The smallest information amount {bit, information} involves one position that can have two equally probable states, so states have probability 1/2. If one position has one possible state, state probability is 1, but this situation has no differences and no information. If one position has three equally probable states, states have probability 1/3, requiring 1.5 information bits. If one position has four equally probable states, states have probability 1/4, requiring two information bits. If two positions each have two equally probable states, pairs have probability 1/4, requiring two information bits.
Smallest quantum-information amount {quantum bit}| {qubit} involves 0 and 1 superposition.
model
Sphere points, with 0 and 1 at pole, can represent superposition. Sphere points have probabilities of obtaining 0 or 1 at decoherence.
information
Qubits have one quantum information bit {Holevo chi}, because output is 0 or 1 after decoherence. This information bit is quantum equivalent of information-theory information bit (Shannon).
entanglement
Quantum particles can be in systems with overall quantum states, so quantum-particle states interact by entanglement.
decoherence
Isolated systems can maintain quantum states, as in superconductivity and quantum Hall effect. Measurements, gravity, and other interactions with larger systems can collapse wavefunctions and cause wave decoherence.
uses
Quantum states can teleport, because entanglement can transfer to another quantum system. Quantum states can use entanglement for cryptography keys. Quantum-mechanical computers use entangled qubits. Quantum computers can find integer prime factors in same way as finding quantum-system energy levels. Quantum error correction can eliminate noise and random interactions of quantum system with environment, by correcting states without knowing what they are. However, unknown-state quantum bit cannot duplicate.
3-Information Theory-Information
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Date Modified: 2022.0225