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Register a new userUniversal and optimal error thresholds for measurement-based entanglement purification
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We investigate measurement-based entanglement purification protocols (EPP) in the presence of local noise and imperfections. We derive a universal, protocol-independent threshold for the required quality of the local resource states, where we show that local noise per particle of up to 24% is tolerable. This corresponds to an increase of the noise threshold by almost an order of magnitude, based on the joint measurement-based implementation of sequential rounds of few-particle EPP. We generalize our results to multipartite EPP, where we encounter similarly high error thresholds.
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We give a review on entanglement purification for bipartite and multipartite quantum states, with the main focus on theoretical work carried out by our group in the last couple of years. We discuss entanglement purification in the context of quantum communication, where we emphasize its close relation to quantum error correction. Various bipartite and multipartite entanglement purification protocols are discussed, and their performance under idealized and realistic conditions is studied. Several applications of entanglement purification in quantum communication and computation are presented, which highlights the fact that entanglement purification is a fundamental tool in quantum information processing.
We investigate entanglement purification protocols based on hashing, where a large number of noisy entangled pairs is jointly processed to obtain a reduced number of perfect, noiseless copies. While hashing and breeding protocols are the only purification protocols that asymptotically obtain a nonzero yield, they are not applicable in a realistic scenario if local gates and measurements are imperfect. We show that such problems can be overcome by a compact measurement-based implementation, yielding entanglement purification schemes with nonzero yield that are applicable also in noisy scenarios, with tolerable noise per particle of several percent. We also generalize these findings to multiparty purification protocols for arbitrary graph states.
To achieve the practical applications of near-term noisy quantum devices, low-cost ways to mitigate the noise damages in the devices are essential. In many applications, the noiseless state we want to prepare is often a pure state, which has recently inspired a range of purification-based quantum error mitigation proposals. The existing proposals either are limited to the suppressions of only the leading-order state preparation errors, or require a large number of long-range gates that might be challenging to implement depending on the qubit architecture. This article will provide an overview of the different purification-based quantum error mitigation schemes and propose a resource-efficient scheme that can correct state preparation errors up to any order while requiring only half of the qubits and less than half of the long-range gates compared to before.
With the advance of quantum information technology, the question of how to most efficiently test quantum circuits is becoming of increasing relevance. Here we introduce the statistics of lengths of measurement sequences that allows one to certify entanglement across a given bi-partition of a multi-qubit system over the possible sequence of measurements of random unknown states, and identify the best measurement strategies in the sense of the (on average) shortest measurement sequence of (multi-qubit) Pauli measurements. The approach is based on the algorithm of truncated moment sequences that allows one to deal naturally with incomplete information, i.e. information that does not fully specify the quantum state. We find that the set of measurements corresponding to diagonal matrix elements of the moment matrix of the state are particularly efficient. For symmetric states their number grows only like the third power of the number $N$ of qubits. Their efficiency grows rapidly with $N$, leaving already for $N=4$ less than a fraction $10^{-6}$ of randomly chosen entangled states undetected.
Fernando Galve emph{et al.} $[Phys. Rev. Lett. textbf{110}, 010501 (2013)]$ introduced discording power for a two-qubit unitary gate to evaluate its capability to produce quantum discord, and found that a $pi/8$ gate has maximal discording power. This work analyzes the entangling power of a two-qubit unitary gate, which reflects its ability to generate quantum entanglement in another way. Based on the renowned Cartan decomposition of two-qubit unitary gates, we show that the magic power of the $pi/8$ gate produces maximal entanglement for a general value of purities for two-qubit states.
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