Certifying Sets of Quantum Observables with Any Full-Rank State.

We show that some sets of quantum observables are unique up to an isometry and have a contextuality witness that attains the same value for any initial state. We prove that these two properties make it possible to certify any of these sets by looking at the statistics of experiments with sequential measurements and using any initial state of full rank, including thermal and maximally mixed states. We prove that this "certification with any full-rank state" (CFR) is possible for any quantum system of finite dimension d≥3 and is robust and experimentally useful in dimensions 3 and 4. In addition, we prove that complete Kochen-Specker sets can be Bell self-tested if and only if they enable CFR. This establishes a fundamental connection between these two methods of certification, shows that both methods can be combined in the same experiment, and opens new possibilities for certifying quantum devices.

Convex Optimization for Nonequilibrium Steady States on a Hybrid Quantum Processor.

Finding the transient and steady state properties of open quantum systems is a central problem in various fields of quantum technologies. Here, we present a quantum-assisted algorithm to determine the steady states of open system dynamics. By reformulating the problem of finding the fixed point of Lindblad dynamics as a feasibility semidefinite program, we bypass several well-known issues with variational quantum approaches to solving for steady states. We demonstrate that our hybrid approach allows us to estimate the steady states of higher dimensional open quantum systems and discuss how our method can find multiple steady states for systems with symmetries.

Robust Self-Testing of Quantum Systems via Noncontextuality Inequalities.

Characterizing unknown quantum states and measurements is a fundamental problem in quantum information processing. In this Letter, we provide a novel scheme to self-test local quantum systems using noncontextuality inequalities. Our work leverages the graph-theoretic framework for contextuality introduced by Cabello, Severini, and Winter, combined with tools from mathematical optimization that guarantee the unicity of optimal solutions. As an application, we show that the celebrated Klyachko-Can-Binicioglu-Shumovsky inequality and its generalization to contextuality scenarios with odd n-cycle compatibility relations admit robust self-testing.

Non-Classical Correlations in n-Cycle Setting.

Quantum communication and quantum computation form the two crucial facets of quantum information theory. While entanglement and its manifestation as Bell non-locality have been proved to be vital for communication tasks, contextuality (a generalisation of Bell non-locality) has shown to be the crucial resource behind various models of quantum computation. The practical and fundamental aspects of these non-classical resources are still poorly understood despite decades of research. We explore non-classical correlations exhibited by some of these quantum as well as super-quantum resources in the n-cycle setting. In particular, we focus on correlations manifested by Kochen-Specker-Klyachko box (KS box), scenarios involving n-cycle non-contextuality inequalities and Popescu-Rohlrich boxes (PR box). We provide the criteria for optimal classical simulation of a KS box of arbitrary n dimension. The non-contextuality inequalities are analysed for n-cycle setting, and the condition for the quantum violation for odd as well as even n-cycle is discussed. We offer a simple extension of even cycle non-contextuality inequalities to the phase space case. Furthermore, we simulate a generalised PR box using KS box and provide some interesting insights. Towards the end, we discuss a few possible interesting open problems for future research. Our work connects generalised PR boxes, arbitrary dimensional KS boxes, and n-cycle non-contextuality inequalities and thus provides the pathway for the study of these contextual and nonlocal resources at their junction.