United Kingdom

We study the entanglement of formation and the quantum discord contained in even and odd multipartite j-spin coherent states. The key element of this investigation is the fact that a single j-spin coherent state is viewed as comprising 2j qubit states. We compute the quantum correlations present in the n even and odd j-spin coherent states by considering all possible bipartite splits of the multipartite system. We discuss the dierent bipartition schemes of quantum systems and we examine in detail the conservation rules governing the distribution of quantum correlations between the dierent qubits of the multipartite system. Finally, we derive the explicit expressions of quantum correlations present in even and odd spin coherent states decomposed in four spin sub-systems. We also analyze the properties of monogamy and we show in particular that the entanglement of the formation and the quantum discord obey the relation of monogamy only for even multipartite j-spin coherent states.

Bristol Quantum Information Technologies Workshop

Entanglement of formation and quantum discord in multipartite j-spin coherent states

monogamy of entanglement of formation; monogamy of quantum discord; quantum correlations; multipartite j-spin coherent states.

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**BQIT is a three day annual workshop** aimed at enabling leading UK and international academics and industrial partners to come together; to explore and discuss future ambitions and challenges in the field of **Quantum Information Technologies.** Since our conception in 2014 we have had 230 speakers and panellists who have presented their work and opinions on a range of topics, from quantum theory to innovation in industry.


### Welcome Message
The BQIT:21 team welcomes you to the eighth Bristol Quantum Information Technologies workshop! 

Last year was the first time in our workshop's history that we had gone fully virtual. The global circumstances that continue to impact us all professionally and personally have forced BQIT once again to be delivered as an all-virtual workshop for 2021. The access this creates to colleagues across the world who would otherwise be unable to join us, as well as being able to make the workshop free for all attendees due to the lower costs involved in delivering an online workshop, are just a couple of the extraordinary benefits of meeting online. This also means that we can welcome three times as many attendees to BQIT than previous years.   

We take this opportunity to thank each of our speakers and poster presenters for contributing their technical content, this year's sponsors, whose support this year enabled BQIT:21 to be free to all attendees, and to all of our attendees for joining us online this year. We recognise the extra energy required to stay connected and motivated during these difficult times, and are hugely encouraged to see so many of you willing to continue to connect with us on an online platform. 

It is our hope that you have a productive and enjoyable time while you engage and interact with BQIT:21, and to everyone that has helped take BQIT:21 online, thank you! 

**The BQIT board and organisation team **


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### This year's workshop agenda is available here: [Virtual BQIT:21](https://drive.google.com/file/d/1QwsSM0ztnxC_lgUKf3TbO3GvnI44AQkY/view?usp=sharing)
For further information, please contact us at: **bqit-admin@bristol.ac.uk**

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Satellite-based quantum key distribution enables quantum-secured communication on a global scale. There are international efforts underway to build and launch satellites capable of Quantum Key Distribution (‘QKD’) e.g. the QUARC, QEYSSat, Micius and SpooQy-1 missions. 
These QKD satellites work with a network of Optical Ground Stations (OGSs) to receive optical signals and distribute cryptographic keys to end users. However, OGSs near metropolitan centres are often subject to high levels of light pollution and suffer from restricted clear lines of sight to the satellite. Further, static ground stations are severely limited by local meteorological conditions. A mobile OGS is not subject to these restrictions and can be used to distribute keys flexibly. This may be useful when performing site surveys in order to derive realistic data on expected key rates and meteorological/geographic conditions. We present our progress towards field-demonstrations of QKD using our mobile OGS to receive both a beacon signal and quantum signal. This OGS is designed to work with our industry lead 6U and research focused 12 U QKD CubeSats.


