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sindhuja

- 3

- 2

" Let V be the N = 2^n dimensional vector space associated with an n-qubit system. Any device that measures this system has an associated direct sum decomposition into orthogonal subspaces V = S1 ⊕ · · · ⊕ Sk for some k ≤ N. The number k corresponds to the maximum number of possible measurement outcomesfor a state measured with that particular device."

Could anyone explain the intuition behind this statement. I think it is a quiet simple beginner level concept which I have not been getting a satisfactory explanation for. Thank you!