The next QUISCO meeting will take place within the Department of Computing Science at the University of Glasgow on the 4th December from 11am to 5pm.

If you plan to attend, please add yourself to the doodle poll here or send an email to s.sharp.1@research.gla.ac.uk for purposes of catering.

**Programme**

11:00 – 11:05 Introduction: Welcome to Glasgow Uni!

11:05 – 11:50 Talk: Vaclav Potochek – Quantum Hilbert Hotel

11:50 – 12:35 Talk: Anna Pappa – Experimental verification of multipartite entanglement in the presence of dishonest parties

12:35 – 13:30 Lunch Break

13:30 – 14:15 Talk: Graeme Weir – Minimum-error measurement of the trine states with unequal prior probabilities

14:15 – 15:00 Talk: Viv Kendon – Minimal ancilla-mediated quantum gates

15:00 – 15:30 Coffee Break

15:30 – 16:15 Talk: Marco Piani – Robustness, robustness, robustness… robustness everywhere!

16:15 – 17:00 Discussion Session

**Abstracts**

**Vaclav Potocek ** (University of Glasgow)

**Quantum Hilbert Hotel**

In 1924 David Hilbert conceived a paradoxical tale involving a hotel with an infinite number of rooms to illustrate some aspects of the mathematical notion of “infinity.” In continuousvariable quantum mechanics we routinely make use of infinite state spaces: here we show that such a theoretical apparatus can accommodate an analog of Hilbert’s hotel paradox. We devise a protocol that, mimicking what happens to the guests of the hotel, maps the amplitudes of an infinite eigenbasis to twice their original quantum number in a coherent and deterministic manner, producing infinitely many unoccupied levels in the process. We demonstrate the feasibility of the protocol by experimentally realizing it on the orbital angular momentum of a paraxial field. This new non-Gaussian operation may be exploited, for example, for enhancing the sensitivity of NOON states, for increasing the capacity of a channel, or for multiplexing multiple channels into a single one.

**Anna Pappa** (University of Edinburgh)

**Experimental verification of multipartite entanglement in the presence of dishonest parties**

Multipartite entanglement is a fundamental resource for quantum information tasks in the context of quantum network applications. One of the main challenges for the future employment of such networks is the necessity to share the underlying entangled states among a large number of parties who wish to perform a distributed computation. In a reallife network, some of these parties may be dishonest, hence it is imperative for any party to be able to verify that the shared state is indeed entangled. This ensures the security of the subsequent computations. In this work, we design, analyse and implement for the fi rst time a distributed protocol for verifying that an untrusted source shares with multiple parties the GHZ state. We consider any number of dishonest parties that collaborate with the source in order to convince the honest parties that the source creates entanglement while in reality this is not the case. We propose a protocol that can tolerate high amounts of losses and we examine in detail how the dishonest parties can use the system imperfections in order to increase their cheating probability. Our implementation is based on a state-of-the-art multipartite entangled photon source, which can produce 3- and 4-party GHZ states with very high fidelity.

**Graeme Weir** (University of Glasgow)

**Minimum-error measurement of the trine states with unequal prior probabilities**

We find the minimum-error measurement strategy for discriminating between the three socalled trine states with unequal prior probabilities. Surprisingly, we find that for a large portion of the regime which we investigate, the optimal measurement is one which only identifies the two most likely states, ignoring the least-probable state altogether.

**Viv Kendon **(Durham University)

**Minimal ancilla-mediated quantum gates**

Most physical implementations of quantum gates employ some sort of ancilla system to control the register qubits and mediate between them. The original Cirac-Zoller gate is of this form. Use of an ancilla can simplify the experimental requirements, and more recent work has been done to find the simplest forms of ancilla-mediated gates under various restrictions. There are two approaches: the ancilla can be measured after interacting with the qubits to enact the gate, or the entire process can be unitary. If the ancilla is measured, the outcomes of the measurements determine a possible correction that must be applied to the qubits, similar to measurement-based quantum computing. The unitary version is deterministic and requires no corrections, but generally requires an extra interaction between the ancilla and the qubits for each gate. Higher dimensional ancillas can also be used, with some extra efficiencies for certain gate sequences. We have characterised minimal forms of interaction that can be used to create a universal set of quantum gates.

- [1] T. J. Proctor, E. Andersson, V. Kendon, Phys.Rev.A 88, 042330 (2013)
- [2] T. J. Proctor, S. Dooley, V. Kendon, Phys.Rev.A 91, 012308 (2015)
- [3] T. J. Proctor, V. Kendon, EPJ Quantum Technology, 1 13 (2014)

**Marco Piani** (University of Strathclyde)

**Robustness, robustness, robustness… Robustness everywhere! **

Robustness is a general approach to quantifying resources in a theory where there is a convex subset of non-resources: this applies, for example, to entanglement, as well as asymmetry and coherence. An approach based on robustness naturally allows one to use efficient and illuminating optimization techniques like semidefinite programming, and can be related to quantum tasks related to discrimination/metrology. I will review some recent results in a number of cases, including—but not limited to!—the mentioned entanglement, asymmetry, and coherence.

Hope to see people there!

Sarah Sharp