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1. Optimal function estimation with photonic quantum sensor networks

   https://doi.org/10.1103/PhysRevResearch.6.013246  

   Bringewatt, Jacob; Ehrenberg, Adam; Goel, Tarushii; Gorshkov, Alexey V (March 2024, Physical Review Research)

   The problem of optimally measuring an analytic function of unknown local parameters each linearly coupled to a qubit sensor is well understood, with applications ranging from field interpolation to noise characterization. Here we resolve a number of open questions that arise when extending this framework to Mach-Zehnder interferometers and quadrature displacement sensing. In particular, we derive lower bounds on the achievable mean square error in estimating a linear function of either local phase shifts or quadrature displacements. In the case of local phase shifts, these results prove, and somewhat generalize, a conjecture by Proctor []. For quadrature displacements, we extend proofs of lower bounds to the case of arbitrary linear functions. We provide optimal protocols achieving these bounds up to small (multiplicative) constants and describe an algebraic approach to deriving new optimal protocols, possibly subject to additional constraints. Using this approach, we prove necessary conditions for the amount of entanglement needed for any optimal protocol for both local phase and displacement sensing. Published by the American Physical Society2024 

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2. On the Capacity Region of a Quantum Switch with Entanglement Purification

   https://doi.org/10.1109/INFOCOM53939.2023.10229003  

   Panigrahy, Nitish K; Vasantam, Thirupathaiah; Towsley, Don; Tassiulas, Leandros (May 2023, IEEE)

   Quantum switches are envisioned to be an integral component of future entanglement distribution networks. They can provide high quality entanglement distribution service to end-users by performing quantum operations such as entanglement swapping and entanglement purification. In this work, we characterize the capacity region of such a quantum switch under noisy channel transmissions and imperfect quantum operations. We express the capacity region as a function of the channel and network parameters (link and entanglement swap success probability), entanglement purification yield and application level parameters (target fidelity threshold). In particular, we provide necessary conditions to verify if a set of request rates belong to the capacity region of the switch. We use these conditions to find the maximum achievable end-to-end user entanglement generation throughput by solving a set of linear optimization problems. We develop a max-weight scheduling policy and prove that the policy stabilizes the switch for all feasible request arrival rates. As we develop scheduling policies, we also generate new results for computing the conditional yield distribution of different classes of purification protocols. The conclusions obtained in this work can yield useful guidelines for subsequent quantum switch designs. 

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3. The Round Complexity of Local Operations and Classical Communication (LOCC) in Random-Party Entanglement Distillation

   https://doi.org/10.22331/q-2023-09-07-1104  

   Liu, Guangkuo; George, Ian; Chitambar, Eric (September 2023, Quantum)

   A powerful operational paradigm for distributed quantum information processing involves manipulating pre-shared entanglement by local operations and classical communication (LOCC). The LOCC round complexity of a given task describes how many rounds of classical communication are needed to complete the task. Despite some results separating one-round versus two-round protocols, very little is known about higher round complexities. In this paper, we revisit the task of one-shot random-party entanglement distillation as a way to highlight some interesting features of LOCC round complexity. We first show that for random-party distillation in three qubits, the number of communication rounds needed in an optimal protocol depends on the entanglement measure used; for the same fixed state some entanglement measures need only two rounds to maximize whereas others need an unbounded number of rounds. In doing so, we construct a family of LOCC instruments that require an unbounded number of rounds to implement. We then prove explicit tight lower bounds on the LOCC round number as a function of distillation success probability. Our calculations show that the original W-state random distillation protocol by Fortescue and Lo is essentially optimal in terms of round complexity. 

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4. Churn-tolerant Leader Election Protocols

   Jiangran Wang, Indranil Gupta (July 2023, Proceedings 43rd IEEE International Conference on Distributed Computing Systems)

   Classical leader election protocols typically assume complete and correct knowledge of underlying membership lists at all participating nodes. Yet many edge and IoT settings are dynamic, with nodes joining, leaving, and failing continuously—a phenomenon called churn. This implies that in any membership protocol, a given node’s membership list may have entries that are missing (e.g., false positive detections, or newly joined nodes whose information has not spread yet) or stale (e.g., failed nodes that are undetected)—these would render classical election protocols incorrect. We present a family of four leader election protocols that are churn-tolerant (or c-tolerant). The key ideas are to: i) involve the minimum number of nodes necessary to achieve safety; ii) use optimism so that decisions are made faster when churn is low; iii) incorporate a preference for electing healthier nodes as leaders. We prove the correctness and safety of our c-tolerant protocols and show their message complexity is optimal. We present experimental results from both a trace- driven simulation as well as our implementation atop Raspberry Pi devices, including a comparison against Zookeeper. 

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5. Distributed quantum sensing with a mode-entangled network of spin-squeezed atomic states

   https://doi.org/10.48550/arXiv.2205.06382  

   Malia, B.K.; Wu, Y.; Martínez-Rincón, J.; Kasevich, M.A. (July 2022, ArXivorg)

   Quantum sensors are used for precision timekeeping, field sensing, and quantum communication. Comparisons among a distributed network of these sensors are capable of, for example, synchronizing clocks at different locations. The performance of a sensor network is limited by technical challenges as well as the inherent noise associated with the quantum states used to realize the network. For networks with only local entanglement at each node, the noise performance of the network improves at best with square root of the number of nodes. Here, we demonstrate that nonlocal entanglement between network nodes offers better scaling with network size. A shared quantum nondemolition measurement entangles a clock network with up to four nodes. This network provides up to 4.5 dB better precision than one without nonlocal entanglement, and 11.6 dB improvement as compared to a network of sensors operating at the quantum projection noise limit. We demonstrate the generality of the approach with atomic clock and atomic interferometer protocols, in scientific and technologically relevant configurations optimized for intrinsically differential comparisons of sensor outputs. 

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