also suppresses direct off-resonant coupling of the internal states. Thus, our scheme allows the production of entanglement for hot trapped ions with laser fields of high intensity, which makes the entanglement speed extremely high.

Entanglement Dynamics of Multipartite Systems Under Decoherence from a Spin Environment

The entanglement evolution of multipartite quantum states under a spin environment is analyzed. Due to interaction, the extent to which the entanglement vanishes depends not only on the size of system and the structure of quantum states, but also on the exchange couplings with environment. The decoherence-free subspaces have been identified by using the linear entropy.

Thermal Entanglement of an XY Two-Qutrit Spin Chain with Dzialoshinski—Moriya Interaction

The effect of Dzialoshinski-Moriya(DM)interaction on thermal entanglement of an XY two-qutrit spinchain is investigated.We find that DM interaction and the anisotropy parameter can enhance quantum thermal entanglementto a maximal value individually.However,when both of them take large values,the entanglement is notenhanced,but is destroyed.Our analysis will shed some light on the understanding of the effect of the DM interactionon thermal entanglement of an XY two-qutrit spin chain.

Entanglement Entropy Signature of Quantum Phase Transitions in a Multiple Spin Interactions Model

Through the Jordan Wigner transformation, the entanglement entropy and ground state phase diagrams of exactly solvable spin model with alternating and multiple spin exchange interactions are investigated by means of Green＇s function theory. In the absence of four-spin interactions, the ground state presents plentiful quantum phases due to the multiple spin interactions and magnetic fields. It is shown that the two-site entanglement entropy is a good indicator of quantum phase transition （QPT）. In addition, the alternating interactions can destroy the magnetization plateau and wash out the spin-gap of low-lying excitations. However, in the presence of four-spin interactions, apart from the second order QPTs, the system manifests the first order OPT at the tricritical point and an additional new phase called ＂spin waves＂, which is due to the collapse of the continuous tower-like low-lying excitations modulated by the four-spin interactions for large three-spin couplings.

Entanglement in the Quantum Phase Transition of the Half-Integer Spin One-Dimensional Heisenberg Model

We use the Bethe’s ansatz method to study the entanglement of spinons in the quantum phase transition of half integer spin one-dimensional magnetic chains known as quantum wires. We calculate the entanglement in the limit of the number of particles . We obtain an abrupt change in the entanglement next the quantum phase transition point of the anisotropy parameter ?from the gapped phase ?to gapless phase .

Perfect Entanglement Transport in Quantum Spin Chain Systems

We propose a mechanism for perfect entanglement transport in anti-ferromagnetic (AFM) quantum spin chain systems with modulated exchange coupling and also for the modulation of on-site magnetic field. We use the principle of adiabatic quantum pumping process for entanglement transfer in the spin chain systems. We achieve the perfect entanglement transfer over an arbitrarily long distance and a better entanglement transport for longer AFM spin chain system than for the ferromagnetic one. We explain analytically and physically—why the entanglement hops in alternate sites. We find the condition for blocking of entanglement transport even in the perfect pumping situation. Our analytical solution interconnects quantum many body physics and quantum information science.