Two-way quantum communication: Generalization of secure quantum information exchange to quantum network

The idea of secure quantum information exchange (SQIE) [J. Phys. B: At. Mol. Opt. Phys.44, 115504 (2011)] is introduced for the secure exchange of single qubit information states between two legitimate users, Alice and Bob. In the present paper, we extend this original SQIE protocol by presenting a scheme, which enables the secure exchange of n-single qubit information states among the n nodes of a quantum network, with the aid of a special kind of 4n-qubit entangled state and the classical assistance of an extra participant Charlie. For experimental realization of our extended SQIE protocol, we suggest an efficient scheme for the generation of a special kind of 4n-qubit entangled state using the interaction between highly detuned Λ-type three-level atoms and optical coherent field. Further, by discussing the various experimental parameters, we show that the special kind 4n-qubit entangled state can be generated with the presently available technology.     

Probabilistic Quantum Information Splitting Based on the Non-maximally Entangled Four-Qubit State

In this paper, we propose a scheme for quantum information splitting based on the non-maximally entangled four-qubit state in order to realize the splitting of the specific two-qubit state |ψ〉 _{A B} =x|00〉+y|11〉. The information splitter will safely share an state to the receiver with help of the controller. Through introducing an auxiliary system and applying several appropriate unitary transformations the information receiver can reconstruct the original state sent by the information splitter. Due to the non-maximally entangled four-qubit state, the total probability that the receiver obtains the original information is P. Furthermore, we discuss the relationship between the successful splitting probability and the concurrence of the entangled state and get a specific expression. In addition, the scheme is tested against external and internal attacks, and we define a function to characterise the security with the concurrence of the entanglement.     

Tripartite Quantum Controlled Teleportation via Seven-Qubit Cluster State

In this paper, a theoretical scheme for tripartite quantum controlled teleportation is presented using the entanglement property of seven-qubit cluster state. This means that Alice wants to transmit a entangled state of particle a to Bob, Charlie wants to transmit a entangled state of particle b to David and Edison wants to transmit a entangled state of particle c to Ford via the control of the supervisor. In the end, we compared the aspects of quantum resource consumption, operation complexity, classical resource consumption, quantum information bits transmitted, success probability and efficiency with other schemes.     

Bidirectional Quantum Teleportation of a Class of <Emphasis Type="Italic">n</Emphasis>-Qubit States by Using (2<Emphasis Type="Italic">n</Emphasis> + <Emphasis Type="Bold">2</Emphasis>)-Qubit Entangled States as Quantum Channel

A new protocol of bidirectional quantum teleportation (BQT) is proposed in which the users can transmit a class of n-qubit state to each other simultaneously, by using (2n + 2)-qubit entangled states as quantum channel. The state of the art approaches can only transmit two-qubit states in each round. This scheme is based on control-not operation, single-qubit measurements and appropriate single-qubit unitary operations. It is shown that the protocol is secure in preparation phase.     

Efficient Three-Party Quantum Dialogue Protocol Based on the Continuous Variable GHZ States

Based on the continuous variable GHZ entangled states, an efficient three-party quantum dialogue protocol is devised, where each legitimate communication party could simultaneously deduce the secret information of the other two parties with perfect efficiency. The security is guaranteed by the correlation of the continuous variable GHZ entangled states and the randomly selected decoy states. Furthermore, the three-party quantum dialogue protocol is directly generalized to an N-party quantum dialogue protocol by using the n-tuple continuous variable GHZ entangled states.     

Teleportation of aTripartite Squeezed Entangled State Via EPR Entangled State with Continuous Variables

A scheme for teleporting an arbitrary tripartite entangled state is proposed when three bipartite entangled states (|η〉) with continuous variables are used as quantum channels. Quantum teleportation can be carried out successfully if the receiver adopts an appropriate unitary transformation. The calculation is greatly simplified by virtue of the Schmidt decompositions of both tripartite entangled state |p _t ,χ ₂,χ ₃〉 and |η〉. Any tripartite state which can be expanded in terms of |p _t ,χ ₂,χ ₃〉 may be teleported in this way due to the completeness of |p _t ,χ ₂,χ ₃〉.     

