On Relativistic Quantum Information Properties of Entangled Wave Vectors of Massive Fermions

We study special relativistic effects on the entanglement between either spins or momenta of composite quantum systems of two spin- \frac12\frac{1}{2} massive particles, either indistinguishable or distinguishable, in inertial reference frames in relative motion. For the case of indistinguishable particles, we consider a balanced scenario where the momenta of the pair are well-defined but not maximally entangled in the rest frame while the spins of the pair are described by a one-parameter (η) family of entangled bipartite states. For the case of distinguishable particles, we consider an unbalanced scenario where the momenta of the pair are well-defined and maximally entangled in the rest frame while the spins of the pair are described by a one-parameter (ξ) family of non-maximally entangled bipartite states. In both cases, we show that neither the spin-spin (ss) nor the momentum-momentum (mm) entanglements quantified by means of Wootters’ concurrence are Lorentz invariant quantities: the total amount of entanglement regarded as the sum of these entanglements is not the same in different inertial moving frames. In particular, for any value of the entangling parameters, both ss and mm-entanglements are attenuated by Lorentz transformations and their parametric rates of change with respect to the entanglements observed in a rest frame have the same monotonic behavior. However, for indistinguishable (distinguishable) particles, the change in entanglement for the momenta is (is not) the same as the change in entanglement for spins. As a consequence, in both cases, no entanglement compensation between spin and momentum degrees of freedom occurs.     

Quantum Entanglement Under Lorentz Transformation

We study the properties of quantum entanglement in moving frames, with a non-maximally entangled bipartite state: $|\phi\rangle=\sqrt{1-\varepsilon}|{\uparrow\uparrow}\rangle +\sqrt{\varepsilon}|{\downarrow\downarrow}\rangle$ , (0<ε<1). We calculate the concurrence of this state under Lorentz transformation and show that if the momenta part of the spin-1/2 pair is appropriately correlated, the concurrence is invariant ( $\mathcal {C}(\rho)=2\sqrt{\varepsilon-\varepsilon^{2}}$ ); despite the entanglement of this state is not maximal, there is no transfer of entanglement between spin and momentum.     

Spin–momenta entanglement in moving frames: Properties of von Neumann entropy

The fact that spin–momentum of massive particles become entangled (disentangled) as seen by moving observers, is used to investigate the properties of von Neumann entropy, as a measure of spin–momentum entanglement. To do so, we partition the total Hilbert space into momentum and spin subspaces so that the entanglement occurs between total spin states and total momenta of two spin- $\frac{1}{2}$ particles. Assuming that the occurrence of spin–momentum states is determined by Gaussian probability distributions, we show that the degree of entanglement ascends for small rapidities, reaches a maximum and diminishes at high rapidity. We further report how the characteristics of this behaviour vary as the widths of distributions change. In particular, a separable state, resulting from equal distribution widths, indeed becomes entangled in moving frames.     

Tripartite entanglement of fermionic system in accelerated frames

The dynamics of tripartite entanglement of fermionic system in noninertial frames through linear contraction criterion when one or two observers are accelerated is investigated. In one observer accelerated case the entanglement measurement is not invariant with respect to the partial realignment of different subsystems and for two observers accelerated case it is invariant. It is shown that the acceleration of the frame does not generate entanglement in any bipartite subsystems. Unlike the bipartite states, the genuine tripartite entanglement does not completely vanish in both one observer accelerated and two observers accelerated cases even in the limit of infinite acceleration. The degradation of tripartite entanglement is fast when two observers are accelerated than when one observer is accelerated. It is shown that tripartite entanglement is a better resource for quantum information processing than the bipartite entanglement in noninertial frames.     

Fidelity for States of Two Spin- $\frac{1}{2}$ Particles in Moving Frames

Fidelity for the spin part of states of two spin- particles is investigated from the viewpoint of moving observers. Using a numerical approach, the behavior of the fidelity in terms of the boost parameter is described for different amounts of spin entanglement and momentum entanglement. It is shown that for the spin entangled states the fidelity decreases less than that of the case of spin product states and there are special cases for which the fidelity remains perfect regardless of moving observers’ velocity. Generally, in the limit of boosts with speeds close to the speed of light, the fidelity saturates, i.e., it reaches to a constant value that depends on the amount of momentum entanglement and the width of the momentum distribution function.     

