Arbitrary Three-qubit State Research Articles

Asymmetric Controlled Bidirectional Remote Preparation of Single- and Three-Qubit Equatorial State in Noisy Environment

We present an asymmetric controlled bidirectional remote preparation scheme under the control of Charlie, where Alice transmits an arbitrary single-qubit equatorial state to Bob and Bob transmits an arbitrary three-qubit equatorial state to Alice. First, the quantum channel is constructed by using <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Hadamard</i> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H}$ </tex-math></inline-formula> ) and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CNOT</i> operations. Second, we consider our scheme in the noiseless environment and construct the appropriate measurement bases. In addition, the participants can recover the prepared states through implementing the corresponding recovery operations determinately. Third, we discuss our scheme in five types of noisy environments (amplitude-damping, phase-damping, bit-flip, phase-flip, and depolarizing noisy environment). The fidelities of the output states are calculated, which depend on the coefficients of the prepared states and the decoherence rates. Finally, some discussions and conclusions are given. Compared with previous schemes, our scheme does not need additional operations or auxiliary qubits. So it is slightly more efficient.

Experimentally identifying the entanglement class of pure tripartite states

We use concurrence as an entanglement measure and experimentally demonstrate the entanglement classification of arbitrary three-qubit pure states on a nuclear magnetic resonance (NMR) quantum information processor. Computing the concurrence experimentally under three different bipartitions, for an arbitrary three-qubit pure state, reveals the entanglement class of the state. The experiment involves measuring the expectation values of Pauli operators. This was achieved by mapping the desired expectation values onto the local $z$ magnetization of a single qubit. We tested the entanglement classification protocol on twenty seven different generic states and successfully detected their entanglement class. Full quantum state tomography was performed to construct experimental tomographs of each state and negativity was calculated from them, to validate the experimental results.

Experimental classification of entanglement in arbitrary three-qubit pure states on an NMR quantum information processor

We undertake experimental detection of the entanglement present in arbitrary three-qubit pure quantum states on an NMR quantum information processor. Measurements of only four observables suffice to experimentally differentiate between the six classes of states which are inequivalent under stochastic local operation and classical communication (SLOCC). The experimental realization is achieved by mapping the desired observables onto Pauli $z$-operators of a single qubit, which is directly amenable to measurement. The detection scheme is applied to known entangled states as well as to states randomly generated using a generic scheme that can construct all possible three-qubit states. The results are substantiated via direct full quantum state tomography as well as via negativity calculations and the comparison suggests that the protocol is indeed successful in detecting tripartite entanglement without requiring any {\it a priori} information about the states.

Controlled bidirectional remote preparation of three-qubit state

We present a novel scheme for controlled bidirectional remote state preparation by using thirteen-qubit entangled state as the quantum channel, where both Alice and Bob transfer an arbitrary three-qubit state to each other simultaneously via the control of Charlie. Firstly, in the ideal environment, we consider our scheme in two cases that the coefficients of prepared state are real and complex, respectively. The corresponding measurement bases are devised. Secondly, we discuss our scheme in four types of noisy environment (bit-flip, phase-flip, amplitude-damping and phase-damping noisy environments) and calculate the corresponding fidelities of the output state. Finally, the efficiency of our scheme is calculated and some discussions are given.

Deterministic remote preparation via the Brown state

We propose two deterministic remote state preparation (DRSP) schemes by using the Brown state as the entangled channel. Firstly, the remote preparation of an arbitrary two-qubit state is considered. It is worth mentioning that the construction of measurement bases plays a key role in our scheme. Then, the remote preparation of an arbitrary three-qubit state is investigated. The proposed schemes can be extended to controlled remote state preparation (CRSP) with unit success probabilities. At variance with the existing CRSP schemes via the Brown state, the derived schemes have no restriction on the coefficients, while the success probabilities can reach 100%. It means the success probabilities are greatly improved. Moreover, we pay attention to the DRSP in noisy environments under two important decoherence models, the amplitude-damping noise and phase-damping noise.

