Linear Quantum Network Research Articles

Low-cost nonlocal Toffoli gate in a linear quantum network topology

Although a Toffoli gate can be equivalently implemented using several single-qubit and two-qubit gates, it will consume much resource, two of which are nonlocal controlled-NOT (CNOT) gates acting on two non-adjacent nodes, especially in distributed quantum computation (DQC). We, for the first time, employ an ancillary qubit to construct a nonlocal Toffoli gate for DQC in linear network topology. The ancillary-qubit-based scheme needs fewer qubits, quantum gates, and entanglement states than that based on quantum teleportation scheme and the entanglement swapping scheme. We also analyze the performance of the three proposed schemes under different application scenarios, and present their pros and cons. Our work will help to implement DQC in noisy intermediate-scale quantum (NISQ) era.

Quantum networks using counterfactual quantum communication

Counterfactual quantum communication is one of the most interesting facets of quantum communication, allowing two parties to communicate without any transmission of quantum or classical particles between the parties involved in the communication process. This aspect of quantum communication originates from the interaction-free measurements where the chained quantum Zeno effect plays an important role. Here, we propose a new counterfactual quantum communication protocol for transmitting an entangled state from a pair of electrons to two independent photons. Interestingly, the protocol proposed here shows that the counterfactual method can be employed to transfer information from house qubits to flying qubits. Following this, we show that the protocol finds uses in building quantum repeaters leading to a counterfactual quantum network, enabling counterfactual communication over a linear quantum network.

Multi-client distributed blind quantum computation with the Qline architecture

Universal blind quantum computing allows users with minimal quantum resources to delegate a quantum computation to a remote quantum server, while keeping intrinsically hidden input, algorithm, and outcome. State-of-art experimental demonstrations of such a protocol have only involved one client. However, an increasing number of multi-party algorithms, e.g. federated machine learning, require the collaboration of multiple clients to carry out a given joint computation. In this work, we propose and experimentally demonstrate a lightweight multi-client blind quantum computation protocol based on a recently proposed linear quantum network configuration (Qline). Our protocol originality resides in three main strengths: scalability, since we eliminate the need for each client to have its own trusted source or measurement device, low-loss, by optimizing the orchestration of classical communication between each client and server through fast classical electronic control, and compatibility with distributed architectures while remaining intact even against correlated attacks of server nodes and malicious clients.

Anonymous conference key agreement in linear quantum networks

Sharing multi-partite quantum entanglement between parties allows for diverse secure communication tasks to be performed. Among them, conference key agreement (CKA) - an extension of key distribution to multiple parties - has received much attention recently. Interestingly, CKA can also be performed in a way that protects the identities of the participating parties, therefore providing anonymity. In this work, we propose an anonymous CKA protocol for three parties that is implemented in a highly practical network setting. Specifically, a line of quantum repeater nodes is used to build a linear cluster state among all nodes, which is then used to anonymously establish a secret key between any three of them. The nodes need only share maximally entangled pairs with their neighbours, therefore avoiding the necessity of a central server sharing entangled states. This linear chain setup makes our protocol an excellent candidate for implementation in future quantum networks. We explicitly prove that our protocol protects the identities of the participants from one another and perform an analysis of the key rate in the finite regime, contributing to the quest of identifying feasible quantum communication tasks for network architectures beyond point-to-point.

Simulating macroscopic quantum correlations in linear networks

Many developing quantum technologies make use of quantum networks of different types. Even linear quantum networks are nontrivial, as the output photon distributions can be exponentially complex. Despite this, they can still be computationally simulated. The methods used are transformations into equivalent phase-space representations, which can then be treated probabilistically. This provides an exceptionally useful tool for the prediction and validation of experimental results, including decoherence. As well as experiments in Gaussian boson sampling, which are intended to demonstrate quantum computational advantage, these methods are applicable to other types of entangled linear quantum networks as well. This paper provides a tutorial and review of work in this area, to explain quantum phase-space techniques using the positive-P and Wigner distributions.

Graph Picture of Linear Quantum Networks and Entanglement

The indistinguishability of quantum particles is widely used as a resource for the generation of entanglement. Linear quantum networks (LQNs), in which identical particles linearly evolve to arrive at multimode detectors, exploit the indistinguishability to generate various multipartite entangled states by the proper control of transformation operators. However, it is challenging to devise a suitable LQN that carries a specific entangled state or compute the possible entangled state in a given LQN as the particle and mode number increase. This research presents a mapping process of arbitrary LQNs to graphs, which provides a powerful tool for analyzing and designing LQNs to generate multipartite entanglement. We also introduce the perfect matching diagram (PM diagram), which is a refined directed graph that includes all the essential information on the entanglement generation by an LQN. The PM diagram furnishes rigorous criteria for the entanglement of an LQN and solid guidelines for designing suitable LQNs for the genuine entanglement. Based on the structure of PM diagrams, we compose LQNs for fundamental N-partite genuinely entangled states.

