We demonstrate superadditivity of one-shot zero-error classical capacity in an asymmetric communication setting where a noisy classical channel is used in parallel with a perfect quantum channel. Each channel individually supports only a fixed number of perfectly distinguishable messages. Their joint use enables transmission of strictly more messages than permitted by the product of the individual capacities. We present explicit constructions achieving this enhancement and establish that replacing the perfect quantum channel with a perfect classical channel eliminates the effect. Finally, we identify a structural criterion on the noisy channel governing this effect and show that the quantum advantage is rooted in Kochen-Specker contextuality.
We demonstrate superadditivity of one-shot zero-error classical capacity in an asymmetric communication setting where a noisy classical channel is used in parallel with a perfect quantum channel. Each channel individually supports only a fixed number of perfectly distinguishable messages. Their joint use enables transmission of strictly more messages than permitted by the product of the individual capacities. We present explicit constructions achieving this enhancement and establish that replacing the perfect quantum channel with a perfect classical channel eliminates the effect. Finally, we identify a structural criterion on the noisy channel governing this effect and show that the quantum advantage is rooted in Kochen-Specker contextuality.
We study the effects of quantum entanglement on the performance of two classical zero-error communication tasks among multiple parties. Both tasks are generalizations of the two-party zero-error channel-coding problem, where a sender and a receiver want to perfectly communicate messages through a one-way classical noisy channel. If the two parties are allowed to share entanglement, there are several positive results that show the existence of channels for which they can communicate strictly more than what they could do with classical resources. In the first task, one sender wants to communicate a common message to multiple receivers. We show that if the number of receivers is greater than a certain threshold then entanglement does not allow for an improvement in the communication for any finite number of uses of the channel. On the other hand, when the number of receivers is fixed, we exhibit a class of channels for which entanglement gives an advantage. The second problem we consider features multiple collaborating senders and one receiver. Classically, cooperation among the senders might allow them to communicate on average more messages than the sum of their individual possibilities. We show that whenever a channel allows single-sender entanglement-assisted advantage, then the gain extends also to the multisender case. Furthermore, we show that entanglement allows for a peculiar amplification of information which cannot happen classically, for a fixed number of uses of the channels.
The zero-error capacity of a noisy classical channel quantifies its ability to transmit information with absolute certainty, i.e., without any error. Unlike Shannon's standard channel capacity, which remains unaffected by pre-shared correlations, zero-error capacity can be enhanced through nonlocal correlations. In this work, we investigate zero-error communication utility of such correlations arising in the 2-2-m Bell scenario, where two parties have two inputs and m possible outcomes per input. For all m\geq2, we construct examples of noisy classical channels with zero zero-error capacity that, when assisted by extremal 2-2-m nonlocal correlations, can transmit one bit of information. While nonlocal correlations arising from quantum entangled states cannot achieve a positive zero-error capacity for these channels, they significantly enhance the probability of successfully transmitting a classical bit in a single use. Extending this analysis to the 2-m-2 Bell scenario, we identify channels with zero zero-error capacity that can nonetheless perfectly transmit log m bits of information when assisted by corresponding extremal nonlocal correlations. Our findings underscore the versatile utility of Bell nonlocal correlations in achieving zero-error communication.
We introduce conclusive identification task for classical channels: a receiver identifies transmitted inputs without error when possible, and responds inconclusively when outputs are ambiguous. For a symmetric not-fully-corrupted channel N:X→X, the single-shot conclusive identification index ci∘(N) counts the maximum number of conclusively identifiable inputs. We show ci∘(N) exhibits a striking superactivation phenomenon: a channel with ci∘(N)=0 achieves ci∘(N⊗idβc)=∣X∣ when assisted by a perfect classical channel of dimension β<∣X∣. The minimum classical assistance required equals the chromatic number χ(SN) of the channel's support graph SN. We provide channel families where the superactivation gap ci∘(N⊗idβc)−ci∘(idβc) can be made arbitrarily large. A noiseless quantum channel of dimension equal to the orthogonal rank ξ(SN) suffices, yielding a strict quantum advantage whenever ξ(SN)<χ(SN). This advantage is demonstrated through three explicit constructions motivated by combinatorial and algebraic state-independent, and state-dependent proofs of Kochen-Specker contextuality. Via the co-normal product of graphs, we analyze the scaling of the quantum advantage ratio χf(SN)/ξ(SN), and present a channel for which quantum assistance is exponentially more efficient than classical. Our results establish SN, rather than the confusability graph GN, as the natural combinatorial object for conclusive identification, revealing that channels deemed useless under Shannon's zero-error framework can exhibit rich superactivation and quantum advantage, with deep connections to quantum contextuality.
Estimating the information transmission capability of a quantum channel remains one of the fundamental problems in quantum information processing. In contrast to classical channels, the information-carrying capability of quantum channels is contextual. One of the most significant manifestations of this is the superadditivity of the channel capacity: the capacity of two quantum channels used together can be larger than the sum of the individual capacities. Here, we present a one-parameter family of channels for which, as the parameter increases, its one-way quantum and private capacities increase while its two-way capacities decrease. We also exhibit a one-parameter family of states with analogous behavior with respect to the one- and two-way distillable entanglement and secret key. Our constructions demonstrate that noise is context dependent in quantum communication. Published by the American Physical Society 2024
Recently the one-shot quantum no-signalling assisted zero-error classical capacity of a quantum channel has been formulated as a semidefinite programming (SDP) depending only on the Choi-Kraus operator space of the channel. In this paper, we study the \textit{activated quantum no-signalling assisted zero-error classical capacity} by first allowing the assistance from some noiseless forward communication channel and later paying back the cost of the helper. We show that the one-shot activated capacity can also be formulated as a SDP and derive a number of striking properties of this number. In particular, this number is additive under direct sum, and is always greater than or equal to the super-dense coding bound. An a remarkable consequence, we find that one bit noiseless classical communication is able to fully activate any classical-quantum channel to achieve its asymptotic capacity, or the semidefinite fractional packing number. We also discuss the condition under which a noisy channel can activate an activatable channel. Interestingly, a channel is able to activate itself if its one-shot capacity is greater than or equal to the Golden Ratio - (1+5)/2. We also show that the asymptotic activated capacity is still equal to the usual no-signalling assisted capacity. Finally, we show that general the asymptotic no-signalling assisted zero-error capacity does not equal to the semidefinite (fractional) packing number by an explicit construction.
The entanglement-assisted capacity of a quantum channel admits an additive single-letter characterization, implying that joint encodings across channel uses cannot increase the ultimate communication rate. Here, we show that this additive picture does not extend to communication reliability. Specifically, we prove that the Petz-Rényi channel information can be strictly superadditive for every α∈[1/2,1), yielding a genuine multi-copy enhancement of the entanglement-assisted random-coding error exponent, even though the entanglement-assisted capacity remains additive. We establish this phenomenon analytically already for measurement channels, which are entanglement-breaking and have additive unassisted capacity. Remarkably, this strict superadditivity is witnessed by a separable, classically correlated two-copy channel-input marginal, demonstrating that no entanglement between the transmitted systems is required. Our results show that, although correlations across channel uses cannot increase the ultimate rate of entanglement-assisted communication, they can enhance its reliability.