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Established physics · Quantum Foundations Bridge · Q3 of 3

Entanglement and no-signaling

A shared quantum state can give strong correlations while each distant observer still sees an uncontrollable local result.

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Picture it

Two laboratories receive the two parts of one entangled pair. Each chooses a measurement direction and records a plus or minus result. For the spin-singlet example, equal directions give opposite results, but neither laboratory chooses its own result. Each local record looks like a fair 50/50 sequence.

More than two matching envelopes

Classical matching envelopes can also give correlations. Entanglement is a joint quantum state that cannot be written as independent states for its parts. Suitable entangled states, tested with different measurement settings, can violate Bell inequalities under the assumptions those tests examine. One matching setting alone does not demonstrate this.

What changes and what stays fixed

Changing a measurement direction changes the joint statistics: how the two lists compare. It does not change the remote observer’s unconditioned 50/50 probabilities in the singlet example. This difference between joint and local statistics is the key to no-signaling.

Why comparison needs an ordinary channel

After the experiment, the laboratories compare settings and results by an ordinary communication channel. They can then sort into correlated subsets. Until that information arrives, the remote laboratory has only its own local list. A correlation revealed by comparison is not a controllable message.

Conditioning is not remote control

Once Alice reports a result, Bob can make a different prediction for the corresponding subset. Alice cannot select which result she obtains. Discarding selected trials also does not help Bob until Alice tells him which trials to keep.

One careful technical level

For ideal spin-½ measurements on a singlet, with outcomes a and b each equal to +1 or −1, P(a,b | α,β) = [1 − ab cos(α − β)]/4. Summing over Alice’s outcomes gives P(b | α,β) = 1/2 for every α. The demonstration calculates this joint table; it is not a hidden-variable mechanism or a Bell-test data simulation.

Work one example

With equal measurement directions, P(+,+) = P(−,−) = 0 and P(+,−) = P(−,+) = 1/2. Bob still sees plus half the time and minus half the time. With directions 90° apart, all four joint outcomes have probability 1/4; Bob’s local odds are unchanged.

Read the demonstration

Equal spin directions: opposite outcomes are certain, but each local sign is 50/50. Directions 90° apart: the four joint outcomes are equally likely, and each local sign remains 50/50.

Keep this: The joint pattern can depend on both settings while the remote local odds remain unchanged. Correlation and controllable communication are different things.

Check your understanding

For a singlet measured along the same direction, what does Bob alone see?

  1. A 50/50 plus/minus sequence
  2. Alice’s chosen message
  3. Only minus results
Answer and explanation

A 50/50 plus/minus sequence

The pair has opposite results, but Bob’s own marginal probabilities are 50/50.

Can Alice choose her individual measurement result to signal Bob?

  1. Yes
  2. No
  3. Only if the laboratories are close
Answer and explanation

No

Alice can choose a setting, but cannot choose the random result needed to encode that message.

What is needed to identify correlated subsets in two saved result lists?

  1. An ordinary exchange of settings and results
  2. A conscious collapse command
  3. Only Bob’s result list
Answer and explanation

An ordinary exchange of settings and results

Comparing the records requires ordinary communication; the remote local list contains no selected-subset labels.

What can suitable Bell tests establish?

  1. Nonclassical correlations violating a Bell bound under its assumptions
  2. A usable faster-than-light channel
  3. A proof that every possible deeper description is excluded
Answer and explanation

Nonclassical correlations violating a Bell bound under its assumptions

Bell bounds constrain explanations with particular assumptions. Their violation does not enable signaling or rule out every possible ontology.

Further reading

MIT OpenCourseWare: Quantum Physics I lecture notes · Quantum Physics III: entanglement and decoherence notes