Assessing dimensions from evolution

Abstract

Using tools from classical signal processing, we show how to determine the dimensionality of a quantum system as well as the effective size of the environment's memory from observable dynamics in a model-independent way. We discuss the dependence on the number of conserved quantities, the relation to ergodicity and prove a converse showing that a Hilbert space of dimension D+2 is sufficient to describe every bounded sequence of measurements originating from any D-dimensional linear equations of motion. This is in sharp contrast to classical stochastic processes which are subject to more severe restrictions: a simple spectral analysis shows that the gap between the required dimensionality of a quantum and a classical description of an observed evolution can be arbitrary large.

5 pages

References in corpus (6)

• Assessing non-Markovian dynamics
• Hybrid Quantum Processors: molecular ensembles as quantum memory for solid state circuits
• Testing the Hilbert space dimension
• Dividing Quantum Channels
• A lower bound on the dimension of a quantum system given measured data
• Unbounded violation of tripartite Bell inequalities

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• Unbounded violations of bipartite Bell Inequalities via Operator Space theory
• A two-qubit Bell inequality for which POVM measurements are relevant
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• QBism: Quantum Theory as a Hero's Handbook
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• Spectral Quantum Tomography
• The inverse eigenvalue problem for quantum channels
• Simulating extremal temporal correlations
• Certifying Quantum Temporal Correlation via Randomized Measurements: Theory and Experiment
• Two Notes on Grover's Search: Programming and Discriminating
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• Model-Independent Simulation Complexity of Complex Quantum Dynamics
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• Classical bounds on two-outcome bipartite Bell expressions and linear prepare-and-measure witnesses: Efficient computation in parallel environments such as graphics processing units
• Orthogonal Projections on Hyperplanes Intertwined With Unitaries
• Device-independent dimension leakage null test on qubits at low operational cost