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arXiv:2605.16093

Unbounded Communication Power of a Qubit

Souradeep Sasmal, Som Kanjilal, Debarshi Das

quant-phSubmitted May 15, 2026• Announced May 18, 2026• 0 citations
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Abstract

Quantum mechanics enables information-processing advantages even at the level of a single qubit. A paradigmatic example is the 2$\to$1 random access code (RAC), where a qubit outperforms a classical bit in retrieving encoded information. In the standard form, however, this quantum advantage is restricted to a single receiver, since decoding measurements inevitably destroy the encoded information. Contrary to this, we address how long the information encoded in a single qubit remains accessible even after multiple decoding, each with a quantum advantage. Introducing preparation distinguishability as an operational resource associated with the sender, we show that its interplay with measurement incompatibility on the receiver's side can mitigate measurement-induced disturbance, thereby enabling an arbitrarily long sequence of receivers to each retain a quantum advantage. Our results show that, even under repeated measurements, the information encoded in a qubit need not be entirely exhausted, revealing a stronger communication feature than previously recognised.

Comments
Preliminary draft. Comments welcome

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Quantum mechanics enables information-processing advantages even at the level of a single qubit. A paradigmatic example is the 2→\to→1 random access code (RAC), where a qubit outperforms a classical bit in retrieving encoded information. In the standard form, however, this quantum advantage is restricted to a single receiver, since decoding measurements inevitably destroy the encoded information. Contrary to this, we address how long the information encoded in a single qubit remains accessible even after multiple decoding, each with a quantum advantage. Introducing preparation distinguishability as an operational resource associated with the sender, we show that its interplay with measurement incompatibility on the receiver's side can mitigate measurement-induced disturbance, thereby enabling an arbitrarily long sequence of receivers to each retain a quantum advantage. Our results show that, even under repeated measurements, the information encoded in a qubit need not be entirely exhausted, revealing a stronger communication feature than previously recognised.
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Abstract A random access code (RAC), corresponding to a communication primitive with various applications in quantum information theory, is an instance of a preparation-and-measurement scenario. In this work, we consider (n, d)-RACs constituting an n-length string, constructed from a d size set of letters, and send an encoding of the string in a single d-level physical system and present their quantum advantages. We first characterize optimal classical RACs and prove that a known classical strategy, called majority-encoding-identity-decoding, is optimal. We then construct a quantum protocol by exploiting only two incompatible measurements (the minimal requirement) and show the advantages beyond the classical one. We also discuss the generality of our results and whether quantum advantages are valid for all types of ( n , d ) ↦ 1 RACs.
A random access code (RAC) is an important communication protocol to obtain information about a randomly specified substring of an nnn-bit string, while only having limited information about the nnn-bit string. Quantum RACs usually utilize either communication of quantum bits or a shared-in-advance quantum state used in conjunction with classical communication. Here we consider the latter version of the quantum protocols under the constraint of single-bit communication and with a shared arbitrary state of two qubits. Taking the worst-case success probability as the figure of merit, we demonstrate that any state with an invertible correlation matrix can be used to outperform the best classical RAC for n=3n=3n=3. We derive an additional condition sufficient to beat the best classical performance in the case of n=2n=2n=2. In particular, separable states turn out to be a useful resource behind the quantum advantage for n=2,3n=2,3n=2,3. For $n\ensuremath{\ge}4$, RACs assisted with a single copy of a quantum state do not outperform the classical RACs.
Measurement incompatibility stipulates the existence of quantum measurements that cannot be carried out simultaneously on single systems. We show that the set of input-output probabilities obtained from ddd-dimensional classical systems assisted with shared randomness is the same as the set obtained from ddd-dimensional quantum strategies restricted to compatible measurements with shared randomness in any communication scenario. Thus, measurement incompatibility is necessary for quantum advantage in communication, and any quantum advantage (with or without shared randomness) in communication acts as a witness to the incompatibility of the measurements at the receiver's end in a semi-device-independent way. We introduce a class of communication tasks---a general version of random access codes---to witness incompatibility of an arbitrary number of quantum measurements with arbitrary outcomes acting on ddd-dimensional systems and provide generic upper bounds on the success metric of these tasks for compatible measurements. We identify all sets of three incompatible rank-one projective qubit measurements that random access codes can witness. Finally, we present the generic relationship between different sets of probability distributions---classical, quantum with or without shared randomness, and quantum restricted to compatible measurements with or without shared randomness---produced in communication scenarios.
Useful applications of quantum information technologies can be found by identifying tasks in which quantum resources outperform their classical counterparts. In this work, we introduce a two-party communication primitive, random exclusion code (REC), which is a single-shot prepare-and-measure protocol where a sender encodes a random message into a shorter sequence and a receiver attempts to a randomly chosen letter in the original message. We present quantum advantages in RECs in two ways: and . We show that RECs with quantum resources achieve higher success probabilities than classical strategies. We verify that, with the additional constraint that successful outcomes occur uniformly and without error, the quantum resources required to describe detection events of RECs have a smaller dimension than classical ones. We also show that a guessing counterpart, random access codes, may not have a dimension advantage over classical resources. Our results elucidate various possibilities of achieving quantum advantages in two-party communication.