Universal Three-Qubit Entanglement Generation Based on Linear Optical Elements and Quantum Non-Demolition Detectors

Recently, entanglement plays an important role in quantum information science. Here we propose an efficient and applicable method which transforms arbitrary three-qubit unknown state to a maximally entangled Greenberger-Horne-Zeilinger state, and the proposed method could be further generalized to multi-qubit case. The proposed setup exploits only linear optical elements and quantum non-demolition detectors using cross-Kerr media. As the quantum non-demolition detection could reveal us the output state of the photons without destroying them. This property may make our proposed setup flexible and can be widely used in current quantum information science and technology.

Quantum Information Splitting of Arbitrary Three-qubit State by Using Five-qubit Cluster state and GHZ-state

In this paper, a new scheme of quantum information splitting (8QIS) by using five-qubit state and GHZ-state as quantum channel is proposed. The sender Alice performs Bell-state measurements (BSMs) on her qubit-pairs respectively,then tells her measurement result to the receivers Bob. If Bob wants to reconstruct the original states, he must cooperates with the controller Charlie, that Charlie performs two single particle measurement on his qubits and tells Bob the results. According to Alice’s and Bob’s results, Bob can reconstruct the initial state by applying appropriate unitary operation.

Pure-state tomography with the expectation value of Pauli operators

We examine the problem of finding the minimum number of Pauli measurements needed to uniquely determine an arbitrary $n$-qubit pure state among all quantum states. We show that only $11$ Pauli measurements are needed to determine an arbitrary two-qubit pure state compared to the full quantum state tomography with $16$ measurements, and only $31$ Pauli measurements are needed to determine an arbitrary three-qubit pure state compared to the full quantum state tomography with $64$ measurements. We demonstrate that our protocol is robust under depolarizing error with simulated random pure states. We experimentally test the protocol on two- and three-qubit systems with nuclear magnetic resonance techniques. We show that the pure state tomography protocol saves us a number of measurements without considerable loss of fidelity. We compare our protocol with same-size sets of randomly selected Pauli operators and find that our selected set of Pauli measurements significantly outperforms those random sampling sets. As a direct application, our scheme can also be used to reduce the number of settings needed for pure-state tomography in quantum optical systems.

Controlled Remote Preparation Via the Brown State with no Restriction

Two controlled remote state preparation protocols via the Brown state as the entangled channel are proposed. One prepares an arbitrary two-qubit state, and the other prepares an arbitrary three-qubit state. It is worth mentioning that Hurwitz matrix equation plays a key role in the construction of measurement basis. Comparing with the previous protocols, the novel schemes have no restriction on the coefficients of the prepared state while keeping the same success probability 50 %. It means that the application of the proposed schemes are more extensive in practice. Moreover, we discuss the special complex coefficient ensembles with unit success probability.

Linear monogamy of entanglement in three-qubit systems.

For any three-qubit quantum systems ABC, Oliveira et al. numerically found that both the concurrence and the entanglement of formation (EoF) obey the linear monogamy relations in pure states. They also conjectured that the linear monogamy relations can be saturated when the focus qubit A is maximally entangled with the joint qubits BC. In this work, we prove analytically that both the concurrence and EoF obey linear monogamy relations in an arbitrary three-qubit state. Furthermore, we verify that all three-qubit pure states are maximally entangled in the bipartition A|BC when they saturate the linear monogamy relations. We also study the distribution of the concurrence and EoF. More specifically, when the amount of entanglement between A and B equals to that of A and C, we show that the sum of EoF itself saturates the linear monogamy relation, while the sum of the squared EoF is minimum. Different from EoF, the concurrence and the squared concurrence both saturate the linear monogamy relations when the entanglement between A and B equals to that of A and C.

Splitting an Arbitrary Three-Qubit State by using an Eight-Qubit Entangled State

We demonstrate that an eight-qubit entangled state can be used to realize the deterministic quantum information splitting of an arbitrary three-qubit state by performing only the Bell-state measurements and single-qubit measurements.

Quantum State Sharing of an Arbitrary Three-Qubit State by Using a Seven-Qubit Entangled State

In this paper, we demonstrate that a seven-qubit entangled state can be used to realize the deterministic quantum state sharing (QSTS) of an arbitrary three-qubit state by performing only the Bell-state measurements and single-qubit measurement.

