Two-qutrit System Research Articles

Bound on distributed entanglement

Using the convex-roof extended negativity and the negativity of assistance as quantifications of bipartite entanglement, we consider the possible remotely distributed entanglement. For two pure states |ϕ⟩AB and |ψ⟩CD on bipartite systems AB and CD, we first show that the possible amount of entanglement remotely distributed on the system AC by joint measurement on the system BD is not less than the product of two amounts of entanglement for the states |ϕ⟩AB and |ψ⟩CD in two-qubit and two-qutrit systems. We also provide some sufficient conditions, for which the result can be generalized into higher-dimensional quantum systems.

Effect of spin-orbit interaction on entanglement of two-qutrit Heisenberg XYZ systems in an inhomogeneous magnetic field

We investigate the properties of spin-orbit interaction in the ground state and thermal entanglement of a two-qutrit Heisenberg XYZ system in the presence of an inhomogeneous magnetic field. Using negativity as entanglement measure, we give the dependence of entanglement on each parameter in detail. The result shows that one can get appropriate entanglement by adjusting the magnetic field, Dzyaloshinskii–Moriya interaction and anisotropy parameter simultaneously.

Effect of Dzyaloshinskii–Moriya anisotropic antisymmetric interaction on optimal dense coding

We study optimal dense coding in the two-qubit and two-qutrit Heisenberg XXX models with Dzyaloshinskii–Moriya anisotropic antisymmetric interaction (DM interaction). Both the DM interaction and the coupling parameter can enhance the maximum dense coding capacity for high temperature. For low temperature, in the two-qutrit system, the coupling parameter still enhances the maximum dense coding capacity, while the DM interaction weakens the capacity of the channel for dense coding.

Thermal entanglement of a two-qutrit Ising system with Dzialoshinski–Moriya interaction

Thermal entanglement of a two-qutrit Ising system in the presence of an external homogeneous magnetic field and Dzialoshinski–Moriya (DM) interaction is investigated. Influences of magnetic field, temperature, and DM interaction on the entanglement have been characterized in terms of negativity for a wide range of parameters. The cases of parallel, antiparallel and transverse magnetic fields are considered. Results of detailed numerical calculations are explained using the analytically determined ground and excited states of the system. It is shown that at a given temperature, control of entanglement can be optimized by utilizing competing effects of the magnetic field and the DM interaction.

Origination and survival of qudit-qudit entanglement in open systems

The exact reduced dynamics for two independent qudits dephasingly coupled to a common zero-temperature, super-Ohmic, bosonic environment is studied. It is shown that the qudit-qudit subsystem initially prepared in a separable state evolves into an entangled state. Details of the entanglement origination depend on both the coupling strength and the spectral properties of the environment as well as on the dimension of the qudit; the environment-induced entanglement can survive in the long-time limit. The entanglement dynamics of initially maximally entangled qudit-qudit states is analyzed for two examples: the qubit-qubit and qutrit-qutrit systems. The theory is applied to negative partial transposition entangled states of a two-qutrit system, which are shown to be distillable (for the assumed initial state) for arbitrary environment parameters.

Large-capability quantum key distribution with entangled qutrits

A secure quantum key distribution protocol is proposed to distribute the three-dimensional secret message in a two-way quantum channel based on the entanglement of two-qutrit quantum system. The present protocol has an advantage over transmitting directly the secret message with large capacity since the distributed message has been imposed on nonorthogonal two-qutrit-entangled states by the sender using the superdense coding via local unitary operations. The security is ensured by the entanglement of the two-qutrit quantum system and the secure transmission of the traveling-particle sequence in the lossless and noiseless channel.

Effect of Intrinsic Decoherence of Milburn's Model on Entanglement of Two-Qutrit States

We analyze the time evolution of entanglement of two-qutrit system within the framework of Milburn's model of intrinsic decoherence. The entanglement evolution relies not only on the parameters of system, but also on the concrete states either pure or mixed. The linear entropy used to measure the extent to which the intrinsic decoherence affects quantum states is evaluated.

