von Neumann measurement scheme
E87774
The von Neumann measurement scheme is a foundational formalism in quantum mechanics that models measurements as interactions between a quantum system and an apparatus, leading to probabilistic outcomes and state collapse.
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
concept in quantum mechanics
→
model of quantum measurement → quantum measurement theory formalism → |
| addresses | relationship between microscopic system and macroscopic apparatus → |
| appliesTo |
continuous-spectrum observables
→
discrete-spectrum observables → |
| assumes |
closed quantum system plus apparatus before measurement
→
unitary evolution of combined system and apparatus during interaction → |
| characterizes |
ideal measurements as repeatable
→
measurements by orthogonal projectors → |
| contrastsWith | generalized measurement (POVM) schemes → |
| coreIdea |
measurement as interaction between system and apparatus
→
probabilistic measurement outcomes → state collapse postulate → |
| describedIn | Mathematical Foundations of Quantum Mechanics → |
| describes | ideal projective measurement → |
| field |
mathematical physics
→
quantum foundations → quantum mechanics → |
| formalizes | observables as self-adjoint operators on Hilbert space → |
| formulatedBy | John von Neumann → |
| influenced |
development of POVM formalism
→
modern quantum information theory treatments of measurement → |
| involves |
entanglement between system and apparatus
→
measurement interaction Hamiltonian → pointer states of measuring apparatus → |
| models |
correlation between system eigenstates and apparatus pointer states
→
transition from quantum superposition to definite outcome → |
| namedAfter | John von Neumann → |
| postulates |
Born rule in quantum mechanics
→
surface form: "Born rule for outcome probabilities"
non-unitary state collapse after measurement → |
| provides | mathematical framework for quantum measurement postulates → |
| relatesTo |
Copenhagen interpretation of quantum mechanics
→
measurement problem in quantum mechanics → projection postulate → wave function collapse → |
| states |
measurement outcomes correspond to eigenvalues of observables
→
post-measurement state is eigenstate associated with observed eigenvalue → |
| timePeriod | 1930s → |
| usesConcept |
Hilbert space
→
eigenvalue → eigenvector → projection operator → self-adjoint operator → spectral decomposition → tensor product of Hilbert spaces → |
Referenced by (1)
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