In this work, we study how to distill two typical multipartite entangled noisy states, the amplitude-damped W state and the amplitude-damped Greenberger-Horne-Zeilinger state. Unlike the currently existing multipartite entanglement purification schemes, our scheme is a single-copy-based scheme, i.e., only one noisy state is needed in each distillation round, and the complicated multilateral controlled-not (cnot) operations are replaced by measurements of local positive-operator-valued measures (POVMs). The results show that local POVM measurements on one copy of the noisy state can project the initial state onto a new state with higher entanglement and nonlocality. In this scheme, although the final state can violate the multipartite Bell inequality, the corresponding initial noisy state does not violate it, which means that this distillation scheme can reveal the hidden genuine multipartite nonlocality of these initial states. For the case of the amplitude-damped W state, if the POVM parameters are appropriately chosen, the fidelity of the output state can approach $1.0$ for all the initial states with fidelity bigger than zero. So this single-copy-based multipartite entanglement distillation scheme has a wide range of distillable fidelities, and it is much simpler than the two-copy- or multiple-copy-based schemes. Furthermore, if the POVM measurement is carried out only on some member qubits rather than all of them, the distillation scheme can succeed too, which will greatly decrease the implementation complexity of the scheme. So this multipartite entanglement distillation scheme may be implementable in some physical system.In this work, we study how to distill two typical multipartite entangled noisy states, the amplitude-damped W state and the amplitude-damped Greenberger-Horne-Zeilinger state. Unlike the currently existing multipartite entanglement purification schemes, our scheme is a single-copy-based scheme, i.e., only one noisy state is needed in each distillation round, and the complicated multilateral controlled-not (cnot) operations are replaced by measurements of local positive-operator-valued measures (POVMs). The results show that local POVM measurements on one copy of the noisy state can project the initial state onto a new state with higher entanglement and nonlocality. In this scheme, although the final state can violate the multipartite Bell inequality, the corresponding initial noisy state does not violate it, which means that this distillation scheme can reveal the hidden genuine multipartite nonlocality of these initial states. For the case of the amplitude-damped W state, if the POVM parameters are appropriately chosen, the fidelity of the output state can approach $1.0$ for all the initial states with fidelity bigger than zero. So this single-copy-based multipartite entanglement distillation scheme has a wide range of distillable fidelities, and it is much simpler than the two-copy- or multiple-copy-based schemes. Furthermore, if the POVM measurement is carried out only on some member qubits rather than all of them, the distillation scheme can succeed too, which will greatly decrease the implementation complexity of the scheme. So this multipartite entanglement distillation scheme may be implementable in some physical system.

Physical Review AJun 18, 201420 citations

Distillation of lossy hyperentangled states

Danyang Chen, Zhi Lin, Ming Yang +3 more

Hyperentanglement has a higher information density than conventional single-degree-of-freedom entanglement, which has attracted much attention due to its fascinating applications in quantum communication. However, since the inevitable interactions between quantum entangled systems and the environment will drive hyperentangled systems into less hyperentangled states or even mixed hyperentangled states, the efficiency and security of quantum communication will be greatly depressed. The currently existing distillation protocols are not universal, i.e., they only work for the lossy hyperentangled states in specific systems. In this paper, based on local positive-operator-valued measures (POVMs), we present a distillation protocol for lossy hyperentangled photonic Bell and Greenberger-Horne-Zeilinger (GHZ) states. The intrinsic property of our protocol is twofold, i.e., the POVM nature of the protocol guarantees that the protocol is a universal one, and the distillation operation on only one of the two degrees of freedom (DOFs) can enhance the fidelity of the system in both DOFs. Furthermore, in the implementation level, our hyperentanglement distillation protocol (HEDP) has other two merits: no auxiliary local entanglement resources and sophisticated single-photon detectors are required, and only one copy of the lossy state will be operated in each distillation round, which show that our HEDPs are relatively simple and feasible.Hyperentanglement has a higher information density than conventional single-degree-of-freedom entanglement, which has attracted much attention due to its fascinating applications in quantum communication. However, since the inevitable interactions between quantum entangled systems and the environment will drive hyperentangled systems into less hyperentangled states or even mixed hyperentangled states, the efficiency and security of quantum communication will be greatly depressed. The currently existing distillation protocols are not universal, i.e., they only work for the lossy hyperentangled states in specific systems. In this paper, based on local positive-operator-valued measures (POVMs), we present a distillation protocol for lossy hyperentangled photonic Bell and Greenberger-Horne-Zeilinger (GHZ) states. The intrinsic property of our protocol is twofold, i.e., the POVM nature of the protocol guarantees that the protocol is a universal one, and the distillation operation on only one of the two degrees of freedom (DOFs) can enhance the fidelity of the system in both DOFs. Furthermore, in the implementation level, our hyperentanglement distillation protocol (HEDP) has other two merits: no auxiliary local entanglement resources and sophisticated single-photon detectors are required, and only one copy of the lossy state will be operated in each distillation round, which show that our HEDPs are relatively simple and feasible.