Local Unitary Invariant Spin-Squeezing in Multiqubit States

We investiage Local Unitary Invariant Spin Squeezing (LUISS) in symmetric and non-symmetric multiqubit states. On developing an operational procedure to evaluate Local Unitary Invariant Spin Squeezing parameters, we explicitly evaluate these parameters for pure as well as mixed non-symmetric multiqubit states. We show that the existence of local unitary invariant version of Kitegawa-Ueda spin squeezing may not witness pairwise entanglement whereas the local unitary invariant analogue of Wineland spin squeezing necessarily implies pairwise entanglement.     

Spin squeezing inequalities for arbitrary spin

We determine the complete set of generalized spin squeezing inequalities, given in terms of the collective angular momentum components, for particles with an arbitrary spin. They can be used for the experimental detection of entanglement in an ensemble in which the particles cannot be individually addressed. We also present a large set of criteria involving collective observables different from the angular momentum coordinates. We show that some of the inequalities can be used to detect k-particle entanglement and bound entanglement.     

Negative Correlations and Entanglement in Higher-Spin Dicke States

We consider entanglement criteria based on the spin squeezing inequalities for arbitrary spin systems. Here we use the negative correlations to detect the entanglement in the system with exchange symmetry. For arbitrary spin systems, we can find that the state is entangled, when the minimal pairwise correlation is negative. Then we give a parameter which is defined by the collective angular momentum operator, to detect the entanglement for the Dicke state with N spin ?1 particles, and the results are as the same as negative correlation. We also consider the directions of negative correlation, the state is entangled in two orthogonal directions for the superposition of Dicke state without parity.     

The Role of Spin in Entanglement Generated by Expanding Spacetime

We investigate the effects of spin on entanglement arising in Dirac field in an expanding spacetime characterized by the Robertson-Walker metric. We present a general approach that allows us to treat the case where only charge conservation is required, as well as the case where also angular momentum conservation is required. We find that in both situations entanglement originated from the vacuum and quantified by subsystem entropy behaves the same and does not qualitatively deviates from the spinless case. Differences only arise when particles and/or antiparticles are present in the input state.     

Spin Fidelity for Three-Qubit Greenberger-Horne-Zeilinger and W States Under Lorentz Transformations

Constructing the reduced density matrix for a system of three massive spin- \frac12\frac{1}{2} particles described by a wave packet with Gaussian momentum distribution and a spin part in the form of GHZ or W state, the fidelity for the spin part of the system is investigated from the viewpoint of moving observers in the jargon of special relativity. Using a numerical approach, it turns out that by increasing the boost speed, the spin fidelity decreases and reaches to a non-zero asymptotic value that depends on the momentum distribution and the amount of momentum entanglement.     

Entanglement creation and storage in two qubits coupling to an anisotropic Heisenberg spin chain

The time evolution of the entanglement of a pair of two spin qubits is investigated when the two qubits simultaneously couple to an environment of an anisotropic Heisenberg XXZ spin chain. The entanglement of the two spin qubits can be created and is a periodic function of the time if the magnetic field is greater than a critical value. If the two spin qubits are in the Bell state, the entanglement can be stored with relatively large value even when the magnetic field is large.     

Detecting entanglement using a double-quantum-dot turnstile

We propose a scheme based on using the singlet ground state of an electron spin pair in a double-quantum-dot nanostructure as a suitable setup for detecting entanglement between electron spins via the measurement of an optimal entanglement witness. Using time-dependent gate voltages and magnetic fields the entangled spins are separated and coherently rotated in the quantum dots and subsequently detected at spin-polarized quantum point contacts. We analyze the coherent time evolution of the entangled pair and show that by counting coincidences in the four exits an entanglement test can be done. This setup is close to present-day experimental possibilities and can be used to produce pairs of entangled electrons "on demand."     

Delocalized entanglement of atoms in optical lattices

We show how to detect and quantify entanglement of atoms in optical lattices in terms of correlation functions of the momentum distribution. These distributions can be measured directly in the experiments. We introduce two kinds of entanglement measures related to the position and the spin of the atoms.     