Concurrence and Negativity as a Family of Two Measures Elaborated for Pure Qudit States

We investigate entangled states of an atomic trapped ion interacting with two phonons in the Λ configuration forming a twelve-dimensional Hilbert space. We study two elaborated measures, namely, the concurrence C and negativity N, which are important in current theoretical studies. Therefore, we work with the three-dimensional reduced density matrix in calculating the measures elaborated for pure qudit states in the ionic–phononic system. To demonstrate the benefits of the family of the two measures elaborated, we perform the calculations for different values of the Lamb–Dicke (LD) parameter η = 0.01, 0.3, and 0.5. Finally, we show that the pure qudit states under study are maximum entangled states.     

Entanglement and Berry Phase in a Parameterized Three-Qubit System

In this paper, we construct a parameterized form of unitary \(\breve {R}_{123}(\theta _{1},\theta _{2},\varphi )\) matrix through the Yang-Baxterization method. Acting such matrix on three-qubit natural basis as a quantum gate, we can obtain a set of entangled states, which possess the same entanglement value depending on the parameters ?? ₁ and ?? ₂. Particularly, such entangled states can produce a set of maximally entangled bases Greenberger-Horne-Zeilinger (GHZ) states with respect to ?? ₁ = ?? ₂ = π/2. Choosing a useful Hamiltonian, one can study the evolution of the eigenstates and investigate the result of Berry phase. It is not difficult to find that the Berry phase for this new three-qubit system consistent with the solid angle on the Bloch sphere.     

Complex Wavelet Transform of the Two-mode Quantum States

By employing the bipartite entangled state representation and the technique of integration within an ordered product of operators, the classical complex wavelet transform of a complex signal function can be recast to a matrix element of the squeezing-displacing operator U ₂(μ, σ) between the mother wavelet vector 〈ψ| and the two-mode quantum state vector |f〉 to be transformed. 〈ψ|U ₂(μ, σ)|f〉 can be considered as the spectrum for analyzing the two-mode quantum state |f〉. In this way, for some typical two-mode quantum states, such as two-mode coherent state and two-mode Fock state, we derive the complex wavelet transform spectrum and carry out the numerical calculation. This kind of wavelet-transform spectrum can be used to recognize quantum states.     

A probabilistic quantum communication protocol using mixed entangled channel

Qubits are realized as polarization state of photons or as superpositions of the spin states of electrons. In this paper we propose a scheme to probabilistically teleport an unknown arbitrary two-qubit state using a non-maximally entangled GHZ-like state and a non-maximally Bell state simultaneously as quantum channels. We also discuss the success probability of our scheme. We perform POVM in the protocol which is operationally advantageous. In our scheme we show that the non-maximal quantum resources perform better than maximal resources.     

Background Independent Quantum Mechanics,Metric of Quantum States,and Gravity: A Comprehensive Perspective

This paper presents a comprehensive perspective of the metric of quantum states with a focus on the geometry in the background independent quantum mechanics. We also explore the possibilities of geometrical formulations of quantum mechanics beyond the quantum state space and Kähler manifold. The metric of quantum states in the classical configuration space with the pseudo-Riemannian signature and its possible applications are explored. On contrary to the common perception that a metric for quantum state can yield a natural metric in the configuration space when the limit ?→0, we obtain the metric of quantum states in the configuration space without imposing the limiting condition ?→0. Here Planck’s constant ? is absorbed in the quantity like Bohr radii \(\frac{1}{2mZ\alpha}\sim a_{0}\). While exploring the metric structures associated with Hydrogen like atom, we witness another interesting finding that the invariant lengths appear in the multiple of Bohr’s radii as: ds ²=a ₀ ² (? Ψ)².     

The checkerboard family of entangled states of two qutrits

By modifying the method of Bruß and Peres, we construct two new families of entangled two qutrit states. For all density matrices ρ in these families we have ρ _ij = 0 for i + j odd. The first family depends on 27 independent real parameters and includes both PPT and NPT states. The second family consists of PPT entangled states. The number of independent real parameters of this family is ≥ 11     

A Logical Approach to Entanglement

In this paper we innovate a logical approach to develop an intuition regarding the phenomenon of quantum entanglement. In the vein of the logic introduced we substantiate that particles that were entangled in the past will be entangled in perpetuity and thereby abide a rule that restricts them to act otherwise. We also introduce a game and by virtue of the concept of Nash equilibrium we have been able to show that entangled particles will mutually correspond to an experiment that is performed on any one of the particle.     

