It has recently been shown that if two completely depolarizing channels are in a superposition of different orders, classical information can be transmitted that would be otherwise lost [1]. Here, we present a generalization of the results of [1] to study communication with arbitrary depolarizing channels and putting to good use indefinite causal order, a new paradigm for quantum information/computation.
It has recently been shown that if two completely depolarizing channels are in a superposition of different orders, classical information can be transmitted that would be otherwise lost [1]. Here, we present a generalization of the results of [1] to study communication with arbitrary depolarizing channels and putting to good use indefinite causal order, a new paradigm for quantum information/computation.
In quantum Shannon theory, the way information is encoded and decoded takes advantage of the laws of quantum mechanics, while the way communication channels are interlinked is assumed to be classical. In this Letter, we relax the assumption that quantum channels are combined classically, showing that a quantum communication network where quantum channels are combined in a superposition of different orders can achieve tasks that are impossible in conventional quantum Shannon theory. In particular, we show that two identical copies of a completely depolarizing channel become able to transmit information when they are combined in a quantum superposition of two alternative orders. This finding runs counter to the intuition that if two communication channels are identical, using them in different orders should not make any difference. The failure of such intuition stems from the fact that a single noisy channel can be a random mixture of elementary, noncommuting processes, whose order (or lack thereof) can affect the ability to transmit information.
In quantum Shannon theory, transmission of information is enhanced by quantum features. Up to very recently, the trajectories of transmission remained fully classical. Recently, a new paradigm was proposed by playing quantum tricks on two completely depolarizing quantum channels i.e., using coherent control in space or time of the two quantum channels. We extend here this control to the transmission of information through a network of an arbitrary number N of channels with arbitrary individual capacity i.e., information preservation characteristics in the case of indefinite causal order. We propose a formalism to assess information transmission in the most general case of N channels in an indefinite causal order scenario yielding the output of such transmission. Then, we explicitly derive the quantum switch output and the associated Holevo limit of the information transmission for N = 2 , N = 3 as a function of all involved parameters. We find in the case N = 3 that the transmission of information for three channels is twice that of transmission of the two-channel case when a full superposition of all possible causal orders is used.
Classically, no information can be transmitted through a depolarising, which is a completely noisy, channel.We show that by combining a depolarising channel with another channel in an indefinite causal order-that is, when there is a superposition of the order that these two channels were applied-it becomes possible to transmit significant information.We consider two limiting cases.When both channels are fully depolarising, the ideal limit is communication of 0.049 bits; experimentally we achieve (3.4 ± 0.2) × 10 -2 bits.When one channel is fully depolarising, and the other is a known unitary, the ideal limit is communication of 1 bit.We experimentally achieve 0.64 ± 0.02 bits.Our results offer intriguing possibilities for future communication strategies beyond conventional quantum Shannon theory.
Completely depolarizing channels are often regarded as the prototype of physical processes that are useless for communication: any message that passes through them along a well-defined trajectory is completely erased. When two such channels are used in a quantum superposition of two alternative orders, they become able to transmit some amount of classical information, but still no quantum information can pass through them. Here, we show that the ability to place N completely depolarizing channels in a superposition of N alternative causal orders enables a high-fidelity heralded transmission of quantum information with error vanishing as 1/N. This phenomenon highlights a fundamental difference with the N=2 case, where completely depolarizing channels are unable to transmit quantum data, even when placed in a superposition of causal orders. The ability to place quantum channels in a superposition of orders also leads to an increase of the classical communication capacity with N, which we rigorously prove by deriving an exact single-letter expression. Our results highlight the more complex patterns of correlations arising from multiple causal orders, which are similar to the more complex patterns of entanglement arising in multipartite quantum systems.
Quantum theory is in principle compatible with scenarios where physical processes occur in an indefinite order, potentially yielding advantages in a broad range of information processing tasks. However, advantages in communication, the most basic form of information processing, have so far remained controversial and hard to prove. Here we provide a framework for assessing the role of causal order in communication, by comparing different causal structures under the constraint that the allowed operations must not generate signaling from signaling-incapable devices. Using this framework, we establish a clear-cut advantage of indefinite causal order, and, at the same time, we identify a series of fundamental limits to the communication power of causal structures in quantum mechanics. Notably, we find that a special form of indefinite causal order, obtained by coherently controlling the order of two processes, enhances the transmission of classical messages in a one-shot scenario, but no quantum operation with indefinite order can offer advantages over shared entanglement when asymptotically many uses of the same communication device are employed. Overall, our results unveil non-trivial relations between communication, causal order, entanglement, and no-signaling quantum processes.
If two identical copies of a completely depolarizing channel are put into a superposition of their possible causal orders, they can transmit nonzero classical information. Here we study how well we can transmit classical information with N depolarizing channels put in superposition of M causal orders via a quantum switch. We calculate the Holevo quantity if the superposition uses only cyclic permutations of channels and find that it increases with M and it is independent of N. For a qubit it never reaches 1 if we are increasing M. On the other hand, the classical capacity decreases with the dimension d of the message system. Further, for N=3 and 4 we studied the superposition of all causal orders and uniformly superposed causal orders belonging to different cosets created by a cyclic permutation subgroup.