Highly efficient remote preparation of an arbitrary three-qubit state via a four-qubit cluster state and an EPR state

An efficient protocol for remotely preparing an arbitrary three-qubit state is devised with a four-qubit cluster state and an Einstein–Podolsky–Rosen state as the shared quantum resource. Using an appropriate set of eight-qubit mutually orthogonal measurement basis, the remote three-qubit preparation is successfully completed with the probability of ${\frac{1}{8}}$ in general case. Then to achieve our concerns of improving the probability of this protocol, some special ensembles of three-qubit states are minutely investigated. As a result, it is shown that the total probability of the RSP protocol, in these particular cases, can be improved to ${\frac{1}{4}}$ and ${\frac{1}{2}}$ , respectively, or even that the RSP protocol can be realized with unit success probability.     

Three schemes of remote information concentration based on ancilla-free phase-covariant telecloning

In this paper, remote information concentration is investigated which is the reverse process of the $1\rightarrow 3$ optimal asymmetric economical phase-covariant telecloning (OAEPCT). The OAEPCT is different from the reverse process of optimal universal telecloning. It is shown that the quantum information via $1\rightarrow 3$ OAEPCT procedure can be remotely concentrated back to a single qubit with a certain probability via several quantum channels. In these schemes, we adopt Bell measurement to measure the joint systems and use projected measurement and positive operator-valued measure to recover the original quantum state. The results shows non-maximally entangled quantum resource can be applied to information concentration.     

Schemes for remotely preparing an arbitrary four-qubit \chi -state

Two schemes via different entangled resources as the quantum channel are proposed to realize remote preparation of an arbitrary four-particle \(\chi \) -state with high success probabilities. To design these protocols, some useful and general measurement bases are constructed, which have no restrictions on the coefficients of the prepared states. It is shown that through a four-particle projective measurement and two-step three-particle projective measurement under the novel sets of mutually orthogonal basis vectors, the original state can be prepared with the probability 50 and 100 %, respectively. And for the first scheme, the special cases of the prepared state that the success probability reaches up to 100 % are discussed by the permutation group. Furthermore, the present schemes are extended to the non-maximally entangled quantum channel, and the classical communication costs are calculated.     

Controlled remote state preparation protocols via AKLT states

In this paper, we proposed two controlled remote state preparation of an arbitrary single-qubit state schemes one for deterministic controlled remote state preparation the other for probabilistic controlled-joint remote state preparation with 2/3 probability. Both of them used the Affleck–Kennedy–Lieb–Tasaki (AKLT) state which consisted of bulk spin-1’s and two spin-1 \(/\) 2’s at the ends. Up to now, no RSP protocols using AKLT gapped ground states as a shared quantum resource had been presented thus far and Fan et al. showed the other AKLT property was that if we performed a Bell measurement on bulk, then a maximally entangled state would be shared by two ends. We utilized these properties to develop our controlled protocols.     

Deterministic remote preparation of arbitrary multi-qubit equatorial states via two-qubit entangled states

We propose an efficient scheme for remotely preparing an arbitrary n-qubit equatorial state via n two-qubit maximally entangled states. Compared to the former scheme (Wei et al. in Quantum Inf Process 16:260, 2017) that has the 50% successful probability when the amplitude factors of prepared states are \(2^{-n{/}2}\), the probability would be increased to 100% by using of our modified proposal. The feasibility of our scheme for remote preparation arbitrary multi-qubit equatorial states is explicitly demonstrated by theoretical studies and concrete examples.     

