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IEEE Conference on Decision and Control (CDC)

Estimation and initialization of quantum network via continuous measurement on single node

Yuzuru Kato, Naoki Yamamoto

Published Dec 1, 2013• 2 citations
Publisher

Abstract

For reliable and consistent quantum information processing carried out on a quantum network, the network structure must be fully known and a desired initial state has to be prepared on it. In this paper, we consider a spin network with only a single node accessible and provide continuous-measurement-based methods to fulfill the above two requirements. More specifically, the measurement results continuously obtained are used to update the estimate of the network structure, which converges to the true structure with high probability; for the latter problem, we further employ an adaptive measurement scheme to deterministically drive the state to a desired target state for network initialization.

DOI
10.1109/cdc.2013.6760160

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For reliable and consistent quantum information processing carried out on a quantum network, the network structure must be fully known and a desired initial state has to be prepared on it. In this paper, we consider a spin network with only a single node accessible and provide continuous-measurement-based methods to fulfill the above two requirements. More specifically, the measurement results continuously obtained are used to update the estimate of the network structure, which converges to the true structure with high probability; for the latter problem, we further employ an adaptive measurement scheme to deterministically drive the state to a desired target state for network initialization.
For reliable and consistent quantum information processing carried out on a quantum network, the network structure must be fully known and a desired initial state must be accurately prepared on it. In this paper, for a class of spin networks with its single node only accessible, we provide two continuous-measurement-based methods to achieve the above requirements; the first one identifies the unknown network structure with high probability, based on continuous-time Bayesian update of the graph structure; the second one is, with the use of adaptive measurement technique, able to deterministically drive any mixed state to a spin coherent state for network initialization.
Motivated by the technical requirements of quantum information processing and nanotechnology, the control of individual quantum systems such as single atoms, ions or even photons has become a highly desirable aim.The monitoring of quantum systems-a direct test and in many cases a prerequisite of their control-has been investigated so far only for certain observables such as the position or momentum of quantum particles.Here, we describe a method to monitor in real time the complete state of a quantum particle with unknown initial state moving in a known potential.The method is based on successively updating an estimate by the results of a continuous position measurement.We demonstrate by numerical simulations that even in a chaotic potential tracking the wave function of a particle is possible, and we show with an example that the monitoring scheme appears to be robust against sudden random perturbations.
Continuous-time measurements are instrumental for a multitude of tasks in quantum engineering and quantum control, including the estimation of dynamical parameters of open quantum systems monitored through the environment. However, such measurements do not extract the maximum amount of information available in the output state, so finding alternative optimal measurement strategies is a major open problem. In this paper we solve this problem in the setting of discrete-time input-output quantum Markov chains. We present an efficient algorithm for optimal estimation of one-dimensional dynamical parameters which consists of an iterative procedure for updating a `measurement filter' operator and determining successive measurement bases for the output units. A key ingredient of the scheme is the use of a coherent quantum absorber as a way to post-process the output after the interaction with the system. This is designed adaptively such that the joint system and absorber stationary state is pure at a reference parameter value. The scheme offers an exciting prospect for optimal continuous-time adaptive measurements, but more work is needed to find realistic practical implementations.
We consider a basic quantum hybrid network model consisting of a number of nodes each holding a qubit, for which the aim is to drive the network to a consensus in the sense that all qubits reach a common state. Projective measurements are applied serving as control means, and the measurement results are exchanged among the nodes via classical communication channels. In this way the quantum-opeartion/classical-communication nature of hybrid quantum networks is captured, although coherent states and joint operations are not taken into consideration in order to facilitate a clear and explicit analysis. We show how to carry out centralized optimal path planning for this network with all-to-all classical communications, in which case the problem becomes a stochastic optimal control problem with a continuous action space. To overcome the computation and communication obstacles facing the centralized solutions, we also develop a distributed Pairwise Qubit Projection (PQP) algorithm, where pairs of nodes meet at a given time and respectively perform measurements at their geometric average. We show that the qubit states are driven to a consensus almost surely along the proposed PQP algorithm, and that the expected qubit density operators converge to the average of the network's initial values.
Quantum networks are of high interest nowadays and a quantum internet has been long envisioned. Network-entanglement adapts the notion of entanglement to the network scenario and network-entangled states are considered to be a resource to overcome the limitations of a given network structure. In this work, we introduce measures of quantum network-entanglement that are well-defined within the general framework of quantum resource theories, which at the same time have a clear operational interpretation characterizing the extra resources necessary to prepare a targeted quantum state within a given network. In particular, we define the network communication cost and the network round complexity, which turn out to be intimately related to graph-theoretic parameters. We also provide methods to estimate these measures by introducing novel witnesses of network-entanglement.
Quantum hybrid networks where classical and quantum components coexist play a fundamental role in quantum communications. We consider a basic quantum hybrid network model consisting of a number of nodes each holding a qubit, for which the aim is to drive the network to a consensus in the sense that all qubits reach a common state. Projective measurements are applied serving as control means, and the measurement results are exchanged among the nodes via classical communication channels. We show how to carry out centralized optimal path planning for the network with all-to-all classical communications, in which case the problem becomes a stochastic optimal control problem with a continuous action space. To overcome the computation and communication obstacles facing the centralized solutions, we also develop a distributed Pairwise Qubit Projection (PQP) algorithm, where pairs of nodes meet at a given time and respectively perform measurements at their geometric average. We show that the qubit states are driven to a consensus almost surely along the proposed PQP algorithm, and that the expected qubit density operators converge to the average of the network's initial values.