On the Pauli graphs on N-qudits

A comprehensive graph theoretical and finite geometrical study of the commutation relations between the generalized Pauli operators of $N$-qudits is performed in which vertices/points correspond to the operators and edges/lines join commuting pairs of them. As per two-qubits, all basic properties and partitionings of the corresponding {\it Pauli graph} are embodied in the geometry of the generalized quadrangle of order two. Here, one identifies the operators with the points of the quadrangle and groups of maximally commuting subsets of the operators with the lines of the quadrangle. The three basic partitionings are (a) a pencil of lines and a cube, (b) a Mermin's array and a bipartite-part and (c) a maximum independent set and the Petersen graph. These factorizations stem naturally from the existence of three distinct geometric hyperplanes of the quadrangle, namely a set of points collinear with a given point, a grid and an ovoid, which answer to three distinguished subsets of the Pauli graph, namely a set of six operators commuting with a given one, a Mermin's square, and set of five mutually non-commuting operators, respectively. The generalized Pauli graph for multiple qubits is found to follow from symplectic polar spaces of order two, where maximal totally isotropic subspaces stand for maximal subsets of mutually commuting operators. The substructure of the (strongly regular) $N$-qubit Pauli graph is shown to be pseudo-geometric, i.\,e., isomorphic to a graph of a partial geometry. Finally, the (not strongly regular) Pauli graph of a two-qutrit system is introduced; here it turns out more convenient to deal with its dual in order to see all the parallels with the two-qubit case and its surmised relation with the generalized quadrangle $Q(4,3)$, the dual of $W(3)$.

Optimal dense coding with thermal entangled states

We study optimal dense coding with thermal entangled states of a two-qubit Heisenberg XX chain and a two-qutrit system. For a two-qubit Heisenberg XX chain, the dense coding capacity is a function of temperature and external magnetic field. Only in the case of an external magnetic field being less than the coupling constant, the optimal dense coding can be realized with thermal entangled states. For a two-qutrit system, we consider the dense coding capacity taking into account of nonlinear coupling constant and an external magnetic field. We find that the nonlinear coupling constant must be less than 0 for dense coding. For the two models, we give the conditions that the parameters of the models have to satisfy a valid dense coding.

Some statistical features of the entanglement changes associated with quantum logical gates

Abstract We investigate the changes in the entanglement of formation Δ E produced by quantum logical gates acting on composite quantum systems. We consider two-qubit, three-qubit, and two-qutrit systems. We prove that the Δ E -distributions generated by different quantum gates that can be obtained from each other by recourse to appropriate local unitary transformations are identical, even if these gates (in general) produce different changes of entanglement on individual states. We also study, numerically, some features of the probabilities for obtaining different values of Δ E . In the case of two-qubit we show that the Δ E -distributions are well fitted by simple q -MaxEnt distributions.

Entanglement of two-qutrit system

In this paper, von Neumann entropy is used to study three kinds of bipartite qutrit model, which represent SU(3) strongly correlated model, three-level Lipkin-Meshkov-Glick model, and spin-1 model. The relation between the ground-state entanglement and the quantum phase transition in those models is exhibited and the connection between the entanglement extremes and the symmetries is also discussed.

Thermal entanglement in two qutrits system

The thermal entanglement in a two-qutrit system with two spins coupled by exchange interaction is investigated in terms of the measure of entanglement called "negativity". It is found that the thermal entanglement is present and evolvements symmetrically between both ferromagnetic and antiferromagnetic exchange couplings with the temperature. Moreover the critical temperature at which the negativity vanishes increases with the exchange coupling constant J. From the temperature and magnetic field dependences we demonstrate that the temperature and the magnetic field can affect the feature of the thermal entanglement significantly.

Qudit quantum-state tomography

Recently quantum tomography has been proposed as a fundamental tool for prototyping a few qubit quantum device. It allows the complete reconstruction of the state produced from a given input into the device. From this reconstructed density matrix, relevant quantum information quantities such as the degree of entanglement and entropy can be calculated. Generally, orthogonal measurements have been discussed for this tomographic reconstruction. In this paper, we extend the tomographic reconstruction technique to two new regimes. First, we show how nonorthogonal measurements allow the reconstruction of the state of the system provided the measurements span the Hilbert space. We then detail how quantum-state tomography can be performed for multiqudits with a specific example illustrating how to achieve this in one- and two-qutrit systems.