Field Demonstration of A Mobile Optical Ground Station for CubeSat Quantum Key Distribution

A workflow for evaluation of entanglement source quality is proposed. Based on quantum state density matri-ces obtained from theoretical models and experimental data, we make an estimate of a potential performance of a quantum entanglement source in quantum key distribution protocols. This workflow is showcased for continuously pumped spontaneous parametric down-conversion (SPDC) source, where it highlights the trade-off between entangled pair generation rate and entanglement quality caused by multiphoton nature of the generated quantum states. We employ this characterization technique to show that secure key rate of down-converted photon pairs is limited to 0.029 bits per detection window due to intrinsic multiphoton contributions. We also report that there exists one optimum gain for continuous-wave down-conversion sources. We find a bound for secure key rate extracted from SPDC sources and make a comparison with perfectly single-pair quantum states, such as those produced by quantum dots.

Effect of source statistics on utilizing photon entanglement in quantum key distribution

We studied the behavior of tunable one-dimensional discrete-time quantum walk (DTQW) in the presence of decoherence, modeled as a noisy quantum channel with bit-flip, phase-flip, and general amplitude damping effects. By tuning the noise level for the respective noise channel, we observed the emergence of the broad class of transport behavior: quantum walk, quantum-classical walk, and classical walk. The robustness of the walk under noise is captured by the scaling exponents. We showed the walk under maximum decoherence from the general damping amplitude channel maintained the robust ballistic spread while retaining the Gaussian-like distribution. This work may be applicable in the optimization or tuning of the quantum walk under noisy channels. 


Scaling exponent analysis of the tunable discrete quantum walk in the noisy channel

Recently, the first integrated Measurement Device Independent Quantum Key Distribution (MDI QKD) system has been implemented here in Bristol. To build on this result and work towards improved security and key rates, a new indium phosphide (InP) transmitter chip has been designed for a second-generation MDI QKD implementation. The new chip contains two laser sources, including a distributed feedback laser to allow for faster pulsing and high-speed phase modulators with a bandwidth of up to 30 GHz. With the new lasers and phase modulators a higher pulse rate will be achieved, leading to better key rates. Additionally, an on-chip photodiode can be used to monitor incoming light. This makes the chip much more resilient against hacking attacks on the receiver side. Since MDI QKD is intrinsically protected against detector attacks, this means that this new MDI QKD system will show great security overall.

An improved chip for MDI QKD

Photons are natural carriers of high-dimensional quantum information, and the encoded qudits can benefit from higher quantum information capacity and noise-resilience. However, schemes to generate the resources needed for high-dimensional quantum computing have so far not been demonstrated for linear optics. Here, we show how to generate GHZ states of arbitrary numbers of photons in arbitrary dimensions using destructive interference in linear optical circuits described by Fourier matrices. We combine our results with recent schemes for qudit Bell measurements to show that universal linear optical quantum computing can be performed in arbitrary dimensions.

A scheme for universal high-dimensional quantum computation with linear optics

Natural language processing (NLP) problems are ubiquitous in classical computing, where they often require millions of dollars on computational resources and billions of parameters to infer sentence meanings. It is not efficient classically to improve these state-of-the-art language models and this means that the required computational resources are expected to scale exponentially with the increase in parameters. With the appearance of quantum computing hardware and simulators, it is worth developing methods to examine such problems on these platforms. 

Quantum Natural Language Processing (QNLP) deals with the design and implementation of NLP models intended to be run on quantum hardware.

We are introducing a version of the popular transformer model in which by the application quantum phenomena we are trying to find a way to bring down the training cost in NISQ computers. We are using the DisCoCat language modeling framework to encode text into quantum gates. The quantum transformer algorithm is created in Qiskit by adding variational quantum circuit layers to the classical transformer. We are also experimenting with different ansatz and cost functions to prevent the barren plateau issue. We will evaluate the model on NLP tasks like classification, machine translation, and next-word prediction.

