Narrow Results

Acting within the framework of geometric quantum mechanics, an interpretation of quantum uncertainty is discussed in terms of Jacobi fields, and a connection with the theory of elliptic curves is outlined, via classical integrability of Schrödinger's dynamics and the cross-ratio interpretation of quantum transition probabilities. Furthermore, a thoroughly geometrical construction of all special unitary representations of the 3-strand braid group on the quantum 1-qubit space is given, and the connection of one of them with elliptic curves admitting complex multiplication automorphisms — the physically relevant one corresponding to the anharmonic ratio — is shown. Also, contact is made with the Temperley–Lieb algebra theoretic constructions of Kauffman and Lomonaco, and it is shown that the standard trace relative to one of the above representations computes the Jones polynomial for particular values of the parameter, for knots arising as closures of 3-strand braids. Subsequently, a geometric entanglement criterion (in terms of Segre embeddings) is discussed, together with a projective geometrical portrait for quantum 2-gates. Finally, Aravind's idea of describing quantum states via knot theory is critically analyzed, and a geometrical picture — involving a blend of SU(2)-representation theory, classical projective geometry, binary trees and Brunnian and Hopf links — is set up in order to describe successive measurements made upon generalized GHZ states, close in spirit to the quantum knot picture again devised by Kauffman and Lomonaco.

In this paper, we present reducible representation of the n² braid group representation which is constructed on the tensor product of n-dimensional spaces. Specifically, it is shown that via a combining method, we can construct more n² dimensional braiding S-matrices which satisfy the braid relations. By Yang–Baxterization approach, we derive a 9 × 9 unitary -matrix according to a 9 × 9 braiding S-matrix we have constructed. The entanglement properties of -matrix is investigated, and the arbitrary degree of entanglement for two-qutrit entangled states can be generated via -matrix acting on the standard basis.

We introduce a new model of interacting spin 1/2. It describes interactions of three nearest neighbors. The Hamiltonian can be expressed in terms of Fredkin gates. The Fredkin gate (also known as the controlled swap gate) is a computational circuit suitable for reversible computing. Our construction generalizes the model presented by Peter Shor and Ramis Movassagh to half-integer spins. Our model can be solved by means of Catalan combinatorics in the form of random walks on the upper half plane of a square lattice (Dyck walks). Each Dyck path can be mapped on a wave function of spins. The ground state is an equally weighted superposition of Dyck walks (instead of Motzkin walks). We can also express it as a matrix product state. We further construct a model of interacting spins 3/2 and greater half-integer spins. The models with higher spins require coloring of Dyck walks. We construct a $SU(k)$ symmetric model (where $k$ is the number of colors). The leading term of the entanglement entropy is then proportional to the square root of the length of the lattice (like in the Shor–Movassagh model). The gap closes as a high power of the length of the lattice [5, 11].

The notion of partial trace of a density operator is essential for the understanding of the entanglement and separability properties of quantum states. In this paper, we investigate these notions putting an emphasis on the geometrical properties of the covariance ellipsoids of the reduced states. We thereafter focus on Gaussian states and we give new and easily numerically implementable sufficient conditions for the separability of all Gaussian states. Unlike the positive partial transposition criterion, none of these conditions is however necessary.

Service quality preference behaviors of both members are considered in service supply chain (SSC) including a service integrator and a service provider with stochastic demand. Through analysis of service quality cost and revenue, the utility functions are established on service quality effort degree and service quality preference level in integrated and decentralized SSC. Nash equilibrium and quantum game are used to optimize the models. By comparing the different solutions, the optimal strategies are obtained in SSC with quality preference. Then some numerical examples are studied and the changing trend of service quality effort is further analyzed by the influence of the entanglement operator and quality preferences.

John Ju Sakurai's classical book in quantum mechanics makes a very illuminative presentation that studies entangled states in a two spin s=1/2 particles system in a singlet state. A Bell's inequality emerges as a consequence. Bell's inequality is a relationship among observables that discriminates between Einstein's locality principle and the nonlocal point of view of orthodox quantum mechanics. Following Sakurai's style we propose, by making natural induction, a generalization for Bell's inequality for any two spin-s particles in a singlet state (s integer or half-integer). This inequality is expressed as a function of a θ parameter, which is a measure of the angle between two possible directions in which the spin is measured. Besides the expression for this general inequality we have found that: (a) for any finite half-integer spin Bell's inequality is violated for some interval of the θ-parameter. The right limit of this interval is fixed and equal to π/2, while the left one comes closer and closer to this value as spin number grows. A function fit shows clearly that the size of this θ-interval over which Bell's inequality is violated diminishes asymptotically to zero as 1/s^1/2; (b) an analogous behavior for any finite integer spin.

For large spins the disagreement between Einstein's locality principle and the nonlocal point of view in orthodox quantum mechanics disappears.

