Contextuality as a resource for measurement-based quantum computation beyond qubits

Abstract

Contextuality-the obstruction to describing quantum mechanics in a classical statistical way-has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality as a computational resource, as follows. If local measurements on a multi-qubit state can be used to evaluate nonlinear boolean functions with only linear control processing, then this computation constitutes a proof of strong contextuality-the possible local measurement outcomes cannot all be pre-assigned. However, this connection is restricted to the special case when the local measured systems are qubits, which have unusual properties from the perspective of contextuality. A single qubit cannot allow for a proof of contextuality, unlike higher-dimensional systems, and multiple qubits can allow for stateindependent contextuality with only Pauli observables, again unlike higher-dimensional generalisations. Here we identify precisely that strong non-locality is necessary in a qudit measurement-based computation (MBC) that evaluates high-degree polynomial functions with only linear control. We introduce the concept of local universality, which places a bound on the space of output functions accessible under the constraint of single-qudit measurements. Thus, the partition of a physical system into subsystems plays a crucial role for the increase in computational power. A prominent feature of our setting is that the enabling resources for qubit and qudit MBC are of the same underlying nature, avoiding the pathologies associated with qubit contextuality.

Decomposable coherence and quantum fluctuation relations

“…shown that these "negative probabilities" are in fact a witness of contextuality -a fundamental feature of quantum mechanics that includes quantum entanglement as a special case [48,49] and is conjectured to be the key ingredient providing speed-ups in quantum computers [50,51].…”

Logical proof of quantum correlations requiring entanglement measurements

“…Recent efforts have been made on understanding contextuality using a graph theory approach [3-6]. Contextuality has shown an advantage in quantum computing [7][8][9][10], in quantum cryptography [11,12], quantum communication [13,14] and state discrimination [15].Contextuality generalizes non-locality [4] and the ability to experimentally observe these two fundamental properties of quantum physics is an important point when it comes to their uses in information technology tasks. It is then one of the most fundamental challenge to develop tools to characterize and classify measurements statistics belonging to different theories.…”

“…Recent efforts have been made on understanding contextuality using a graph theory approach [3-6]. Contextuality has shown an advantage in quantum computing [7][8][9][10], in quantum cryptography [11,12], quantum communication [13,14] and state discrimination [15].…”

“…The three rectangles (red, blue and green) represent the sets of events appearing in the eqs. (10) to (12). The 'X' (red) represents the events with probability null to have the saturation of the exclusivity principle.…”

Teoria de recursos para contextualidade generalizada

“…can be used to apply the contextuality monotones that are associated with the convexity structure of the noncontextual polytope: the contextual fraction is our case study here due to it's importance for application in quantum computing, see (Abramsky et al, 2017), (Frembs et al, 2018). We propose the following, in light of (Abramsky et al, 2017), suppose that B is a possible behavior for the operational scenario given.…”