The 'Noncausal Causality' of Quantum Information

Bin Dai, Yuan Luo

In this paper, the model of wiretap channel has been reconsidered for the case that the main channel is controlled by channel state information (side information), and it is available at the transmitter in a noncausal manner (termed here noncausal side information) or causal manner (termed here causal side information). Inner and outer bounds are derived on the capacity-equivocation regions for the noncausal and causal manners, and the secrecy capacities for both manners are described and bounded, which provide the best transmission rate with perfect secrecy. Moreover, for the case that the side information is available at the transmitter in a memoryless manner (termed here memoryless side information), both the capacity-equivocation region and the secrecy capacity are determined. The results of this paper extend the previous work on wiretap channel with noncausal side information by providing an outer bound on the capacity-equivocation region. In addition, we find that the memoryless side information can not help to obtain the same secrecy capacity as that of the causal case, and this is different from the well known fact that the memoryless manner can achieve the capacity of the channel with causal side information.

Alastair A. Abbott

Časlav Brukner

Hachiro Fujita

The wiretap channel with causal/noncausal side information at the transmitter is an extension of the original wiretap channel of Wyner to the multi-user case and has been investigated by several authors. Although much effort has been made to establish the secrecy capacity, it is still elusive even if the wiretap channel is physically degraded. In this paper, for a physically degraded wiretap channel, we show a lower bound on the secrecy capacity for the causal case and an upper bound for the noncausal case. We also show that under a certain condition, the secrecy capacity for the causal case is the same as that for the noncausal case. To illustrate the usefulness of our theoretical result, we introduce the concept of a symmetric wiretap channel with state, for which the above condition is easily checked, and we give some examples in which the secrecy capacity can be computed numerically.

Martin Ringbauer

Ricardo Silveira, Patrick Andriolo, Davide Poderini +2 more

Quantum processes can exhibit indefinite causal order, allowing coherent superpositions of distinct orderings of events. Whether such processes generate genuinely noncausal statistics, however, depends not only on their global causal structure but also on the local operations available to the parties. Here, we restrict communication to the classical outcomes of local operations, yielding a causal polytope with new causal inequalities that can be violated using measure-and-reprepare, entanglement-breaking instruments requiring no coherent transmission through the laboratories. Using a semidefinite-programming framework, we bound the achievable violations and reveal noncausal correlations that satisfy all conventional input-signalling inequalities, demonstrating that restricting the information available for communication can uncover forms of indefinite causal order inaccessible under less restrictive operational assumptions.