Remotely and Conclusively Mapping One Finite Set of Qudit States onto Another Assisted by Qubit Entanglements

Alice and Bob are two remote parties. We propose a probabilistic method which allows Alice to map remotely and conclusively Bob’s set of nonorthogonal symmetric d-level quantum states onto another. The procedure we use is a remote positive operator valued measurement (POVM) in Bob’s (2d-1)-level direct sum space. We construct a quantum network for implementing this (2d-1)-level remote nonunitary POVM with (d-1) two-level remote unitary rotations. The fact that the two-level remote rotation, which is hired to rotate remotely a basis vector, can been implementing rapidly using only one ebit (a two-level Einstein-Podolsky-Rosen (EPR) pair) and one cbit (classical communication) is notable. This scheme is simpler but with less resource, which will make it more feasible and suitable for large-scale quantum network.     

Control of Quantum Echo and Bell State Swapping of Two Atomic Qubits in the Two-Mode Vacuum Field Environment

We investigate quantum echo control and Bell state swapping for two atomic qubits (TAQs) coupling to two-mode vacuum cavity field (TMVCF) environment via two-photon resonance. We discuss the effect of initial entanglement factor ?? and relative coupling strength R=g₁/g₂ on quantum state fidelity of TAQs, and analyze the relation between three kinds of quantum entanglement(C(ρ_a),C(ρ_f),S(ρ_a)) and quantum state fidelity, then reveal physical essence of quantum echo of TAQs. It is shown that in the identical coupling case R=1, periodic quantum echo of TAQs with π cycle is always produced, and the value of fidelity can be controlled by choosing appropriate ?? and atom-filed interaction time. In the non-identical coupling case R≠1, quantum echoes with periods of π, 2π and 4π can be formed respectively by adjusting R. The characteristics of quantum echo results from the non-Markovianity of TMVCF environment, and then we propose Bell state swapping scheme between TAQs and two-mode cavity field.     

Bit-Oriented Quantum Public-Key Cryptosystem Based on Bell States

Quantum public key encryption system provides information confidentiality using quantum mechanics. This paper presents a quantum public key cryptosystem (QPKC) based on the Bell states. By Holevo’s theorem, the presented scheme provides the security of the secret key using one-wayness during the QPKC. While the QPKC scheme is information theoretic security under chosen plaintext attack (CPA). Finally some important features of presented QPKC scheme can be compared with other QPKC scheme.     

Relativistic constraints on the distinguishability of orthogonal quantum states

The constraints imposed by special relativity on the distinguishability of quantum states are discussed. An explicit expression relating the probability of an error in distinguishing two orthogonal single-photon states to their structure, the time t at which a measurement starts, and the interval of time T elapsed from the start of the measurement until the time at which the outcome is obtained by an observer is given as an example.     

Quantum Cryptography,Quantum Communication,and Quantum Computer in a Noisy Environment

First, we study several information theories based on quantum computing in a desirable noiseless situation. (1) We present quantum key distribution based on Deutsch’s algorithm using an entangled state. (2) We discuss the fact that the Bernstein-Vazirani algorithm can be used for quantum communication including an error correction. Finally, we discuss the main result. We study the Bernstein-Vazirani algorithm in a noisy environment. The original algorithm determines a noiseless function. Here we consider the case that the function has an environmental noise. We introduce a noise term into the function f(x). So we have another noisy function g(x). The relation between them is g(x) = f(x) ± O(??). Here O(??) ? 1 is the noise term. The goal is to determine the noisy function g(x) with a success probability. The algorithm overcomes classical counterpart by a factor of N in a noisy environment.     

Teleportation through <Emphasis Type="Italic">W</Emphasis>-class states

The possibility of using entangled states of the W class either as a quantum channel for teleportation or as states to be teleported is analyzed. The protocols are determined through the unitary transformation of the schemes based on the Greenberger-Horne-Zeilinger (GHZ) channel. It is shown that the main feature of new quantum channels of the W class is a set of nonlocal operators capable of recovering an unknown state.     

Kraus Operator-Sum Solution to the Master Equation Describing the Single-Mode Cavity Driven by an Oscillating External Field in the Heat Reservoir

Exploiting the thermo entangled state approach, we successfully solve the master equation for describing the single-mode cavity driven by an oscillating external field in the heat reservoir and then get the analytical time-evolution rule for the density operator in the infinitive Kraus operator-sum representation. It is worth noting that the Kraus operator M _{l, m} is proved to be a trace-preserving quantum operation. As an application, the time-evolution for an initial coherent state ρ _|β〉 = |β〉〈β| in such an environment is investigated, which shows that the initial coherent state decays to a new mixed state as a result of thermal noise, however the coherence can still be reserved for amplitude damping.