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

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

Published Feb 4, 2016• 0 citations
OpenAlex

Abstract

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

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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-12\frac{1}{2}21​ 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 mmm-particle cluster states for measurement based quantum computing, such that the resource states can have entanglement entropies approaching zero as O(1/poly(m))\mathcal{O}(1 / poly(m))O(1/poly(m)).
In this paper we present a protocol for the implementation of a positive-operator-valued measure (POVM) on massive fermionic qubits. We present methods for implementing nondispersive qubit transport, spin rotations, and spin polarizing beam-splitter operations. Our scheme attains linear opticslike control of the spatial extent of the qubits by considering ground-state electrons trapped in the minima of surface acoustic waves in semiconductor heterostructures. Furthermore, we numerically simulate a high-fidelity POVM that carries out Procrustean entanglement distillation in the framework of our scheme, using experimentally realistic potentials. Our protocol can be applied not only to pure ensembles with particle pairs of known identical entanglement, but also to realistic ensembles of particle pairs with a distribution of entanglement entropies. This paper provides an experimentally realizable design for future quantum technologies.
Multi-particle cluster states play a significant role in quantum information processing. However, due to the inevitable interaction with the environment in the transmission process, the fidelity of entanglement decreases. To distill the perfect cluster states, we present two schemes for arbitrary six-particle cluster states. POVM local unitary operators that are obtained by solving the equation according to the properties of cluster states are used in the first protocol. The second protocol is based on cross-Kerr nonlinearity which is exploited to check parity between original qubit with ancillary single qubit and it can achieve a higher probability of success through iteration. Furthermore, we can generalize the first method to concentrate entanglement on even number of particles. Our protocol will be useful in practical applications.
We devise and examine two procrustean entanglement concentration schemes using Quantum Non- Demolition (QND) interaction Hamiltonians in the continuous variable regime, applicable for light, for atomic ensembles or in a hybrid setting. We thus expand the standard entanglement distillation toolbox to the use of a much more general, versatile and experimentally feasible interaction class. The first protocol uses Gaussian ancillary modes and a non-Gaussian post-measurement, the second a non-Gaussian ancillary mode and a Gaussian post-measurement. We explicitly calculate the density matrix elements of the non-Gaussian mixed states resulting from these protocols using an elegant Wigner-function based method in a numerically efficient manner. We then quantify the entanglement increase calculating the Logarithmic Negativity of the output state and discuss and compare the performance of the protocols.
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.
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 1.01.01.0 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.
High-fidelity entanglement shared between distant quantum systems is an essential resource for quantum communication and computation. Entanglement distillation addresses this need by converting multiple noisy Bell pairs into fewer higher-fidelity pairs, using only local quantum operations and classical communication. However, this approach typically requires a substantial overhead in the number of qubits. To bypass this hurdle, we propose to leverage the high-dimensional Hilbert space of a single pair of bosonic systems to store a large amount of entanglement, replacing the need for multi-qubit systems. To distill entanglement in such a setup, we devise a new entanglement distillation protocol, tailored for bosonic systems. The protocol converts a highly-entangled noisy state between two bosonic systems into a lower-dimensional but high-fidelity entangled state, using only local bosonic operations. We show that our protocol significantly enhances the fidelity of the entangled state in the presence of naturally occurring loss and dephasing errors. Compared to methods relying on multiple Bell pairs, our scheme offers a more hardware-efficient strategy, providing a practical route toward the realization of entanglement distillation.