Physical Review AAug 28, 20207 citations

Atomic Models

WORLD SCIENTIFIC eBooksAug 1, 19960 citations

POVMs and hidden variables

Allen Stairs

Physics Letters AJan 24, 20072 citations

A local non-iterative method for the implementation of Procrustean entanglement distillation

David R. M. Arvidsson-Shukur, E. T. Owen, C. H. W. Barnes

We present a local non-iterative method for the implementation of Procrustean entanglement distillation on a pair of entangled qubits using a positive-operator-valued measure (POVM). We show that this POVM can be applied equally to massless and massive qubits in hybrid quantum systems. For massless particles we consider single photons, for which the POVM can be implemented using standard linear optics components. For massive particles, we consider spin- $\frac{1}{2}$ particles. Numerical solutions to the time-dependent Schr\odinger equation show how the POVM can be applied to these qubits using gaussian wavepackets. Our non-iterative method can be applied, not only to pure ensembles with particle pairs of known identical entanglement, but also to ensembles of particle pairs with a distribution of different entanglement entropies. The outlined protocol eases the requirement for the creation of $m$ -particle cluster states for measurement based quantum computing, such that the resource states can have entanglement entropies approaching zero as $\mathcal{O}(1 / poly(m))$ .We present a local non-iterative method for the implementation of Procrustean entanglement distillation on a pair of entangled qubits using a positive-operator-valued measure (POVM). We show that this POVM can be applied equally to massless and massive qubits in hybrid quantum systems. For massless particles we consider single photons, for which the POVM can be implemented using standard linear optics components. For massive particles, we consider spin-$\frac{1}{2}$ particles. Numerical solutions to the time-dependent Schr\odinger equation show how the POVM can be applied to these qubits using gaussian wavepackets. Our non-iterative method can be applied, not only to pure ensembles with particle pairs of known identical entanglement, but also to ensembles of particle pairs with a distribution of different entanglement entropies. The outlined protocol eases the requirement for the creation of $m$-particle cluster states for measurement based quantum computing, such that the resource states can have entanglement entropies approaching zero as $\mathcal{O}(1 / poly(m))$.

Feb 4, 20160 citations

1.0

for all the initial states with fidelity bigger than zero. So this single-copy-based multipartite entanglement distillation scheme has a wide range of distillable fidelities, and it is much simpler than the two-copy- or multiple-copy-based schemes. Furthermore, if the POVM measurement is carried out only on some member qubits rather than all of them, the distillation scheme can succeed too, which will greatly decrease the implementation complexity of the scheme. So this multipartite entanglement distillation scheme may be implementable in some physical system.

\frac{1}{2}

particles. Numerical solutions to the time-dependent Schr\odinger equation show how the POVM can be applied to these qubits using gaussian wavepackets. Our non-iterative method can be applied, not only to pure ensembles with particle pairs of known identical entanglement, but also to ensembles of particle pairs with a distribution of different entanglement entropies. The outlined protocol eases the requirement for the creation of

m

-particle cluster states for measurement based quantum computing, such that the resource states can have entanglement entropies approaching zero as

\mathcal{O}(1 / poly(m))