Quantum Depolarizing Channels: The Standard Noise
The depolarizing channel replaces a state with the maximally mixed state with some probability. Its representation, properties and uses as a noise model.
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Quantum Dephasing Channels and Phase Noise
Dephasing channels destroy phase coherence while leaving populations intact. Their mathematical description, effects and mitigation.
Entanglement Witnesses: Detecting Entanglement
Entanglement witnesses are observables that detect entanglement without full tomography. How they are built and used in experiments.
Quantum Symmetric States and Permutation Invariance
Symmetric states are unchanged when their particles are permuted. Their structure, entanglement properties and uses in computing and cryptography.
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-Broadcasting Theorem for Mixed States
The no-broadcasting theorem extends no-cloning to mixed states: non-commuting states cannot be broadcast. Its statement, proof and uses.
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 Entanglement: What It Is and What It Is Not
What quantum entanglement is and what it is not: its history, Bell tests, applications, and why it cannot be used to send signals faster than light.
Quantum Deep Learning: Depth on Real Hardware
What deep learning on quantum hardware looks like today: quantum neural networks, hybrid models, training algorithms and depth limits.