Entanglement polygon inequalities for a class of mixed states

The study on the entanglement polygon inequality of multipartite systems has attracted much attention.However,most of the results are on pure states.Here we consider the property for a class of mixed states,which are the reduced density matrices of generalizedW-class states in multipartite higher dimensional systems.First we show the class of mixed states satisfies the entanglement polygon inequalities in terms of Tsallis-q entanglement,then we propose a class of tighter inequalities for mixed states in terms of Tsallis-q entanglement.At last,we get an inequality for the mixed states,which can be regarded as a relation for bipartite entanglement.

Quantum correlations and entanglement in coupled optomechanical resonators with photon hopping via Gaussian interferometric power analysis

Quantum correlations that surpass entanglement are of great importance in the realms of quantum information processing and quantum computation.Essentially,for quantum systems prepared in pure states,it is difficult to differentiate between quantum entanglement and quantum correlation.Nonetheless,this indistinguishability is no longer holds for mixed states.To contribute to a better understanding of this differentiation,we have explored a simple model for both generating and measuring these quantum correlations.Our study concerns two macroscopic mechanical resonators placed in separate Fabry–Pérot cavities,coupled through the photon hopping process.this system offers a comprehensively way to investigate and quantify quantum correlations beyond entanglement between these mechanical modes.The key ingredient in analyzing quantum correlation in this system is the global covariance matrix.It forms the basis for computing two essential metrics:the logarithmic negativity(E_(N)^(m))and the Gaussian interferometric power(P_(G)^(m)).These metrics provide the tools to measure the degree of quantum entanglement and quantum correlations,respectively.Our study reveals that the Gaussian interferometric power(P_(G)^(m))proves to be a more suitable metric for characterizing quantum correlations among the mechanical modes in an optomechanical quantum system,particularly in scenarios featuring resilient photon hopping.

Tuning mechanical behaviors of highly entangled hydrogels with the random distribution of mobile entanglements

Highly entangled hydrogels exhibit excellent mechanical properties,including high toughness,high stretchability,and low hysteresis.By considering the evolution of randomly distributed entanglements within the polymer network upon mechanical stretches,we develop a constitutive theory to describe the large stretch behaviors of these hydrogels.In the theory,we utilize a representative volume element(RVE)in the shape of a cube,within which there exists an averaged chain segment along each edge and a mobile entanglement at each corner.By employing an explicit method,we decouple the elasticity of the hydrogels from the sliding motion of their entanglements,and derive the stress-stretch relations for these hydrogels.The present theoretical analysis is in agreement with experiment,and highlights the significant influence of the entanglement distribution within the hydrogels on their elasticity.We also implement the present developed constitutive theory into a commercial finite element software,and the subsequent simulations demonstrate that the exact distribution of entanglements strongly affects the mechanical behaviors of the structures of these hydrogels.Overall,the present theory provides valuable insights into the deformation mechanism of highly entangled hydrogels,and can aid in the design of these hydrogels with enhanced performance.

Nonreciprocal mechanical entanglement in a spinning optomechanical system

Quantum entanglement between distant massive mechanical oscillators is an important resource in sensitive measurements and quantum information processing.We achieve the nonreciprocal mechanical entanglement in a compound optomechanical device consisting of two mechanical oscillators and a spinning whispering-gallery mode(WGM)optical microresonator.It is found that obvious nonreciprocal mechanical entanglement emerges in this system in the presence of the Sagnac effect which is induced by the rotation of the WGM resonator,and the nonreciprocal region can be controlled by tuning the angular velocity of the rotation.The nonreciprocity originates from the breaking of the time-reversal symmetry of this multimode system due to the presence of the Sagnac effect.The optomechanical coupling and the mechanical interaction provide cooling channels for the first and second mechanical oscillators,respectively.Two mechanical oscillators can be cooled simultaneously.The simultaneous cooling and the mechanical coupling of two mechanical oscillators ensure the generation of mechanical entanglement.Furthermore,an optimal mechanical entanglement can be achieved when the moderate optical frequency detuning and the driving power are chosen.The thermal noise of the mechanical environment has a negative effect on mechanical entanglement.Our scheme provides promising opportunities for research of quantum information processing based on phonons and sensitive measurements.

