Quantum networks : state transmission and network operation

Abstract

Quantum information science is believed to create the next technological revolution. As key ingredients of quantum information science, quantum networks enable various technologies such as secure communication, distributed quantum sensing, quantum cloud computing, and next-generation positioning, navigation, and timing. The main task of quantum networks is to enable quantum communication among different nodes in the network. This includes the topics such as the transmission of quantum states involving multiple parties, the processing of quantum information at end nodes, and the distribution of entanglement among remote nodes. Since quantum communication has its own peculiar properties that have no classical counterparts, the protocols and strategies designed for classical communication networks are not well-suited for quantum ones. This calls for new concepts, paradigms, and methodologies tailored for quantum networks.

To that end, this thesis studies the design and operation of quantum networks, with focus on the following three topics: state transmission, queueing delay, and remote entanglement distribution. The first part develops protocols to broadcast quantum states from a transmitter to N different receivers. The protocols exhibit resource tradeoffs between multiparty entanglement, broadcast classical bits (bcbits), and broadcast quantum bits (bqubits), where the latter two are new types of resources put forth in this thesis. We prove that to send 1 bqubit to N receivers using shared entanglement, O(logN) bcbits are both necessary and sufficient. We also show that the protocols can be implemented using poly(N) basic gates composed of single-qubit gates and CNOT gates. The second part introduces a tractable model for analyzing the queuing delay of quantum data, referred to as quantum queuing delay (QQD).

The model employs a dynamic programming formalism and accounts for practical aspects such as the finite memory size. Using this model, we develop a cognitive-memory-based policy for memory management and show that this policy can decrease the average queuing delay exponentially with respect to memory size. The third part offers a design of remote entanglement distribution (RED) protocols that maximize the entanglement distribution rate (EDR). We introduce the concept of enodes, representing the entangled quantum bit (qubit) pairs in the network. This concept enables us to design the optimal RED protocols based on the solutions of some linear programming problems. Moreover, we investigate RED in a homogeneous repeater chain, which is a building block for many quantum networks. In particular, we determine the maximum EDR for homogeneous repeater chains in a closed form. The contributions of this work provide guidelines for the design and implementation of quantum networks.