Suppose that m senders want to transmit classical information to n receivers with zero probability of error using a noisy multipartite communication channel. The senders are allowed to exchange classical, but not quantum, messages among themselves, and the same holds for the receivers. If the channel is classical, a single use can transmit information if and only if multiple uses can. In sharp contrast, we exhibit, for each m and n with m>1 or n>1, a quantum channel of which a single use is not able to transmit information yet two uses can. This latter property requires and is enabled by quantum entanglement.
Suppose that m senders want to transmit classical information to n receivers with zero probability of error using a noisy multipartite communication channel. The senders are allowed to exchange classical, but not quantum, messages among themselves, and the same holds for the receivers. If the channel is classical, a single use can transmit information if and only if multiple uses can. In sharp contrast, we exhibit, for each m and n with m>1 or n>1, a quantum channel of which a single use is not able to transmit information yet two uses can. This latter property requires and is enabled by quantum entanglement.
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.
We introduce the task of random-receiver quantum communication, in which a sender transmits a quantum message to a receiver selected from a list of n spatially separated parties.At the moment of transmission, the choice of receiver is unknown to the sender.Later, it becomes known to the n parties, who coordinate their actions by exchanging classical messages.In normal conditions, random-receiver quantum communication requires a noiseless quantum communication channel between the sender and each of the n receivers.In contrast, we show that random-receiver quantum communication can take place through noisy, entanglement-breaking channels if the order of such channels is coherently controlled by a quantum bit that is accessible through measurements.While this phenomenon is achieved with a single control qubit, it cannot be mimicked by adding a noiseless qubit channel from the sender to any of the receivers, or more generally, from the sender to any subset of k < n parties.
We study various super-activation effects in the following zero-error communication scenario: One sender wants to send classical or quantum information through a noisy quantum channel to one receiver with zero probability of error. First we show that there are quantum channels of which a single use is not able to transmit classical information perfectly yet two uses can. This is achieved by employing entangled input states between different uses of the given channel and thus cannot happen for classical channels. Second we exhibit a class of quantum channel with vanishing zero-error classical capacity such that when a noiseless qubit channel or one ebit shared entanglement are available, it can be used to transmit log2d noiseless qubits, where 2d is the dimension of input state space. Third we further construct quantum channels with vanishing zero-error classical capacity when assisted with classical feedback can be used to transmit both classical and quantum information perfectly. These striking findings not only indicate both the zero-error quantum and classical capacities of quantum channels satisfy a strong super-additivity beyond any classical channels, but also highlight the activation power of auxiliary physical resources in zero-error communication.
A fundamental limitation of quantum communication is that a single qubit can carry at most one bit of classical information. For an important class of quantum communication channels, known as entanglement breaking, this limitation holds even if the sender and receiver share entangled particles. But does this mean that, for the purpose of communicating classical messages, a noisy entanglement-breaking qubit channel can be replaced by a noisy bit channel? Here we answer the question in the negative. We introduce a game, similar to the Monty Hall problem in classical statistics, where a sender assists a receiver in finding a valuable item (the "prize") hidden in one of four possible boxes, while avoiding a hazardous item (the "bomb") hidden in one of the remaining three boxes. We show that no classical strategy using a noisy bit channel can ensure that the bomb is avoided, even if the sender and receiver share arbitrary amounts of randomness. In contrast, communication of a qubit through a class of noisy entanglement-breaking channels, which we call quantum not channels, allows the players to deterministically avoid the bomb and to find the prize with a guaranteed nonzero probability. Our findings show that the communication of classical messages through a noisy entanglement-breaking qubit channel assisted by quantum entanglement cannot, in general, be simulated by communication through a noisy bit channel assisted by classical correlations.
A fundamental limitation of quantum communication is that a single qubit can carry at most 1 bit of classical information. For an important class of quantum communication channels, known as entanglement-breaking, this limitation holds even if the sender and receiver share entangled particles. But does this mean that, for the purpose of communicating classical messages, a noisy entanglement-breaking qubit channel can be replaced by a noisy bit channel? Here we answer the question in the negative. We introduce a game, similar to the Monty Hall problem in classical statistics, where a sender assists a receiver in finding a valuable item (the prize) hidden into one of four possible boxes, while avoiding a hazardous item (the bomb) hidden in one of the remaining three boxes. We show that no classical strategy using a noisy bit channel can ensure that the bomb is avoided, even if the sender and receiver share arbitrary amounts of randomness. In contrast, communication of a qubit through a class of noisy entanglement-breaking channels, which we call quantum NOT channels, allows the players to deterministically avoid the bomb and to find the prize with a guaranteed nonzero probability. Our findings show that the communication of classical messages through a noisy entanglement-breaking qubit channel assisted by quantum entanglement cannot, in general, be simulated by communication through a noisy bit channel assisted by classical correlations.
Given one or more uses of a classical channel, only a certain number of messages can be transmitted with zero probability of error. The study of this number and its asymptotic behavior constitutes the field of classical zero-error information theory. We show that, given a single use of certain classical channels, entangled states of a system shared by the sender and receiver can be used to increase the number of (classical) messages which can be sent without error. In particular, we show how to construct such a channel based on any proof of the Kochen-Specker theorem. We investigate the connection to pseudotelepathy games. The use of generalized nonsignaling correlations to assist in this task is also considered. In this case, an elegant theory results and, remarkably, it is sometimes possible to transmit information with zero error using a channel with no unassisted zero-error capacity.