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.

Nonlinearly induced entanglement in dissipatively coupled optomechanical system

Nonlinearly induced steady-state photon–phonon entanglement of a dissipative coupled system is studied in the bistable regime. Quantum dynamical characteristics are analysed by solving the mean-field and fluctuation equations of the system. It is shown that dissipative coupling can induce bistable behaviour for the effective dissipation of the system.Under suitable parameters, one of the steady states significantly reduces the dissipative effect of the system. Consequently,a larger steady-state entanglement can be achieved compared to linear dynamics. Furthermore, the experimental feasibility of the parameters is analysed. Our results provide a new perspective for the implementation of steady-state optomechanical entanglement.

Generation of macroscopic entanglement in ensemble systems based on silicon vacancy centers

Entanglement in macroscopic systems,as a fundamental quantum resource,has been utilized to propel the advancement of quantum technology and probe the boundary between the quantum and classical realms.This study focuses on a unique hybrid quantum system comprising of an ensemble of silicon vacancy(SiV)centers coupled to phononic waveguides in diamond via strain interactions.By employing two sets of time-dependent,non-overlapping driving fields,we investigate the generation process and dynamic properties of macroscopic quantum entanglement,providing fresh insights into the behavior of such hybrid quantum systems.Furthermore,it paves the way for new possibilities in utilizing quantum entanglement as an information carrier in quantum information processing and quantum communication.

Genuine entanglement under squeezed generalized amplitude damping channels with memory

We study genuine entanglement among three qubits undergoing a noisy process that includes dissipation, squeezing,and decoherence. We obtain a general solution and analyze the asymptotic quantum states. We find that most of these asymptotic states can be genuinely entangled depending upon the parameters of the channel, memory parameter, and the parameters of the initial states. We study Greenberger–Horne–Zeilinger(GHZ) states and W states, mixed with white noise,and determine the conditions for them to be genuinely entangled at infinity. We find that for these mixtures, it is possible to start with a bi-separable state(with a specific mixture of white noise) and end with genuine entangled states. However, the memory parameter μ must be very high. We find that in contrast to the two-qubit case, none of the three-qubit asymptotic states for n → ∞ are genuinely entangled.

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.

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.

Entanglement and Volume Monogamy Features of Permutation Symmetric N-Qubit Pure States with N-Distinct Spinors: GHZ and States

We explore the entanglement features of pure symmetric N-qubit states characterized by N-distinct spinors with a particular focus on the Greenberger-Horne-Zeilinger (GHZ) states and , an equal superposition of W and obverse W states. Along with a comparison of pairwise entanglement and monogamy properties, we explore the geometric information contained in them by constructing their canonical steering ellipsoids. We obtain the volume monogamy relations satisfied by states as a function of number of qubits and compare with the maximal monogamy property of GHZ states.

Quantum Computingvia Entanglement in Geometric Algebra Approach

The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme.

Revised Geometric Measure of Entanglement for Multipartite and Continuous Variable Systems

Based on the revised geometric measure of entanglement （RGME） proposed by us [J. Phys. A： Math. Theor. 40 （2007） 3507], we obtain the RGME of multipartite state including three-qubit GHZ state, W state, and the generalized Smolin state （GSS） in the presence of noise and the two-mode squeezed thermal state. Moreover, we compare their RGME with geometric measure of entanglement （GME） and relative entropy of entanglement （RE）. The results indicate RGME is an appropriate measure of entanglement. Finally, we define the Gaussian GME which is an entangled monotone.

