Wigner Function：from Ensemble Average of Density Operator to Its Matrix Element in Entangled Pure States

We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangled states are defined in the enlarged Fock space with a fictitious freedom.

Simple Procedure for Entanglement Transformation of Bipartite Pure States

An explicit procedure for transforming one bipartite entangled state into another via local operations and classical communication （LOCC） is presented. Our procedure is much simper than the previous ones in the sense that, it only involves two steps and the explicit expression of local general measurement used in the procedure can be obtained by solving a set of linear equations. Furthermore, this procedure is still applicable in high dimensional case.

Separability of Pure States and Mixed States of the Quantum Network of Two Nodes

This article discusses the separability of the pure states and mixed states of the quantum network of two nodes by means of the criterion of no entanglement in terms of the covariance correlation tensor in quantum network theory, i.e. for a composite system consisting of two nodes. The covariance correlation tensor is equal to zero for all possible and .

Generation of Arbitrary Pure States for Three-dimensional Motion of a Trapped Ion

In this paper, we propose a scheme for generating an arbitrary three-dimensional pure state of vibrational motion of a trapped ion. Our scheme is based on a sequence of laser pulses, which are tuned to the appropriate vibrational sidebands with respect to the appropriate electronic transition.

Quantum secure direct communication with quantum encryption based on pure entangled states

This paper presents a scheme for quantum secure direct communication with quantum encryption. The two authorized users use repeatedly a sequence of the pure entangled pairs （quantum key） shared for encrypting and decrypting the secret message carried by the travelling photons directly. For checking eavesdropping, the two parties perform the single-photon measurements on some decoy particles before each round. This scheme has the advantage that the pure entangled quantum signal source is feasible at present and any eavesdropper cannot steal the message.

Multiparty quantum secret conference based on quantum encryption with pure entangled states

We present a scheme for multiparty quantum remote secret conference （MQRSC） with pure entangled states, not maximally entangled multipartite quantum systems. The conferees first share a private quantum key, a sequence of pure entangled states and then use them to encode and decode the secret messages. The conferees exploit the decoy-photon technique to ensure the security of the transmission of qubits. This MQRSC scheme is more feasible and efficient than others.

Analytic Expression of Geometric Discord in Arbitrary Mixture of any Two Bi-qubit Product Pure States

Quantum correlations in a family of states comprising any mixture of a pair of arbitrary bi-qubit product pure states are studied by employing geometric discord [Phys. Rev. Lett. 105(2010) 190502] as the quantifier. First, the inherent symmetry in the family of states about local unitary transformations is revealed. Then, the analytic expression of geometric discords in the states is worked out. Some concrete discussions and analyses on the captured geometric discords are made so that their distinct features are exposed. It is found that, the more averagely the two bi-qubit product states are mixed, the bigger geometric discord the mixed state owns. Moreover, the monotonic relationships of geometric discord with different parameters are revealed.

Quantum entanglement swapping of two arbitrary biqubit pure states

In this paper, the issue of swapping quantum entanglements in two arbitrary biqubit pure states via a local bipartite entangledstate projective measure in the middle node is studied in depth, especially with regard to quantitative aspects. Attention is mainly focused on the relation between the measure and the final entanglement obtained via swapping. During the study, the entanglement of formation(EoF) is employed as a quantifier to characterize and quantify the entanglements present in all involved states. All concerned EoFs are expressed analytically; thus, the relation between the final entanglement and the measuring state is established.Through concrete analyses, the measure demands for getting a certain amount of a final entanglement are revealed. It is found that a maximally entangled final state can be obtained from any two given initial entangled states via swapping with a certain probability;however, a peculiar measure should be performed. Moreover, some distinct properties are revealed and analyzed. Such a study will be useful in quantum information processes.

Monogamous nature of symmetric N-qubit states of the W class: Concurrence and negativity tangle

Using Majorana representation of symmetric N-qubit pure states, we have examined the monogamous nature of the family of states with two-distinct spinors, the W class of states. We have evaluated the N-concurrence tangle and showed that all the states in this family have vanishing concurrence tangle. The negativity tangle for the W class of states is shown to be non-zero, illustrating the fact that the concurrence tangle is always lesser than or equal to the negativity tangle in a pure N-qubit state.

Probabilistic teleportation of an arbitrary pure state of two atoms

In the context of microwave cavity QED, this paper proposes a new scheme for teleportation of an arbitrary pure state of two atoms. The scheme is very different from the previous ones which achieve the integrated state measurement, it deals in a probabilistic but simplified way. In the scheme, no additional atoms are involved and thus only two atoms are required to be detected. The scheme can also be used for the teleportation of arbitrary pure states of many atoms or two-mode cavities.

Two-qubit pure state tomography by five product orthonormal bases

In this paper, we focus on two-qubit pure state tomography. For an arbitrary unknown two-qubit pure state, separable or entangled, it has been found that the measurement probabilities of 16 projections onto the tensor products of Pauli eigenstates are enough to uniquely determine the state. Moreover, these corresponding product states are arranged into five orthonormal bases. We design five quantum circuits, which are decomposed into the common gates in universal quantum computation, to simulate the five projective measurements onto these bases. At the end of each circuit, we measure each qubit with the projective measurement {｜0〉〈0 ｜,｜1〉,〈1｜ }. Then, we consider the open problem whether three orthonormal bases are enough to distinguish all two-qubit pure states. A necessary condition is given. Suppose that there are three orthonormal bases {B1,B2,B3}. Denote the unitary transition matrices from B1 to {B2,B3 } as U1 and U2. All 32 elements of matrices U1 and U2 should not be zero. If not, these three bases cannot distinguish all two-qubit pure states.