Programmable linear quantum networks with a multimode fibre

Reconfigurable quantum circuits are fundamental building blocks for the implementation of scalable quantum technologies. Their implementation has been pursued in linear optics through the engineering of sophisticated interferometers. While such optical networks have been successful in demonstrating the control of small-scale quantum circuits, scaling up to larger dimensions poses significant challenges. Here, we demonstrate a potentially scalable route towards reconfigurable optical networks based on the use of a multimode fibre and advanced wavefront-shaping techniques. We program networks involving spatial and polarisation modes of the fibre and experimentally validate the accuracy and robustness of our approach using two-photon quantum states. In particular, we illustrate the reconfigurability of our platform by emulating a tunable coherent absorption experiment. By demonstrating reliable reprogrammable linear transformations, with the prospect to scale, our results highlight the potential of complex media driven by wavefront shaping for quantum information processing.

Uncertainty decomposition of quantum networks in SLH framework

SummaryThis paper presents a systematic method to decompose uncertain linear quantum input‐output networks into uncertain and nominal subnetworks, when uncertainties are defined in SLH representation. To this aim, two decomposition theorems are stated, which show how an uncertain quantum network can be decomposed into nominal and uncertain subnetworks in cascaded connection and how uncertainties can be translated from SLH parameters into state‐space parameters. As a potential application of the proposed decomposition scheme, robust stability analysis of uncertain quantum networks is briefly introduced. The proposed uncertainty decomposition theorems take account of uncertainties in all three parameters of a quantum network and bridge the gap between SLH modeling and state‐space robust analysis theory for linear quantum networks.

Entanglement in a linear coherent feedback chain of nondegenerate optical parametric amplifiers

This paper is concerned with linear quantum networks of $N$ nondegenerate optical parametric amplifiers (NOPAs), with $N$ up to 6, which are interconnected in a coherent feedback chain. Each network connects two communicating parties (Alice and Bob) over two transmission channels. In previous work we have shown that a dual-NOPA coherent feedback network generates better Einstein-Podolsky-Rosen (EPR) entanglement (i.e., more two-mode squeezing) between its two outgoing Gaussian fields than a single NOPA, when the same total pump power is consumed and the systems undergo the same transmission losses over the same distance. This paper aims to analyze stability, EPR entanglement between two outgoing fields of interest, and bipartite entanglement of two-mode Gaussian states of cavity modes of the $N$-NOPA networks under the effect of transmission and amplification losses, as well as the effect of time delays on the outgoing fields. It is numerically shown that, in the absence of losses and delays, the network with more NOPAs in the chain requires less total pump power to generate the same degree of EPR entanglement. Moreover, we report on the internal entanglement synchronization that occurs in the steady state between certain pairs of Gaussian oscillator modes inside the NOPA cavities of the networks.

From quantum multiplexing to high-performance quantum networking

Our objective was to design a quantum repeater capable of achieving one million entangled pairs per second over a distance of 1000km. We failed, but not by much. In this letter we will describe the series of developments that permitted us to approach our goal. We will describe a mechanism that permits the creation of entanglement between two qubits, connected by fibre, with probability arbitrarily close to one and in constant time. This mechanism may be extended to ensure that the entanglement has high fidelity without compromising these properties. Finally, we describe how this may be used to construct a quantum repeater that is capable of creating a linear quantum network connecting two distant qubits with high fidelity. The creation rate is shown to be a function of the maximum distance between two adjacent quantum repeaters.

Avoiding entanglement sudden death via measurement feedback control in a quantum network

In this paper, we consider a linear quantum network composed of two distantly separated cavities that are connected via a one-way optical field. When one of the cavities is damped and the other undamped, the overall cavity state obtains a large amount of entanglement in its quadratures. This entanglement, however, immediately decays and vanishes in a finite time. That is, entanglement sudden death occurs. We show that the direct measurement feedback method proposed by Wiseman can avoid this entanglement sudden death, and, further, enhance the entanglement. It is also shown that the entangled state under feedback control is robust against signal loss in a realistic detector, indicating the reliability of the proposed direct feedback method in practical situations.

Explicit effective Hamiltonians for general linear quantum-optical networks

Linear optical networks are devices that turn classical incident modes by a linear transformation into outgoing ones. In general, the quantum version of such transformations may mix annihilation and creation operators. We derive a simple formula for the effective Hamiltonian of a general linear quantum network, if such a Hamiltonian exists. Otherwise we show how the scattering matrix of the network is decomposed into a product of three matrices that can be generated by Hamiltonians.