Detection and quantification of entanglement with measurement-device-independent and universal entanglement witness

Entanglement is the key resource in quantum information processing,and an entanglement witness(EW)is designed to detect whether a quantum system has any entanglement.However,prior knowledge of the target states should be known first to design a suitable EW,which weakens this method.Nevertheless,a recent theory shows that it is possible to design a universal entanglement witness(UEW)to detect negative-partial-transpose(NPT)entanglement in unknown bipartite states with measurement-device-independent(MDI)characteristic.The outcome of a UEW can also be upgraded to be an entanglement measure.In this study,we experimentally design and realize an MDI UEW for two-qubit entangled states.All of the tested states are well-detected without any prior knowledge.We also show that it is able to quantify entanglement by comparing it with concurrence estimated through state tomography.The relation between them is also revealed.The entire experimental framework ensures that the UEW is MDI.

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.

A Protocol for Conversion of Path-Spin to Spin-Spin Quantum Entanglement

The present model deals with a protocol which involves the generation and conversion of entanglement from pathspin(P-S)hybrid entanglement associated with half-spin particle to spin-spin(S-S)interparticle entanglement.This protocol finds its applications in quantum information processing via a series of operations which include a beam splitter,spin flipper,spin measurement,classical channel,unitary transformations.Finally,it leads to two particles having completely entangled spin variables,without any requirement of any simultaneous operation on the two particles.

Quantum teleportation by entanglement swapping with trapped ions

An effective teleportation scheme for an unknown ionic internal state via trapped ions is proposed without joint Bell-state measurement （BSM）. In the constructed quantum channel process, we make use of entanglement swapping to avoid decrease in entanglement during the distributing of particles. Thus our scheme provides new prospects for quantum teleportatlon in a longer distance. The distinct advant.age of our scheme is insensitive to the heating of vibrational mode. Furthermore, our scheme has no any individual optical access, and the successful probability also can reach 1.

An important property of entanglement： pairwise entanglement that can only be transferred by an entangled pair

Based on the calculation of all the pairwise entanglements in the n （n ≤ 6）-qubit Heisenberg XX open chain with system impurity, we find an important result： pairwise entanglement can only be transferred by an entangled pair. The non-nearest pairwise entanglements will have the possibility to exist as long as there has been even number of qubits in their middle. This point indicates that we can obtain longer distance entanglement in a solid system.

Optimal entanglement concentration for three-photon W states with parity check measurement

We present an efficient entanglement concentration protocol（ECP） for the less-entangled W state with some identical conventional polarized single photons.In the protocol,two of the parties say Alice and Charlie should perform the parity check measurements and they can ultimately obtain the maximally entangled W state with a certain success probability.Otherwise,they can obtain another less-entangled W state,which can be reconcentrated into the maximally entangled W state.By iterating this ECP,a high success probability can be achieved.This ECP may be an optimal one and it is useful in current quantum information processing.

Entanglement Dynamics and Bell Violations of Two Atoms in Tavis-Cummings Model with Phase Decoherence

Considering the dipole-dipole coupling intensity between two atoms and the field in the Fock state, the entanglement dynamics between two atoms that are initially entangled in the system of two two-level atoms coupled to a single mode cavity in the presence of phase decoherence has been investigated. The two-atom entanglement appears with periodicity without considering phase decoherence, however, the phase decoherence causes the decay of entanglement between two atoms, with the increasing of the phase decoherence coefficient, the entanglement will quickly become a constant value, which is affected by the two-atom initial state. Meanwhile the two-atom quantum state will forever stay in the maximal entangled state when the initial state is proper even in the presence of phase decoherence. On the other hand, the Bell violation and the entanglement do not satisfy the monotonous relation, a large Bell violation implies the presence of a large amount of entanglement under certain conditions, while a large Bell violation corresponds to a little amount of entanglement in certain situations. However, the violation of Bell-CHSH inequality can reach the maximal value if two atoms are in the maximal entangled state, or vice versa.