A highly efficient scheme for joint remote preparation of multi-qubit W state with minimum quantum resource

We present a highly efficient scheme for perfect joint remote preparation of an arbitrary \( 2^{n} \)-qubit W state with minimum quantum resource. Both the senders Alice and Bob intend to jointly prepare one \( 2^{n} \)-qubit W state for the remote receiver Charlie. In the beginning, they help the remote receiver Charlie to construct one n-qubit intermediate state which is closely related to the target \( 2^{n} \)-qubit W state. Afterward, Charlie introduces auxiliary qubits and applies appropriate operations to obtain the target \( 2^{n} \)-qubit W state. Compared with previous schemes, our scheme requires minimum quantum resource and least amount of classical communication. Moreover, our scheme has a significant potential for being adapted to remote state preparation of other special states.     

Vortex and entanglement occurring in propagating states through coupled lossy waveguides

A separable input state consisting of an $n$ -photon Fock state and a coherent state propagating through coupled waveguides is investigated in detail. We obtained the analytical solutions for the state vector evolution, the wavefunction or probability distribution in the quadrature space and the $P$ -function in the phase space. It is proved that the propagating states may evolve into quantum vortex states even for coupled lossy waveguides by appropriately selecting the propagation time. Based on the analytical $P$ -function in phase space and the relative linear entropy for the propagating state, it is found that the propagating state may be entangled and non-classical. Specially, in absence of loss, the degree of entanglement only depends on the photon number $n$ of the input Fock state but is independent of the displacement parameter $\alpha $ associated with the input coherent state. Moreover, for coupled lossy waveguides the entanglement evolution can exhibit new features.     

Remote information concentration via W state: reverse of ancilla-free phase-covariant telecloning

In this paper, we investigate generalized remote information concentration as the reverse process of ancilla-free phase-covariant telecloning (AFPCT) which is different from the reverse process of optimal universal telecloning. It is shown that the quantum information via $1\rightarrow 2$ AEPCT procedure can be remotely concentrated back to a single qubit with a certain probability by utilizing (non-)maximally entangled $W$ states as quantum channels. Our protocols are the generalization of Wang’s scheme (Open J Microphys 3:18–21. doi:10.4236/ojm.2013.31004, 2013). And von Neumann measure and positive operator-valued measurement are performed in the maximal and non-maximal cases respectively. Relatively the former, the dimension of measurement space in the latter is greatly reduced. It makes the physical realization easier and suitable.     

Geometric discord and measurement-induced nonlocality for well known bound entangled states

We employ geometric discord and measurement induced nonlocality to quantify quantumness of some well-known bipartite bound entangled states, namely the two families of Horodecki’s ( $2\otimes 4, 3\otimes 3$ and $4\otimes 4$ dimensional) bound entangled states and that of Bennett et al.’s in $3\otimes 3$ dimension. In most of the cases our results are analytic and both the measures attain relatively small value. The amount of quantumness in the $4\otimes 4$ bound entangled state of Benatti et al. and the $2\otimes 8$ state having the same matrix representation (in computational basis) is same. Coincidently, the $2m\otimes 2m$ Werner and isotropic states also exhibit the same property, when seen as $2\otimes 2m^2$ dimensional states.     

Quantum teleportation through noisy channels with multi-qubit GHZ states

We investigate two-party quantum teleportation through noisy channels for multi-qubit Greenberger–Horne–Zeilinger (GHZ) states and find which state loses less quantum information in the process. The dynamics of states is described by the master equation with the noisy channels that lead to the quantum channels to be mixed states. We analytically solve the Lindblad equation for \(n\) -qubit GHZ states \(n\in \{4,5,6\}\) where Lindblad operators correspond to the Pauli matrices and describe the decoherence of states. Using the average fidelity, we show that 3GHZ state is more robust than \(n\) GHZ state under most noisy channels. However, \(n\) GHZ state preserves same quantum information with respect to Einstein–Podolsky–Rosen and 3GHZ states where the noise is in \(x\) direction in which the fidelity remains unchanged. We explicitly show that Jung et al.’s conjecture (Phys Rev A 78:012312, 2008), namely “average fidelity with same-axis noisy channels is in general larger than average fidelity with different-axes noisy channels,” is not valid for 3GHZ and 4GHZ states.     