Topological ordered phases are gapped states of matter that are characterized by non-local entanglement in their ground state wave functions instead of a local order parameter. In this paper, we review some of the basic results on the entanglement structure of topologically ordered phases. In particular, we focus on the notion and uses of "topological entanglement entropy" in two and higher dimensions, and also briefly review the relation between entanglement spectrum and the spectrum of the physical edge states for chiral topological states. Furthermore, we discuss a curvature expansion for the entanglement entropy which sharpens the nonlocality of topological entanglement entropy.

In this paper, we study the origin of the quantum particle entanglement. Particles will have one mixed wave function as soon as they are created, which are called quantum particle entanglement. Electron spin states are used as an example to discuss this topic. When two electrons are created simultaneously, they have two different mixed quantum spin states. Before the measurement of its spin, we cannot determine its spin state. However, as soon as the spin of one of the electrons is determined (measured), the spin of the other will definitely be in the opposite state, regardless of how far they are away from each other. This paper uses the mechanism that the wave packet spreads as soon as they are created and then the wave packet shrinks when it undergoes a measurement to interpret this spooky phenomenon mentioned above.

The Dzyaloshinsky–Moriya (DM) interaction contributes to some unusual and interesting magnetic properties in real materials, thus playing an important role in the degree of quantum entanglement in Heisenberg quantum spin models. In [C. S. Castro, O. S. Duarte, D. P. Pires, D. O. Soares-Pinto and M. S. Reis, Phys. Lett. A380, 1571 (2016)], it has been investigated about the non-locality and the thermal entanglement in a dipolar spin thermal system without DM interaction. In this work, we study the entanglement in the thermal state of inhomogeneous Heisenberg coupling under the presence of the DM interaction along the $z$-axis. More precisely, we analyze the effect of the DM interaction on non-locality phenomena and quantum entanglement as measured by negativity and Von Neumann entropy. We show that by comparing with [C. S. Castro, O. S. Duarte, D. P. Pires, D. O. Soares-Pinto and M. S. Reis, Phys. Lett. A380, 1571 (2016)], the local quantum states become more pronounced, when the DM interaction is taken into account. This fact is well confirmed by noting that Von Neumann entropy is destroyed in the presence of the DM interaction. It can be deduced that the Dzyaloshinsky–Moriya (DM) interaction makes the thermal states less correlated.

We investigate and quantify bipartite and tripartite entanglement measures in two- and three-flavor neutrino oscillations. The bipartite entanglement is analogous to the entanglement swapping resulting from a beam splitter in quantum optics. We calculate various entanglement measures, such as the concurrence, negativity, and three-tangle for the three-neutrino system. The significant result is that a monogamy inequality in terms of negativity leads to a residual entanglement, implying genuine tripartite entanglement in the three-neutrino system. We establish an analogy of the three-neutrino state with a generalized W-state class in quantum optics.

The no-masking theories show that it is impossible to mask the set of all qubit states into the quantum correlation of bipartite qubit system or tripartite qubit system. In this paper, we give a new proof of the no-masking situation of the tripartite qubit system. Recent work has shown that there exists a universal masker which can mask an arbitrary set of qubit states in four-qubit systems perfectly by means of the maximum entangled states. Here we show that there exist more than one masking scheme even for the same multipartite qubit system. Basing on the maximum entangled states we give the deterministic masking scenario for N-qubit system. In practice, decoherence hinders us from obtaining the maximum entangled states. From this viewpoint, the masking scenario based on non-maximum entangled states becomes more universal. Furthermore, we provide an approximate quantum masking scenario and investigate the relation between approximate masking and quantum entanglement.

The Weyl geometry promises potential applications in gravity and quantum mechanics. We study the relationships between the Weyl geometry, quantum entropy and quantum entanglement based on the Weyl geometry endowing the Euclidean metric. We give the formulation of the Weyl Ricci curvature and Weyl scalar curvature in the n-dimensional system. The Weyl scalar field plays a bridge role to connect the Weyl scalar curvature, quantum potential and quantum entanglement. We also give the Einstein–Weyl tensor and the generalized field equation in 3D vacuum case, which reveals the relationship between Weyl geometry and quantum potential. Particularly, we find that the correspondence between the Weyl scalar curvature and quantum potential is dimension-dependent and works only for the 3D space, which reveals a clue to quantize gravity and an understanding why our space must be 3D if quantum gravity is compatible with quantum mechanics. We analyze numerically a typical example of two orthogonal oscillators to reveal the relationships between the Weyl scalar curvature, quantum potential and quantum entanglement based on this formulation. We find that the Weyl scalar curvature shows a negative dip peak for separate state but becomes a positive peak for the entangled state near original point region, which can be regarded as a geometric signal to detect quantum entanglement.

The axion particle is the outcome of the proposed Peccei–Quinn mechanism for solving the strong CP problem. Axion is also a popular dark matter candidate. Thus, there is an increased interest in establishing its existence. Axions couple to two photons and most experiments search for the transition of an axion into a photon, in the presence of a magnetic field. In our study, we examine the coupling of the axion into a pair of entangled photons. The presence of a magnetic field changes the polarization correlations of the entangled photons, thus offering an unambiguous signature for axion existence.

