Past exam of the quantum information course of the University of Cambridge 2014 Paper 1 3 c Solution 2026-10-20
Schrödinger's cat exposes the quantum measurement problem by correlating a microscopic alternative with macroscopically distinct records. Under unitary evolution a schematic state becomesThe difficulty is explaining why a definite macroscopic outcome is observed if the isolated total state is always governed by the linear Schrödinger equation. It is not a claim that one classically contradictory record has literally been observed. Environmental interactions rapidly entangle the records with different environment states, making their reduced density matrix approximately diagonal. That explains the practical loss of interference but does not, by itself, turn a global pure superposition into a selected single branch.
Wigner's friend places an observer's physical memory inside the quantum description. A friend measuring can become correlated asConditioned on one friend record, the corresponding relative state contains a definite outcome. An external observer applying unitary theory to the perfectly isolated entire laboratory instead assigns the entangled vector . In principle, a coherent joint measurement could distinguish it from the collapsed mixturewhereas projecting the pure state onto succeeds with probability one. Preserving that laboratory coherence, including all records and environment correlations, is an extreme idealization for macroscopic observers.
The paradox concerns how state assignment, definite records and universal unitary dynamics fit together. It does not show that an observer can send messages faster than light or that consciousness must be given a special dynamical role. The many-worlds interpretation retains the global unitary state with branch-relative records; interpretations with a physical collapse must specify when and how unitary evolution changes. Stating the chosen assumptions prevents the friend's conditional state and the external observer's unconditioned state from being treated as the same mathematical object.