Quantum Information Splitting of Arbitrary Three-Qubit State by Using Seven-Qubit Entangled State

In this paper, we propose a scheme of quantum information splitting arbitrary three-qubit state by using seven-qubit entangled as quantum channel. The sender Alice first performs Bell-state measurements (BSMs) on her qubits pairs respectively and tells her measurement outcome to authorizers Bob to reconstruct the original state, then Charlie should carries out single-qubit measurement (SQM) on his qubits. According to the results from Alice and Charlie, Bob can reconstruct the original state by applying an appropriate unitary operation. After analyzing, the method achieved the desired effect of quantum information splitting (QIS). We also realize the QIS of arbitrary three-qubit state in cavity quantum electrodynamics (QED).

Quantum Information Splitting of Arbitrary Three-Qubit State by Using Four-Qubit Cluster State and GHZ-State

A scheme is proposed for quantum information splitting of arbitrary three-qubit state by using four-qubit cluster state and GHZ state as quantum channel. In the scenario, assume that the sender is called Alice, the receiver is called Bob and the controller id called Charlie. First of all, Alice performs Bell-state measurements on her qubit paris (A, 1), (B, 3), (C, 5), respectively. And then tells Charlie and Bob measure results via a classical channel. It is impossible for Bob to reconstruct the original state with local operation; if Charlie allows Bob to reconstruct the original states, he needs to perform a single particle measurement on his particle and tells Bob the results. According to the information from Alice and Charlie, Bob can reconstruct the original state with an appropriate unitary operation of his qubits 2, 4, 6.We also consider the problem of security attacks .This protocol is considered to be secure.

Quantum Teleportation of an Arbitrary Three-Qubit State Using GHZ-Like States

A new application of the GHZ-like state is investigated for teleportation of an arbitrary three-qubit state. We demonstrate that three sets of GHZ-like states can be used to realize the perfect teleportation of an arbitrary three-qubit state by performing only the three-qubit von-Neumann projective measurements.

Quantum Information Splitting of an Arbitrary Three-Qubit State Via a Seven-Qubit Maximally Entangled State

Recently Zha et al. (J. Phys. A: Math. Theor. 45:255–302 2012) have proposed a seven-particle maximally entangled state. In this paperwe propose a schemes for splitting three-qubit states by using seven-particle maximally entangled state as the quantum channel. After the sender performs Bell-basis measurements on her particles, and the cooperators operate single-particle measurements on their particles, the state receiver can reconstruct the original state of the sender by applying the appropriate unitary operation.

Controlled Teleportation of an Arbitrary Three-Qubit State by Using Two Four-Qubit Entangled States

We demonstrate that two four-qubit entangled states can be used to realize the deterministic controlled teleportation of an arbitrary three-qubit state by performing only the Bell-state measurements.

Splitting an Arbitrary Three-Qubit State by Using Seven-Qubit Composite GHZ-Bell State

We present a scheme for quantum information splitting of an arbitrary three-qubit state by using a seven-qubit composite GHZ-Bell state as quantum channel. We illustrate the procedure in the ion-trap systems, but the scheme can also be realized in other systems.

Quantum Information Splitting of an Arbitrary Three-Qubit State Using a Seven-Qubit Entangled State

We propose a seven-qubit entangled channel that can be used to realize the deterministic quantum information splitting of an arbitrary three-qubit state. We describe the construction of this channel and explicitly demonstrate how the protocol works. In this scheme, three Bell state measurements and a single-qubit measurement are indispensable.

Joint Remote Preparation of an Arbitrary Three-Qubit State with Mixed Resources

Our purpose in this paper is, by constructing some useful measurement bases, to show that two senders can jointly prepare an arbitrary three-qubit state to a remote receiver via some shared mixed resources. Then, the success probability can be improved by using the permutation group to classify the preparation state. Furthermore, this scheme can be extended to multiple senders, or prepare four-qubit |χ〉 and five-qubit Brown state.