Waiting to measure can unlock an unbounded quantum communication advantage

What changes when the receiver waits?

Suppose Alice and Bob share an entangled quantum state. Alice receives an input and sends Bob a classical message. Bob must then produce an answer. Their shared entanglement can help reduce the communication needed, but there are two different ways to use it.

In a non-adaptive protocol, Bob’s quantum measurement does not depend on Alice’s message. He can use that message afterward to process his measurement outcome classically. In an adaptive protocol, he can instead wait and let the message determine which quantum measurement he performs.

Armin Tavakoli, of Lund University, studies how far apart these approaches can be. His theoretical preprint, submitted to arXiv on November 8, 2026, presents an unbounded separation across a growing family of tasks. It reports mathematical proofs, not an experimental demonstration. The supplied record does not establish peer-reviewed publication.

A game of avoiding forbidden answers

The construction is an exclusion game. Alice receives a set of forbidden labels, and Bob must output a label outside it. Bob has no separate input.

For any positive integer M, the forbidden set contains M labels. Each label combines one of three choices with an index running through R possibilities, where R = M² + 1.

The classical obstacle is simple. Fix any shared randomness in a protocol whose message has only M possible values. Bob then has at most M corresponding answers available. One allowed forbidden set contains all those answers, so Alice cannot send any message that makes him succeed on that input. Shared randomness cannot turn such strategies into a protocol that always succeeds.

Because Bob has no independent input, non-adaptive entanglement-assisted protocols are equivalent here to classical communication with shared randomness. The same impossibility therefore applies to them.

Tavakoli constructs an adaptive solution using a maximally entangled state of local dimension R and three mutually unbiased measurement bases. Alice’s measurement is designed so that, after she sends its outcome, Bob’s corresponding measurement cannot produce a forbidden label.

Only one classical message is transmitted, with three possible values: a trit. This does not mean three separate transmissions. For every M, this three-valued adaptive message succeeds on a task that an M-valued non-adaptive message cannot solve exactly.

The unbounded result concerns the family as M grows, not an infinite communication requirement for each individual finite game. The paper also identifies the construction as a counterexample to a conjecture that d entanglement-assisted message values could always be simulated using d² classical values.

Finite entanglement puts a ceiling on the gap

The advantage has an important resource requirement. Every adaptive protocol using finite-dimensional entanglement admits an exact non-adaptive simulation with a finite message alphabet.

When Bob has no independent input, the paper gives the bound M ≤ dR: the simulator needs no more than d times Bob’s entanglement dimension in possible message values. For scenarios where Bob also receives an input, the supplementary material establishes a finite bound depending only on d and R, although the construction is much more costly and is not claimed to be optimal.

Thus, an unbounded advantage cannot come from holding both the adaptive message alphabet and entanglement dimension fixed.

Small errors sharply limit the separation

A second limitation comes from relaxing exactness. Bob can guess Alice’s message in advance and perform the corresponding measurement on each of several independent copies of their shared state. Alice then sends the index of the first correct guess. If none succeeds, she sends a failure flag and Bob supplies a locally chosen output.

Increasing the number of copies makes that failure less likely. The resulting non-adaptive message alphabet scales as O(d log(1/ε)), where ε measures the worst-case total-variation error between output distributions.

For example, the paper shows that any three-valued adaptive protocol can be simulated to error at most one millionth using 36 non-adaptive message values. Whether the general scaling is optimal remains open. A nonzero mixture of output noise independent of Alice’s input also permits finite-cost exact simulation.

The result therefore establishes an idealized separation, not a demonstrated practical communication system. Very large advantages require high-dimensional entanglement and exceptionally precise observations. The manuscript also discloses that its technical results originated from ChatGPT-6 Astra; Tavakoli states that he checked them for correctness and assumes responsibility for the content.