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arXiv:1208.2553 · Physical Review A

Purification to locally maximally entangleable states

T. Carle, Barbara Kraus, Wolfgang Dür, Julio I. de Vicente

Published Jan 25, 2013• 18 citations
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Abstract

Locally maximally entangleable states (LMESs) constitute a large set of multipartite states, containing, for instance, all stabilizer states. LMESs are uniquely characterized by $({2}^{n}\ensuremath{-}1)$ phases, where $n$ denotes the number of qubits. We consider here those LMESs whose phases are either 0 or $\ensuremath{\pi}$ and present a multipartite entanglement purification protocol for arbitrary such states. In contrast to all previously known recurrence protocols, this protocol uses a different ingredient, which is required due to the quantum correlations contained in the various LMESs. We compare this scheme to previously known entanglement purification protocols and show that the direct purification performs better than previously known protocols.

DOI
10.1103/physreva.87.012328

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Locally maximally entangleable states (LMESs) constitute a large set of multipartite states, containing, for instance, all stabilizer states. LMESs are uniquely characterized by (2n\ensuremath−1)({2}^{n}\ensuremath{-}1)(2n\ensuremath−1) phases, where nnn denotes the number of qubits. We consider here those LMESs whose phases are either 0 or \ensuremathπ\ensuremath{\pi}\ensuremathπ and present a multipartite entanglement purification protocol for arbitrary such states. In contrast to all previously known recurrence protocols, this protocol uses a different ingredient, which is required due to the quantum correlations contained in the various LMESs. We compare this scheme to previously known entanglement purification protocols and show that the direct purification performs better than previously known protocols.
Multipartite entanglement purification is revisited by using the Local operations and classical communications(LOCCs). We demonstrate our idea by considering the tripartite case, i.e. the purification of tripartite entanglement. We express the general tripartite entangled states in a special representation of total spin operators J1232J_{123}^{2}J1232​ and % J_{12}^{2} of tripartite system with eigenvalues 15/4 and 2 respectively. This basis is a \textit{genuine basis} because it consists of of all the genuine entangled states of tripartite system. Our protocol is a recurrence one, and only two copies of the initial mixed tripartite entangled states are needed in each round. It is shown that if the initial fidelity is larger than a threshold 0.4, the purification process will succeed.The yield of the current protocol is higher than the previous multipartite entanglement purification protocols. As a by-product, we can get a bipartite pure Bell state when the purification protocol fails for W state. Our protocol also shows that there may be some special kind of tripartite entanglement which belongs to neither W-type entanglement nor GHZ-type entanglement.
Entanglement purification protocols are fundamental primitives in quantum communication, enabling the distillation of high-quality entanglement using only local operations and classical communication. For large multipartite states, however, existing purification schemes typically require substantial resources and become progressively inefficient as system size increases. We introduce a new type of multipartite entanglement purification, Localized Entanglement Purification (LEP), a family of protocols that purify entanglement at the level of network regions rather than globally. By exploiting spatial noise asymmetries, LEP reduces resource consumption and enables scalable purification strategies for larger quantum systems.
We introduce entanglement purification protocols for ddd-level systems (qudits) with improved efficiency as compared to previous protocols. While we focus on protocols for bipartite systems, we also propose generalizations to multipartite qudit systems. The schemes we introduce include recurrence protocols that operate on two copies, as well as hashing protocols that operate on large ensembles. We analyze properties of the protocols with respect to minimal required fidelity and yield, and study their performance in the presence of noise and imperfections. We determine error thresholds and study the dependence on local dimension. We find that our schemes do not only outperform previous approaches, but also show an improved robustness and better efficiency with increasing dimension. While error thresholds for different system sizes are not directly comparable, our results nevertheless suggest that quantum information processing using qudits, in particular for long-distance quantum communication, may offer an advantage over approaches based on qubit systems.
Entanglement purification allows the creation of qubit pairs of arbitrarily high fidelity with respect to a maximally entangled state, starting from a larger number of low-fidelity pairs. Purification requires quantum memory, a role for which electron spins are well suited. However, using existing recurrence protocols involving symmetric local two-qubit operations for spin qubits turns out to be rather unpractical. We present an efficient purification protocol requiring only a single pulsed Heisenberg- or XY-type exchange interaction between two qubit pairs. In contrast to known protocols, we allow for asymmetric bilateral two-qubit operations where the two communication parties operate differently on their qubits. In the optimal version of our protocol, the local two-qubit interactions in the case of Heisenberg exchange correspond to the swap\sqrt{swap}swap​ gate and its inverse.
We present multiparty entanglement purification protocols that are capable of purifying arbitrary graph states directly. We develop recurrence and breeding protocols and compare our methods with strategies based on bipartite entanglement purification in static and communication scenarios. We find that direct multiparty purification is of advantage with respect to achievable yields and minimal required fidelity in static scenarios, and with respect to obtainable fidelity in the case of noisy operations in both scenarios.
Abstract Entanglement between distant quantum systems is a critical resource for implementing quantum communication. This property is affected by external agents and can be restored by employing efficient entanglement purification protocols. In this work, we propose an entanglement purification protocol based on two entangling two-qubit operations that replace the usual controlled-NOT (CNOT) gate. These operations arise from a generalised quantum measurement and can be understood as measurement operators in a positive operator-valued measure. Furthermore, two variants of the core protocol are introduced and their performances are studied in terms of the overall success probability of reaching a Bell state and the number of purifiable states. Based on rank-two states, we can obtain analytical expressions for the success probability that we extend and refine using numerical calculations to the case of maximally entangled states. We also consider more general rank-three states to show that our procedure is in general more convenient compared to purification protocols based on Bell diagonal states. Finally, we test the protocols using initial random states. In all cases, we find a better performance and a larger amount of purifiable states using our schemes compared to the CNOT-based protocol.