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We construct a linear system non-local game which can be played perfectly using a limit of finite-dimensional quantum strategies, but which cannot be played perfectly on any finite-dimensional Hilbert space, or even with any tensor-product strategy. In particular, this shows that the set of (tensor-product) quantum correlations is not closed. The constructed non-local game provides another counterexample to the middle Tsirelson problem, with a shorter proof than our previous paper (though at the loss of the universal embedding theorem). We also show that it is undecidable to determine if a linear system game can be played perfectly with a finite-dimensional strategy, or a limit of finite-dimensional quantum strategies.
The strength of a homogeneous polynomial (or form) $f$ is the smallest length of an additive decomposition expressing it whose summands are reducible forms. We show that the set of forms with bounded strength is not always Zariski-closed. In particul
We describe a simple method to derive high performance semidefinite programming relaxations for optimizations over complex and real operator algebras in finite dimensional Hilbert spaces. The method is very flexible, easy to program and allows the us
Quantum kicked top is a fundamental model for time-dependent, chaotic Hamiltonian system and has been realized in experiments as well. As the quantum kicked top can be represented as a system of qubits, it is also popular as a testbed for the study o
We discuss the analogy between topological entanglement and quantum entanglement, particularly for tripartite quantum systems. We illustrate our approach by first discussing two clearly (topologically) inequivalent systems of three-ring links: The Bo
In this work, we investigate the possibility of compressing a quantum system to one of smaller dimension in a way that preserves the measurement statistics of a given set of observables. In this process, we allow for an arbitrary amount of classical