Quantum Transformer

Entanglement between remote matter systems is the cornerstone of quantum information transfer, crucial for establishing quantum secure communication between distant parties as well as for distributed quantum information processing architectures. This can be done via the implementation of cooperative light-matter coupling between coherently controllable matter qubits. This can manifest in collective rate enhancements, such as those at the heart of super radiance [1], but also includes effects such as measurement-induced remote entanglement via path erasure [2]. Here, we report coherent control of cooperative emission from two indistinguishable solid-state emitters, brought into resonance via Stark tuning. We characterize the indistinguishability of the emitters and the degree of correlation in the initial state of the joint system by observing the emergence of the bunched correlation peak in the intensity correlation experiment [3], the primary signature of cooperative emission. We find that due to the substantial spatial separation between the emitters, the cooperative emission lifetime is unchanged from the spontaneous emission lifetimes of the uncorrelated emitters. This highlights the fact that the bunched correlation peak in the intensity correlation is not a sufficient witness of superradiant behavior. Finally, in a stark departure from a pair of uncorrelated emitters, we observe photon statistics resembling that of a weak coherent state in Hong-Ou-Mandel type two-photon interference measurements. These experiments establish a new way to control and characterize cooperative behavior between distant matter qubits using the full quantum optics toolbox, a key stepping stone on the route to realizing large-scale quantum photonic network.

[1] R. H. Dicke, Phys. Rev. 93, 99 (1954). [2] S. Wolf et. Al., Phys. Rev. Lett. 124, 063603 (2020). [3] A. Sipahigil et. al., Science 354, 847-850 (2016).

Coherent Control of Cooperative Photon Emission from Indistinguishable Quantum Emitters

Energy-based neural networks adopt the principles of statistical physics to guarantee their self-regulation. Contrary to probabilistic models, they do not need labels to train and normalization efforts to compute their scores. Shaping the energy function brings substantial power and flexibility to a learning process, which is normally framed as an optimization problem. 

The energy landscape for the modern neural network architectures comprises high but thin barriers surrounding shallow local minima. While there is no clear understanding of convergence dynamics produced by classical optimization techniques, quantum annealing which allows tuning the underlying quantum dynamics and has a hardware implementation looks promising.

To deepen the understanding of the potential of quantum tunnelling in energy-based optimization, this study suggests adopting a new paradigm of simulation or "gamification". We analyse the convergence dynamics through building a real (classical) and the alternate (quantum) world, where we can model, observe, and control the behaviour of neurons, communities of neurons, and different types of interactions between them facing open challenges in AI.

Classical versus quantum convergence dynamics in energy-based neural networks

In this presentation, we introduce and study the Quantum Measurement Detection Algorithms (QMDA), whose objective is to detect weather unwanted measurements are being made in a quantum circuit or not. A QMDA is a quantum circuit that includes three unitary matrices, one of them being applied numerous times consecutively, and whose initial state is fixed when no foreign measurements occur. One of the most basic yet effective examples is the Elitzur-Vaidman bomb-tester, which is generalized, among other similar circuits, in the QMDA definition; however, the algorithms studied in this work must be prepared for detecting measurements that are made in an unknown basis. We will show some key properties and limitations of these algorithms, as well as studying the performance of the Elitzur-Vaidman bomb-tester. We finish the presentation suggesting different extensions of the definition that may lead to more effective algorithms and that englobe other existing ones like the counterfactual communication algorithm.

Quantum Measurement Detection Algorithms

To investigate the fundamental nature of matter and its interactions, particles are accelerated to very high energies and collided within detectors, producing a multitude of other particles that are scattered in all directions. These particles leave signals of their passage while transversing the detector. The problem of track reconstruction is to recover the original trajectories from these signals. This represents a very demanding data analysis problem, and it will become even more so as the luminosity of the next generation accelerators keeps increasing.
Approaches to track reconstruction based on quantum information technologies have recently been put forward. In order to access the potential for a quantum speedup for this problem, we start by elaborating a computational complexity analysis of a standard tracking algorithm, the Combinatorial Track Finder. First, we find that it is possible to improve the classical complexity of the original algorithm.
We further show that we can use quantum search algorithms to reach a lower quantum computational complexity. To the best of our knowledge, this is the first computational complexity-level demonstration of a quantum advantage for a state-of-the-art track reconstruction method.
Work developed in collaboration with A.Ambainis, P.Bargassa, M.Dimitrijevs, A.Glos, M.Kālis, A.Kumar, A.Locāns, Y.Omar, S.Pratapsi, G.Quinta, A.Rivošs, J.Seixas.

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Entanglement of formation and quantum discord in multipartite j-spin coherent states

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