Quantum Computing
Foundations of qubits — superposition, entanglement, measurement, no free signaling.
Mechanisms
Measure and the slit chooses
Measurement is apparatus choosing a slit story — not a gentle peek.
The qubit can then optionally be measured, in which case either of the states |0⟩ and |1⟩ is observed, as the measurement apparatus detects through which slit the photon passes.
Why it matters
Measurement is apparatus choosing a slit story — not a gentle peek.
Use when: When "observe" is used as if it were free.
Unmeasured qubit keeps interference
Superposition is useful only while uncollapsed — interference is the payload.
If a measurement is not taken, the qubit will be in a superposition of |0⟩ and |1⟩, and its onward evolution can involve the interference of these two components.
Why it matters
Superposition is useful only while uncollapsed — interference is the payload.
Use when: When explaining why you cannot peek mid-algorithm without killing the advantage.
Unitary as Bloch-sphere map
Gates are rigid rotations of the sphere — no leaking off the surface.
As a single-qubit unitary maps a single-qubit state to another single-qubit state, a unitary transformation is itself an operation that maps all of the points on the surface of the Bloch sphere to other points on the surface of the Bloch sphere.
Why it matters
Gates are rigid rotations of the sphere — no leaking off the surface.
Use when: When visualizing quantum ops as geometry, not algebra.
Arguments
Collapse kills superluminal signaling fantasy
Entanglement plus local measurement does not give Bob Alice's message — only shared randomness after collapse.
Whereas if Alice has measured her qubit, then Bob's qubit has collapsed – it is either in state 0, or state 1 (each with probability 1/2).
Why it matters
Entanglement plus local measurement does not give Bob Alice's message — only shared randomness after collapse.
Use when: When someone claims spooky action equals a phone.
Definitions
n-qubit state as 2^n complex unit vector
Dimension explodes as 2^n — the cost of the state space is the feature.
Together, postulates 1 and 4 state that an n-qubit quantum state is represented by a 2^n-element complex unit vector.
Why it matters
Dimension explodes as 2^n — the cost of the state space is the feature.
Use when: When classical intuition expects linear growth in bits.