Quantum superposition information

Quantum superposition of states and decoherence

Quantum superposition is a fundamental principle of quantum mechanics that states that linear combinations of solutions to the Schrödinger equation are also solutions of the Schrödinger equation. This follows from the fact that the Schrödinger equation is a linear differential equation in time and position. More precisely, the state of a system is given by a linear combination of all the eigenfunctions of the Schrödinger equation governing that system.

An example is a qubit used in quantum information processing. A qubit state is most generally a superposition of the basis states $|0\rangle$ and $|1\rangle$ :

|\Psi \rangle =c_{0}|0\rangle +c_{1}|1\rangle ,

where $|\Psi \rangle$ is the quantum state of the qubit, and $|0\rangle$ , $|1\rangle$ denote particular solutions to the Schrödinger equation in Dirac notation weighted by the complex numbers $c_{0}$ and $c_{1}$ . Here $|0\rangle$ corresponds to the classical 0 bit, and $|1\rangle$ to the classical 1 bit. The probabilities of measuring the system in the $|0\rangle$ or $|1\rangle$ state are given by $|c_{0}|^{2}$ and $|c_{1}|^{2}$ respectively (see the Born rule).

The interference fringes in the double-slit experiment provide another example of the superposition principle.

Quantum superposition information

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$i\hbar {\frac {d}{dt}}\|\Psi \rangle ={\hat {H}}\|\Psi \rangle$ Schrödinger equation
Introduction Glossary History
Background Classical mechanics Old quantum theory Bra–ket notation Hamiltonian Interference
Fundamentals Complementarity Decoherence Entanglement Energy level Measurement Nonlocality Quantum number State Superposition Symmetry Tunnelling Uncertainty Wave function Collapse
Experiments Bell's inequality Davisson–Germer Double-slit Elitzur–Vaidman Franck–Hertz Leggett–Garg inequality Mach–Zehnder Popper Quantum eraser Delayed-choice Schrödinger's cat Stern–Gerlach Wheeler's delayed-choice
Formulations Overview Heisenberg Interaction Matrix Phase-space Schrödinger Sum-over-histories (path integral)
Equations Dirac Klein–Gordon Pauli Rydberg Schrödinger
Interpretations Bayesian Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Local Superdeterminism Many-worlds Objective collapse Quantum logic Relational Transactional Von Neumann–Wigner
Advanced topics Relativistic quantum mechanics Quantum field theory Quantum information science Quantum computing Quantum chaos EPR paradox Density matrix Scattering theory Quantum statistical mechanics Quantum machine learning
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