Double- and multi-photon pair production and electron-positron entanglement

We investigate entanglement of electrons and positrons produced via absorption by a vacuum of two or several photons from two external electromagnetic waves. The waves are modelled by finite-length focused pulses. Structures of the arising electron and positron wave packets are investigated in the momentum and coordinate representations. Conditional and unconditional widths of these wave packets, as well as the Schmidt number K are found, and they are used to evaluate the degree of entanglement. The conditions are found when entanglement is large. It is shown that the highest entanglement can be reached at nonrelativistic energies of electrons and positrons. Possibilities of observing the entanglement effects in experiments on pair production are discussed.     

Entanglement of spin pairs in alternating open spin-1/2 chains with the XY Hamiltonian

We investigate entanglement of spin pairs in alternating open spin chains (s = 1/2) with spin-spin interactions (SSI) in the thermodynamic equilibrium state in an external magnetic field. The reduced density matrix of an arbitrarily chosen spin pair was calculated. The entanglement of a spin pair was evaluated with the Wootters criterion. The temperature at which the entangled state arises in the chosen pair was determined. Entanglement (concurrence) is shown to oscillate as a function of the position of a spin pair in the chain. The results demonstrate the dependence of the entanglement in arbitrarily chosen pairs of neighboring spins on the temperature, the position of the spin pair in the chain, chain length, and the ratio between the SSI constants. Qualitative explanation of these dependences is offered. The role of the terminal spins in the generation of entanglement is explained.     

Relativity of quantum states in entanglement swapping

The entanglement swapping protocol is analyzed in a relativistic setting, where shortly after the entanglement swapping is performed, a Bell test is performed. For an observer in the laboratory frame, a Bell violation is observed between the qubits with the swapped entanglement. In a moving frame, the order of the measurements is reversed, and a Bell violation is observed even though the particles are not entangled, directly or indirectly, or at any point in time. Although the measurement results are identical, the wavefunctions for the two frames are starkly different — one is entangled and the other is not. Furthermore, for boosts in a perpendicular direction, in the presence of decoherence, we show that the maximum Bell violation can occur across non-simultaneous points in time. This is a signature of entanglement that is spread across both space and time, showing both non-local and non-simultaneous aspects of entanglement.     

Entanglement swapping with pure orbital angular momentum Bell-state analysis

We investigate a framework of an orbital angular momentum (OAM) entanglement swapping in a multi-dimensional Hilbert space with the spin angular momentum (SAM)-based orbital angular momentum (OAM) Bell-sate analysis. By the implementations of entanglement swapping with the SAM and OAM Bell-state measurements subsequently, the OAM entanglement states (qudits) are generated and then transferred between photons in multi-dimensional Hilbert space in a point-to-point fashion. In the proposed scheme, two pairs of the SAM-based OAM hybrid entanglement photons are deployed to conduct the successive SAM and OAM Bell-state measurements. It provides an alternative technique to transfer pure OAM Bell-states in qudits, which illustrates a possible experimental approach for devising a full repeater in a complex quantum computation network where entanglement swapping serves as a critical constituent.     

大气信道中单光子轨道角动量纠缠特性的研究

本文讨论了大气信道中轨道角动量纠缠光子对的纠缠度, 并利用von Karman大气湍流谱来建立双光子纠缠度的模型, 分析了大气湍流对不同轨道角动量纠缠光子对纠缠度的影响. 研究表明: 在大气信道中, 由于大气湍流的存在, 纠缠光子对的纠缠度随着传输距离z的增加而减小; 大气湍流强度越大, 纠缠光子对的纠缠度下降的越快, 纠缠光子对传输的距离越小; 在湍流强度相同的大气信道轨道角动量指数越大的纠缠光子对, 纠缠度下降得越慢, 纠缠光子对传输的距离越远.     

Entanglement and elementary excitations in quantum spin chain

The entanglement induced by elementary excitations in the XX spin chain is investigated by Bethe ansatz method. The reduced density matrix and correlation function between any pair of spins can be obtained for ground and all excited states with N qubits. Rely on them we show the explicit and general relations between entanglement and elementary excitations in XX spin chain. We further show our method can be extend to other integrable models.