Quantum K-Means Clustering and Its Speedup
Quantum versions of k-means clustering, how they compute distances between points, the claimed speedups and the data loading caveat.
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Quantum Stein’s Lemma and Asymptotic Testing
Quantum Stein’s lemma sets the optimal error exponent for telling two quantum states apart, given by the quantum relative entropy.
Entropic Uncertainty Relations, Explained
Entropic uncertainty relations express the uncertainty principle with entropies instead of standard deviations. Their forms, tests and uses.
Quantum Divergence Measures Between States
Divergences between quantum states, including relative entropy, fidelity, trace distance and Jensen-Shannon divergence, and where each is used.
Quantum Measurement Entropy and Information Gain
How measurement relates to entropy and information gain in quantum systems, and what uncertainty relations say about the trade-offs.
Renyi Entropies and Their Quantum Versions
Rényi entropies generalize Shannon and von Neumann entropy with a parameter alpha. Definitions, properties and uses in entanglement studies.
POVM: Measurement Beyond Projective Operators
Positive operator-valued measures describe the most general quantum measurements. Their definition, properties and uses beyond projective measurements.
Quantum Measurement Theory: What Collapse Means
Quantum measurement theory: observables, measurement operators, collapse, decoherence and the measurement problem, with the Zeno and eraser effects.
The Superposition Principle: Linearity in Quantum
The superposition principle says any linear combination of quantum states is also a valid state. History, examples, experiments and uses.
The No-Deleting Theorem: The Other Side of Cloning
The no-deleting theorem shows that one of two copies of an unknown quantum state cannot be deleted against the other. Meaning and consequences.
The No-Cloning Theorem and Why It Holds
The no-cloning theorem, proved by Wootters, Zurek and Dieks in 1982, forbids copying an unknown quantum state. The proof and its consequences.
Quantum Cloning: Approximate Copying Machines
Perfect cloning is impossible, but approximate quantum cloning machines can make imperfect copies. Types, fidelity limits and experiments.