Quantum Markov Chains and Conditional Independence
Quantum Markov chains describe memoryless quantum processes and states with conditional independence. Their structure and applications.
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Tagged: Quantum Information Theory
69 articles
Squashed Entanglement and Its Useful Properties
Squashed entanglement is an entanglement measure with useful properties such as additivity and monogamy. Its definition and applications.
Strong Subadditivity: The Hardest Entropy Inequality
Strong subadditivity, proved by Lieb and Ruskai in 1973, is the key inequality of quantum entropy. Its statement, proof ideas and uses.
Quantum Subadditivity of Entropy, Explained
Subadditivity says the entropy of a whole is at most the sum of its parts. How it works for quantum systems and what entanglement changes.
The Quantum Asymptotic Equipartition Property
The quantum asymptotic equipartition property says that many copies of a state concentrate on a typical subspace. Why it underlies compression.
The No-Cloning Theorem: The Proof in Three Lines
The no-cloning theorem forbids copying an unknown quantum state, and its proof takes only a few lines of linear algebra. Proof and consequences.
Quantum Decoherence: Why Quantum States Break Down
Decoherence is the loss of quantum behavior through interaction with the environment. Causes, time scales, experiments and mitigation.
Quantum Markov Models and Hidden State Inference
Quantum Markov models and hidden quantum Markov models describe processes with quantum states. Transitions, inference and applications.
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.
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.