Joint remote state preparation between multi-sender and multi-receiver

In this work, novel schemes for joint remote state preparation are presented, which involve N senders and 2 receivers as well as N senders and 3 receivers. The receivers can simultaneously reconstruct different qubit states containing the joint information from all senders. Compared with the protocols proposed by Su et al. (Int J Quantum Inf 10:1250006 (2012), the information of the prepared states in our schemes is distributed in a different way. Our protocols can be applied not only to states with real parameters but also ones with complex parameters. Moreover, the N-to-2 protocol is suitable for general qubit states besides equatorial states, and the receivers need not to perform any measurements and CNOT gates to reconstruct the states.     

Generation of NOON states via Raman transitions in a bimodal cavity

We propose a scheme for generation of NOON states via Raman transitions. In the scheme, a double $\varLambda $ -type three-level atom is trapped in a high-Q bimodal cavity which is initially in vacuum states. After a series of operations and suitable interaction time, we can obtain highly nonclassical entangled states of one atom and N photons. Then it can easily be converted to purely photonic NOON states by application of a single projective measurement on the atom. The successful probability and fidelity of the scheme are finally discussed.     

An optical gate for simultaneous fusion of four photonic W or Bell states

In order to create large-scale polarization entangled W states, there have been several proposals and some experimental demonstrations. An outstanding proposal is a simple setup which probabilistically fuses two W states of arbitrary sizes $n\ge 3$ and $m\ge 3$ , creating a W state of size $n+m-2$ (Ozdemir et al., in: New J Phys 13:103003, 2011). Using this setup as building blocks, we propose a new setup which can fuse four W states simultaneously. The proposed setup can fuse W states of size 2, i.e. Bell states, as well. We study the resource cost of our fusion process for two main scenarios, i.e. starting from sizes 2 and 3. We present some cost efficient cases, as compared to the previous work.     

Remote preparation of an arbitrary multi-qubit state via two-qubit entangled states

We propose a novel scheme for remote preparation of an arbitrary n-qubit state with the aid of an appropriate local \(2^n\times 2^n\) unitary operation and n maximally entangled two-qubit states. The analytical expression of local unitary operation, which is constructed in the form of iterative process, is presented for the preparation of n-qubit state in detail. We obtain the total successful probabilities of the scheme in the general and special cases, respectively. The feasibility of our scheme in preparing remotely multi-qubit states is explicitly demonstrated by theoretical studies and concrete examples, and our results show that the novel proposal could enlarge the applied range of remote state preparation.     

Entropic measure and hypergraph states

We investigate some properties of the entanglement of hypergraph states in purely hypergraph theoretical terms. We first introduce an approach for computing local entropic measure on qubit $t$ of a hypergraph state by using the Hamming weight of the so-called $t$ -adjacent subhypergraph. Then, we quantify and characterize the entanglement of hypergraph states in terms of local entropic measures obtained by using the above approach. Our results show that full-rank hypergraph states of more than two qubits can not be converted into any graph state under local unitary transformations.     

Multi-party quantum state sharing of an arbitrary multi-qubit state via \chi -type entangled states

By using the \(\chi \) -type entangled states, a novel scheme for multi-party quantum state sharing (MQSTS) of an arbitrary multi-qubit state is investigated. It is shown that the MQSTS scheme can be faithfully realized by performing appropriate Bell state measurements, Z basis measurements and local unitary operations, rather than multi-qubit entanglement or multi-particle joint measurements. Thus, our MQSTS scheme is more convenient in a practical application than some previous schemes. Furthermore, its intrinsic efficiency for qubits approaches 100 %, and the total efficiency really approaches the maximal value, which is higher than those of the previous MQSTS schemes. Finally, we analyze the security from the views of participant attack and outside attack in detail.     

