Passing a qubit along can beat splitting it—but the task matters

Two ways to share quantum information

Quantum measurements can disturb the system being measured. That creates a challenge when several receivers want to extract useful information from the same preparation: an early observer’s gain can reduce what remains for others.

Satyaki Manna, Arindam Mitra and Sumit Mukherjee compare two approaches in an arXiv preprint. In sequential sharing, observers measure a quantum system in turn and pass the resulting system onward. Carefully chosen measurements can leave useful information for later observers. In parallel sharing, a quantum channel converts the original system into several outputs, which receivers measure separately.

These outputs are not perfect copies of an arbitrary quantum state. The study explicitly works within quantum broadcasting’s limitations, allowing imperfect distribution instead.

This is a theoretical investigation based on mathematical proofs and explicit protocols, not a reported laboratory experiment. The supplied manuscript is an arXiv preprint; the evidence does not establish peer-reviewed publication.

Two receivers and three receivers behave differently

The authors first compare the complete outcome probabilities the two arrangements can produce. They hold the communicated system’s dimension fixed: each receiver gets a system with the same number of quantum levels as the original.

For two receivers, they prove that every parallel strategy can be reproduced sequentially. The construction combines the broadcasting operation and the first receiver’s measurement into one quantum instrument—an operation describing both a measurement outcome and the state left afterward.

The reverse does not hold. In a sequential chain, the first observer’s measurement choice can affect what the second receives. Separate parallel receivers cannot influence one another’s outcome probabilities merely by changing their local measurement choices.

With three receivers, however, parallel strategies can generate statistics that a fixed-dimension sequential chain cannot reproduce. The authors construct an example that sends the original qubit to the middle receiver and distributes an entangled pair to the first and third. Matching the middle receiver’s perfect discrimination of specified states leaves the sequential chain unable to reproduce the required correlations between the other two.

That resource detail matters: this example uses an entangled pair supplied by the broadcasting channel. It is not three imperfect copies of the input, and the separation depends on restricting what each sequential observer can forward.

When simultaneous advantage is impossible

The paper next considers communication tasks scored by a weighted sum of outcome probabilities. Here, quantum advantage means exceeding the best classical score under the stated communication constraints—not faster computing or greater energy efficiency.

For tasks with two decoding measurement choices, the authors prove that two parallel receivers cannot both exceed the corresponding classical bound. Their argument uses measurement compatibility: measurements on different outputs can be represented as jointly measurable operations on the input, which restricts their combined performance.

A concrete example is a random access code. A sender receives a string and communicates a limited-size message; a receiver is asked to guess one randomly selected entry. For two input bits encoded into one qubit, parallel sharing cannot give two receivers an advantage over the classical benchmark.

The authors contrast this with a cited sequential protocol allowing arbitrarily many receivers to obtain an advantage in that task. The resulting gap concerns the number of advantaged receivers. It does not establish an arbitrarily large improvement in each receiver’s guessing accuracy.

They also rule out simultaneous parallel advantage for the ordinary three-bit, one-bit-message random access code, whose classical success limit is 75%.

A restriction changes the benchmark

Parallel sharing does work in the three-bit parity-oblivious variant. Here, the message must reveal nothing about the parity—whether the sum is odd or even—of any subset containing two or more input bits.

This additional rule lowers the classical success limit to two-thirds. The authors encode the three-bit strings into qubit states and apply a universal quantum cloning channel. Each receiver measures one imperfect clone according to which bit they must guess.

For symmetric cloning, their calculation gives each receiver a success probability of approximately 69.245%, above two-thirds. That same score would not beat the ordinary game’s 75% benchmark. The advantage therefore depends crucially on comparing strategies under the same parity restriction.

What remains open

The work supplies task-specific limits and a two-receiver construction, not a universal ranking of all quantum networks. For more measurement choices, its general bound does not always settle whether parallel advantage is possible. Characterizing useful broadcasting channels and exploring other resource constraints remain open directions.

The central lesson is that sharing quantum advantage depends jointly on measurement disturbance, communication resources and the rules defining the classical comparison.