Superposition is not a readable list of classical answers

A qubit can be written as |ψ⟩ = α|0⟩ + β|1⟩, with |α|² + |β|² = 1. A measurement in this basis returns 0 or 1 with probabilities |α|² and |β|². Relative phase can affect interference, so a coherent superposition is not merely a classical mixture caused by ignorance. But a measurement produces a classical outcome; it does not expose all amplitudes at once. IBM Quantum Learning describes measurement as selecting one basis state with its corresponding probability.

Read the Bell-state labels carefully

The two-qubit state |Φ+⟩ = (|00⟩ + |11⟩)/√2 yields 00 or 11 in the standard basis, each with probability one half. By contrast, |Ψ+⟩ = (|01⟩ + |10⟩)/√2. Thus the sum of 00 and 11 is Φ+, not Ψ+. Entanglement describes joint correlations; it does not let one observer choose a remote outcome and send a message through it.

Bell, CHSH, and what an experiment measured

Bell’s 1964 paper examined how locality constrains hidden-variable explanations of quantum statistics. The experimentally oriented CHSH proposal was published by Clauser, Horne, Shimony, and Holt in 1969; these are distinct works. In the CHSH setup, local hidden-variable models obey |S| ≤ 2, while quantum theory permits a maximum of 2√2. That is a theoretical bound, not the value every experiment must measure and not a promise of perfect correlations. IBM Quantum’s CHSH tutorial derives the classical bound and quantum ceiling and shows noisy simulator and hardware results below the maximum. Aspect, Dalibard, and Roger reported a 1982 photon-polarization experiment using time-varying analyzers; its measured correlations agreed with quantum predictions and violated Bell inequalities by five standard deviations. The paper abstract reports that result rather than claiming every run reached the quantum maximum.

A worked measurement example and its limits

Prepare |Φ+⟩ and measure both qubits once in the standard basis: the record is either 00 or 11. Under ideal preparation and measurement, repeated trials approach equal frequencies, but a finite sample need not split exactly 50–50. Measuring in a different basis changes the correlation pattern. An n-qubit state may have 2ⁿ basis amplitudes in its mathematical description, but one readout does not return 2ⁿ answers. Algorithms must arrange interference and measurement so useful statistics can be extracted; hardware noise also affects outcomes.

Quantum teleportation combines a shared entangled pair, a measurement on the input, classical bits sent to the receiver, and a receiver-side correction. The input is measured, the receiver needs the classical message before applying the correction, and the protocol therefore neither preserves a second copy nor enables faster-than-light communication. This is an idealized protocol outline, not a hardware-performance or universal security guarantee. See IBM Quantum’s teleportation lesson.

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