Informational correlation between two parties of a quantum system: spin-1/2 chains

We introduce the informational correlation \(E^{AB}\) between two interacting quantum subsystems \(A\) and \(B\) of a quantum system as the number of arbitrary parameters \(\varphi _i\) of a unitary transformation \(U^A\) (locally performed on the subsystem \(A\) ) which may be detected in the subsystem \(B\) by the local measurements. This quantity indicates whether the state of the subsystem \(B\) may be effected by means of the unitary transformation applied to the subsystem \(A\) . Emphasize that \(E^{AB}\ne E^{BA}\) in general. The informational correlations in systems with tensor product initial states are studied in more details. In particular, it is shown that the informational correlation may be changed by the local unitary transformations of the subsystem \(B\) . However, there is some non-reducible part of \(E^{AB}(t)\) which may not be decreased by any unitary transformation of the subsystem \(B\) at a fixed time instant \(t\) . Two examples of the informational correlations between two parties of the four-node spin-1/2 chain with mixed initial states are studied. The long chains with a single initially excited spin (the pure initial state) are considered as well.     

Optimal multipartite entanglement concentration of electron-spin states based on charge detection and projection measurements

We propose an optimal entanglement concentration protocol (ECP) for nonlocal $N$ -electron systems in a partially entangled Greenberger–Horne–Zeilinger (GHZ) pure state, resorting to charge detection and the projection measurement on an additional electron. For each nonlocal $N$ -electron system in a partially entangled GHZ state, one party in quantum communication, say Alice first entangles it with an additional electron, and then, she projects the additional electron into an orthogonal basis for dividing the $N$ -electron systems into two groups. In the first group, the $N$ parties obtain a subset of $N$ -electron systems in a maximally entangled state directly. In the second group, they obtain some less-entangled $N$ -electron systems which are the resource for the entanglement concentration in the next round. By iterating the entanglement concentration process several times, the present ECP has the maximal success probability, the theoretical limit of an ECP as it just equals to the entanglement of the partially entangled state, far higher than others. Moreover, this ECP for an $N$ -electron GHZ-type state requires only one additional electron, not two or more, and it does not resort to a collective unitary evolution, far different from others, which may decrease the difficulty for its implementation in experiment. When it is used for an $N$ -electron W-type state, $N-1$ additional electrons are required only.     

Generation of atomic NOON states via adiabatic passage

We propose a scheme for generating atomic NOON states via adiabatic passage. In the scheme, a double \(\Lambda \) -type three-level atom is trapped in a bimodal cavity, and two sets of \(\Lambda \) -type three-level atoms are translated into and outside of two single-mode cavities, respectively. The three cavities connected by optical fibers are always in vacuum states. After a series of operations and suitable interaction time, we can obtain arbitrary large- \(n\) NOON states of two sets of \(\Lambda \) -type three-level atoms in distant cavities by performing a single projective measurement on the double \(\Lambda \) -type three-level atom. Our scheme is robust against the spontaneous emissions of atoms, the decays of fibers, and photon leakage of cavities, due to the adiabatic elimination of atomic excited states and the application of adiabatic passage.     

D-Separation and computation of probability distributions in Bayesian networks

Consider a family ${(X_i)_{i \in I}}$ of random variables endowed with the structure of a Bayesian network, and a subset S of I. This paper examines the problem of computing the probability distribution of the subfamily ${(X_{a})_{a \in S}}$ (respectively the probability distribution of ${ (X_{b})_{b \in {\bar{S}}}}$ , where ${{\bar{S}} = I - S}$ , conditional on ${(X_{a})_{a \in S}}$ ). This paper presents some theoretical results that makes it possible to compute joint and conditional probabilities over a subset of variables by computing over separate components. In other words, it is demonstrated that it is possible to decompose this task into several parallel computations, each related to a subset of S (respectively of ${{\bar{S}}}$ ); these partial results are then put together as a final product. In computing the probability distribution over ${(X_a)_{a \in S}}$ , this procedure results in the production of a structure of level two Bayesian network structure for S.