Question

On general Hilbert spaces, measurements are formalized using a measure that assigns subsets to these operators. For 10 points each:
[10m] Name these operators that can be expressed as sums of outer products. The probability of measuring a given value for an observable can be computed by constructing one of these idempotent operators, which map a state onto a desired subspace.
ANSWER: projection operators [accept projection-valued measure]
[10h] For a generic state, this object can be written as a convex combination of projection operators. The expectation value of an observable A can be written as the trace of the following: this object times A.
ANSWER: density matrix [or density operator; prompt on rho]
[10e] By the completeness relation, the sum of the projection operators for each eigenspace is this matrix. This matrix is a diagonal matrix whose diagonal entries are all equal to one.
ANSWER: identity matrix [prompt on I]
<RA, Physics>

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Johns HopkinsGeorge Washington B1001020