This paper presents an analytical investigation of the teleportation and the thermal entanglement of two identical qubits in the ground state of graphene lattices. The elastic interaction between the two qubits is considered as a scattering process. The modified Hamiltonian and density matrix of the system were presented. The teleportation and the entanglement of two-qubit system are analyzed through the study of the average fidelity of teleportation $F_A$, the concurrence ${𝒞}$ and the entanglement of formation ${{ℰ}}_f$. The results depend on the temperature $T$ and also on the parameters of the system as the $\chi$ parameter of the interaction potential and $\gamma$ band parameter. The study shows that the teleportation and the entanglement decrease when the temperature $T$ increases but they become all the more important as the parameters $\chi$ and $\gamma$ increase.

Studying quantum entanglement in systems of indistinguishable particles, in particular anyons, poses subtle challenges. Here, we investigate a model of one-dimensional anyons defined by a generalized algebra. This algebra has the special property that fermions in this model are composites of anyons. A Hubbard-like Hamiltonian is considered that allows hopping between nearest neighbor sites not just for the fundamental anyons, but for the fermionic anyon composites. Some interesting results regarding the quantum entanglement of these particles are obtained.

Electron spin qubits in silicon quantum dots are an attractive candidate for large-scalable quantum computation. An essential step for quantum information processing based on spin qubits is to realize the spatially separated two-qubit gate and entanglement with high fidelity. Here, we consider two spin qubits coupled to a common superconducting resonator in circuit quantum electrodynamics. We investigate the long-range two-qubit iSWAP gate mediated by virtual microwave photons using a Gaussian smoothing pulse. We show that the entangling gate fidelity can reach $91.0\%$ under realistic experimental conditions and analyze the factors limiting gate fidelity. Moreover, we numerically demonstrate the generation of remote Bell entangled states of spin qubits with high fidelity. In addition, this spin–resonator architecture can be used to implement quantum algorithms using our scheme. These results pave the way for quantum information processing with spin qubits.

In this paper, the origin of disentanglement for two specific sub-classes of $X$-states namely maximally nonlocal mixed states (MNMSs) and maximally entangled mixed states (MEMSs) is investigated analytically for a physical system consisting of two spatially separated qubits interacting with a common vacuum bath. The phenomena of entanglement sudden death (ESD) and the entanglement sudden birth (ESB) are observed, but the characteristics of ESD and ESB are found to be different for the case of two-photon coherence and single photon coherence states. The role played by initial coherence for the underlying entanglement dynamics is investigated. Further, the entanglement dynamics of MNMSs and MEMSs under different environmental noises namely phase damping, amplitude damping and random telegraph noise (RTN) noise with respect to the decay and revival of entanglement is analyzed. It is observed that the single photon coherence states are more robust against the sudden death of entanglement, indicating the usability of such states in the development of technologies for the practical implementation of quantum information processing tasks.

We know that space and time are treated almost equally in classical physics, but we also know that this is not the case for quantum mechanics. A quantum description of both space and time is important to really understand the quantum nature of reality. The Page–Wootters mechanism of quantum time is a promising starting point, according to which the evolution of the quantum system is described by the entanglement between it and quantum temporal degrees of freedom. In this paper, we consider a qubit clock that is entangled with a quantum system due to the Wigner rotation induced by Lorentz transformation. We study how this time-system entanglement depends on the rapidity of the Lorentz boost. We consider the case of a spin-1/2 particle with Gaussian momentum distribution as a concrete example. We also compare the time-system entanglement entropy with the spin-momentum entanglement entropy and find that the former is smaller than the latter.

This study investigates the entanglement properties of disordered free fermion systems undergoing an Anderson phase transition from a delocalized to a localized phase. The entanglement entropy is employed to quantify the degree of entanglement, with the system randomly divided into two subsystems. To explore this phenomenon, one-dimensional tight-binding fermion models and Anderson models in one, two, and three dimensions are utilized. Comprehensive numerical calculations reveal that the entanglement entropy, determined using random bi-partitioning, follows a volume-law scaling in both the delocalized and localized phases, expressed as $\mathrm{\text{EE}}\propto L^D$, where D represents the dimension of the system. Furthermore, the role of short and long-range correlations in the entanglement entropy and the impact of the distribution of subsystem sites are analyzed.

In this paper, a channel-optimized quantum communication scheme with imperfect Bell states is being considered, based on quantum teleportation and error correction codes technology. In this scheme, a novel “combination code” technique is proposed to protect the pre-shared Bell states from storage errors and to safeguard the information-encoded states from noisy channels. Ultimately, it is revealed by Monte Carlo simulation results that the channel fidelity of the proposed channel-optimized quantum communication scheme with imperfect Bell states is significantly advantageous over standard quantum error-correcting code (QECC) and entanglement-assisted quantum error-correcting code (EAQECC) communication schemes.