QUANTUM MEASUREMENT &
FOUNDATIONS EXAM QUESTION AND
CORRECT ANSWERS (VERIFIED
ANSWERS) PLUS RATIONALES 2026 Q&A
INSTANT DOWNLOAD PDF
1. The Born rule states that the probability of a measurement outcome is
given by
A. The eigenvalue itself
B. The expectation value
C. The squared modulus of the projection of the state onto the eigenstate
D. The trace of the Hamiltonian
Answer: C
Rationale: The Born rule assigns probabilities as the squared magnitude of the
inner product between the state vector and the eigenstate of the observable.
2. A quantum observable is mathematically represented by
A. A vector
B. A scalar
C. A Hermitian operator
D. A unitary matrix
Answer: C
Rationale: Hermitian operators ensure real eigenvalues corresponding to
measurable quantities.
3. Wavefunction collapse occurs when
A. The system evolves unitarily
, B. The Hamiltonian changes
C. A measurement is performed
D. Time reverses
Answer: C
Rationale: Collapse is postulated to occur during measurement, projecting the
state onto an eigenstate.
4. Which interpretation treats the wavefunction as a complete description of
reality?
A. Statistical interpretation
B. Copenhagen interpretation
C. Ensemble interpretation
D. Relational interpretation
Answer: B
Rationale: The Copenhagen view considers the wavefunction as the complete
description until measurement.
5. In a projective measurement, the post-measurement state is
A. A mixed state
B. The original state
C. An eigenstate of the measured observable
D. A coherent superposition
Answer: C
Rationale: Projective measurements collapse the system into an eigenstate
corresponding to the measured eigenvalue.
6. Which condition ensures two observables are simultaneously measurable?
A. Equal eigenvalues
B. Degeneracy
C. They commute
D. They are unitary
, Answer: C
Rationale: Commuting operators share a common eigenbasis, allowing
simultaneous measurement.
7. The measurement postulate introduces which fundamental feature absent
from Schrödinger evolution?
A. Linearity
B. Determinism
C. Non-unitarity
D. Continuity
Answer: C
Rationale: Collapse is non-unitary, unlike Schrödinger time evolution.
8. POVMs generalize projective measurements by allowing
A. Only orthogonal projectors
B. Deterministic outcomes
C. Non-orthogonal measurement operators
D. Classical probabilities
Answer: C
Rationale: POVMs include effects that are not orthogonal projectors, modeling
realistic measurements.
9. A mixed quantum state is best represented by
A. A wavefunction
B. A projector
C. A density operator
D. A unitary matrix
Answer: C
Rationale: Density operators describe statistical mixtures of pure states.
10.The trace of a density matrix equals
A. Zero
B. The energy
FOUNDATIONS EXAM QUESTION AND
CORRECT ANSWERS (VERIFIED
ANSWERS) PLUS RATIONALES 2026 Q&A
INSTANT DOWNLOAD PDF
1. The Born rule states that the probability of a measurement outcome is
given by
A. The eigenvalue itself
B. The expectation value
C. The squared modulus of the projection of the state onto the eigenstate
D. The trace of the Hamiltonian
Answer: C
Rationale: The Born rule assigns probabilities as the squared magnitude of the
inner product between the state vector and the eigenstate of the observable.
2. A quantum observable is mathematically represented by
A. A vector
B. A scalar
C. A Hermitian operator
D. A unitary matrix
Answer: C
Rationale: Hermitian operators ensure real eigenvalues corresponding to
measurable quantities.
3. Wavefunction collapse occurs when
A. The system evolves unitarily
, B. The Hamiltonian changes
C. A measurement is performed
D. Time reverses
Answer: C
Rationale: Collapse is postulated to occur during measurement, projecting the
state onto an eigenstate.
4. Which interpretation treats the wavefunction as a complete description of
reality?
A. Statistical interpretation
B. Copenhagen interpretation
C. Ensemble interpretation
D. Relational interpretation
Answer: B
Rationale: The Copenhagen view considers the wavefunction as the complete
description until measurement.
5. In a projective measurement, the post-measurement state is
A. A mixed state
B. The original state
C. An eigenstate of the measured observable
D. A coherent superposition
Answer: C
Rationale: Projective measurements collapse the system into an eigenstate
corresponding to the measured eigenvalue.
6. Which condition ensures two observables are simultaneously measurable?
A. Equal eigenvalues
B. Degeneracy
C. They commute
D. They are unitary
, Answer: C
Rationale: Commuting operators share a common eigenbasis, allowing
simultaneous measurement.
7. The measurement postulate introduces which fundamental feature absent
from Schrödinger evolution?
A. Linearity
B. Determinism
C. Non-unitarity
D. Continuity
Answer: C
Rationale: Collapse is non-unitary, unlike Schrödinger time evolution.
8. POVMs generalize projective measurements by allowing
A. Only orthogonal projectors
B. Deterministic outcomes
C. Non-orthogonal measurement operators
D. Classical probabilities
Answer: C
Rationale: POVMs include effects that are not orthogonal projectors, modeling
realistic measurements.
9. A mixed quantum state is best represented by
A. A wavefunction
B. A projector
C. A density operator
D. A unitary matrix
Answer: C
Rationale: Density operators describe statistical mixtures of pure states.
10.The trace of a density matrix equals
A. Zero
B. The energy
