Robert Ivan Booth | LIP6 - Équipe QI

Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements

Fri, 02 Dec 2022 00:00:00 +0000

Quantum computers will provide considerable speedups with respect to their classical counterparts. However, the identification of the innately quantum features that enable these speedups is challenging. In the continuous-variable setting - a promising paradigm for the realisation of universal, scalable, and fault-tolerant quantum computing - contextuality and Wigner negativity have been perceived as two such distinct resources. Here we show that they are in fact equivalent for the standard models of continuous-variable quantum computing. While our results provide a unifying picture of continuous-variable resources for quantum speedup, they also pave the way towards practical demonstrations of continuous-variable contextuality, and shed light on the significance of negative probabilities in phase-space descriptions of quantum mechanics.

Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements

Fri, 02 Dec 2022 00:00:00 +0000

Complete ZX-calculi for the stabiliser fragment in odd prime dimensions

Mon, 22 Aug 2022 00:00:00 +0000

We introduce a family of ZX-calculi which axiomatise the stabiliser fragment of quantum theory in odd prime dimensions. These calculi recover many of the nice features of the qubit ZX-calculus which were lost in previous proposals for higher-dimensional systems. We then prove that these calculi are complete, i.e. provide a set of rewrite rules which can be used to prove any equality of stabiliser quantum operations. Adding a discard construction, we obtain a calculus complete for mixed state stabiliser quantum mechanics in odd prime dimensions, and this furthermore gives a complete axiomatisation for the related diagrammatic language for affine co-isotropic relations.

Measurement-based quantum computation beyond qubits

Tue, 22 Feb 2022 00:00:00 +0000

However, the vast majority of the work on MBQC has focused on architectures using the simplest possible quantum system: the qubit. It remains an open question how much of this work can be lifted to other quantum systems. In this thesis, we begin to tackle this question, by introducing analogues of the measurement calculus for higher- and infinite-dimensional quantum systems. More specifically, we consider the case of qudits when the local dimension is an odd prime, and of continuous-variable systems familiar from the quantum physics of free particles. In each case, a calculus is introduced and given a suitable interpretation in terms of quantum operations. We then relate the resulting models to the standard circuit models, using graph-theoretical tools called “flow” conditions.

Measurement-based quantum computation beyond qubits

Tue, 22 Feb 2022 00:00:00 +0000

Measurement-based quantum computation (MBQC) is an alternative model for quantum computation, which makes careful use of the properties of the measurement of entangled quantum systems to perform transformations on an input. It differs fundamentally from the standard quantum circuit model in that measurement-based computations are naturally irreversible. This is an unavoidable consequence of the quantum description of measurements, but begets an obvious question: when does an MBQC implement an effectively reversible computation? The measurement calculus is a framework for reasoning about MBQC with the remarkable feature that every computation can be related in a canonical way to a graph. This allows one to use graph-theoretical tools to reason about MBQC problems, such as the reversibility question, and the resulting study of MBQC has had a large range of applications. However, the vast majority of the work on MBQC has focused on architectures using the simplest possible quantum system: the qubit. It remains an open question how much of this work can be lifted to other quantum systems. In this thesis, we begin to tackle this question, by introducing analogues of the measurement calculus for higher- and infinite-dimensional quantum systems. More specifically, we consider the case of qudits when the local dimension is an odd prime, and of continuous-variable systems familiar from the quantum physics of free particles. In each case, a calculus is introduced and given a suitable interpretation in terms of quantum operations. We then relate the resulting models to the standard circuit models, using graph-theoretical tools called “flow” conditions.

Wigner negativity is equivalent to contextuality for generalised position and momentum measurements

Fri, 01 Oct 2021 16:00:00 +0100

Understanding what differentiates a quantum system from a classical one is a crucial question, both foundationally and for quantum information applications. In this work, we consider two non-classical features of quantum systems: negativity of the Wigner function and contextuality. We prove that these two notions coincide when one considers measurements of linear combinations of position and momentum operators. Amongst other consequences, our result implies that contextuality is a crucial resource for continuous-variable quantum computations.