Perfect Quantum Teleportation via Bell States

Quantum mechanics shows superiority than classical mechanics in many aspects and quantum entanglement plays an essential role in information processing and some computational tasks such as quantum teleportation(QT).QT was proposed to transmit the unknown states,in which EPR pairs,the entangled states,can be used as quantum channels.In this paper,we present two simple schemes for teleporting a product state of two arbitrary single-particle and an arbitrary two-particle pure entangled state respectively.Alice and Bob have shared an entangle state.Two Bell states are used as quantum channels.Then after Alice measuring her qubits and informing Bob her measurement results,Bob can perfectly reconstruct the original state by performing corresponding unitary operators on his qubits.It shown that a product state of two arbitrary single-particle and an arbitrary two-particle pure entangled state can be teleported perfectly,i.e.the success probabilities of our schemes are both 1.

Degree of Entanglement and Violation of Bell Inequality by Two-Spin-1/2 States

Bell inequality is violated by the quantum mechanical predictions made from an entangled state of the composite system. In this paper we examine this inequality and entanglement measures in the construction of the coherent states for two-qubit pure and mixed states, we find a link to some entanglement measures through some new parameters （amplitudes of coherent states）. Conditions for maximal entanglement and separability are then established for both pure and mixed states. Finally, we analyze and compare the violation of Bell inequality for a class of mixed states with the degree of entanglement by applying the formalism of Horodecki et al.

Liquid Nuclear Magnetic Resonance Implementation of Quantum Computation in Subspace

Based on the logical labelling method, we prepare an effective pure state in a subsystem of a three spin system via liquid nuclear magnetic resonance technique. Then with this subspace effective pure state we implement the Deutsch-Jozsa algorithm. The tomography for the subspace effective pure state and the corresponding spectrum of the output for the Deutsch-Jozsa algorithm agree with theoretical predictions, which shows that we have successfully implemented the Deutsch-Jozsa algorithm in a subsystem of a nuclear spin system and demonstrated a subspace quantum computation.

Entanglement Dynamics of Two Qubits Coupled to a Noise Environment

We study the time evolution of two two-state systems （two qubits） initially in the pure entangled states or the maximally entangled mixed states interacting with the individual environmental noise. It is shown that due to environment noise, all quantum entangled states are very fragile and become a classical mixed state in a short-time limit. But the environment can affect entanglement in very different ways. The type of decoherence process for certain entangled states belongs to amplitude damping, while the others belong to dephasing decoherenee.

Partial Trace Method for Deriving Density Operators of Light Field

With the help of technique of integration within an ordered product of operators we can fully display the partial trace method to deduce some new density operators of light field. The general form of single-mode density operator is derived in this way from a normalized two-mode generalized squeezed pure state density operator.

Knotted Picture of a Quantum Network of Two Nodes

This article discusses the variation of the knotted picture of the quantum pure state with the variation of the complex coefficients α and β. It is shown that there are three kinds of link that correspond to three different ranks of the matrix of covariance correlation tensor, i.e., the zero rank corresponds to trivial link, the rank one corresponds to the two-component link with two crossings, and the rank three corresponds to the two-component link with four crossings.

A New Type of Accessible Environmental Influences on Neutrino Oscillation

Considering a new type of environment influences, we use a two-energy-level quantum system to investigate neutrino oscillations in medium. Besides the matter effects derived by Wolfenstein, there may exist extra terms due to a unitary evolution of the system between pure and mixed states, so the evolution equation is modified obviously. We show that the extra terms may play some role and induce observable effects in solar neutrino problem, especially, in the long baseline neutrino oscillation experiments which are under serious consideration recently, if the parameters fall into a suitable region.

Transformations of multilevel coherent states under coherence-preserving operations

Quantum coherence,emerging from the"superposition"of quantum states,is widely used in various information processing tasks.Recently,the resource theory of multilevel quantum coherence is attracting substantial attention.In this paper,we mainly study the transformations of resource pure states via free operations in the theoretical framework for multilevel coherence.We prove that any two multilevel coherent resource pure states can be interconverted with a nonzero probability via a completely positive and trace non-increasing k-coherence-preserving map.Meanwhile,we present the condition of the interconversions of two multilevel coherent resource pure states under k-coherence-preserving operations.In addition,we obtain that in the resource-theoretic framework of multilevel coherence,no resource state is isolated,that is,given a multilevel coherent pure state|ψ>,there exists another multilevel coherent pure state|Φ>and a k-coherence-preserving operation∧k,such that∧k(|Φ>)=|ψ>.

PURE STATE APPROACH TO C(X) x_αZ_n

Consider a C*-system (C(X), z n, α), where α is a homeomorphism of X such that α￣n= id.The authors characterize the pure state space of C(X) xα z n) the transition probability and orientation on it. Two special cases (free action and n = 2) are studied in detail.