Abstract Certain quantum devices, such as half-wave plates and quarter-wave plates in quantum optics, are bidirectional, meaning that the roles of their input and output ports can be exchanged. Bidirectional devices can be used in a forward mode and a backward mode, corresponding to two opposite choices of the input-output direction. They can also be used in a coherent superposition of the forward and backward modes, giving rise to new operations with indefinite input-output direction. In this work we explore the potential of input-output indefiniteness for the transfer of classical and quantum information through noisy channels. We first formulate a model of communication from a sender to a receiver via a noisy channel used in indefinite input-output direction. Then, we show that indefiniteness of the input-output direction yields advantages over standard communication protocols in which the given noisy channel is used in a fixed input-output direction. These advantages range from a general reduction of noise in bidirectional processes, to heralded noiseless transmission of quantum states, and, in some special cases, to a complete noise removal. The noise reduction due to input-output indefiniteness can be experimentally demonstrated with current photonic technologies, providing a way to investigate the operational consequences of exotic scenarios characterised by coherent quantum superpositions of forward-time and backward-time processes.
Abstract Certain quantum devices, such as half-wave plates and quarter-wave plates in quantum optics, are bidirectional, meaning that the roles of their input and output ports can be exchanged. Bidirectional devices can be used in a forward mode and a backward mode, corresponding to two opposite choices of the input-output direction. They can also be used in a coherent superposition of the forward and backward modes, giving rise to new operations with indefinite input-output direction. In this work we explore the potential of input-output indefiniteness for the transfer of classical and quantum information through noisy channels. We first formulate a model of communication from a sender to a receiver via a noisy channel used in indefinite input-output direction. Then, we show that indefiniteness of the input-output direction yields advantages over standard communication protocols in which the given noisy channel is used in a fixed input-output direction. These advantages range from a general reduction of noise in bidirectional processes, to heralded noiseless transmission of quantum states, and, in some special cases, to a complete noise removal. The noise reduction due to input-output indefiniteness can be experimentally demonstrated with current photonic technologies, providing a way to investigate the operational consequences of exotic scenarios characterised by coherent quantum superpositions of forward-time and backward-time processes.
Bidirectional devices are devices for which the roles of the input and output ports can be exchanged. Mathematically, these devices are described by bistochastic quantum channels, namely completely positive linear maps that are both trace-preserving and identity-preserving. Recently, it has been shown that bidirectional quantum devices can, in principle, be used in ways that are incompatible with a definite input-output direction, giving rise to a new phenomenon called input-output indefiniteness. Here we characterize the most general forms of input-output indefiniteness, associated with a hierarchy of higher-order transformations built from transformations of bistochastic quantum channels. Some levels of the hierarchy correspond to transformations that combine bistochastic channels in a definite causal order, while generally using each channel in an indefinite input-output direction. For other levels of the hierarchy, the indefiniteness can involve both the local input-output direction of each process and the global causal order among the processes. On the foundational side, the hierarchy of higher-order transformations characterized here can be regarded as the largest set of physical processes compatible with a time-symmetric variant of quantum theory, where the possible state transformations are restricted to bistochastic channels.
Abstract Quantum mechanics is compatible with scenarios where the relative order between two events can be indefinite. Here we show that two independent instances of a noisy process can behave as a perfect quantum communication channel when used in a coherent superposition of two alternative orders. This phenomenon occurs even if the original process has zero capacity to transmit quantum information. In contrast, perfect quantum communication does not occur when the message is sent directly from the sender to the receiver through a superposition of alternative paths, with an independent noise process acting on each path. The possibility of perfect quantum communication through independent noisy channels highlights a fundamental difference between the superposition of orders in time and the superposition of paths in space.
Usual scenarios of fault-tolerant computation are concerned with the fault-tolerant realization of quantum algorithms that compute classical functions, such as Shor's algorithm for factoring. In particular, this means that input and output to the quantum algorithm are classical. In contrast to stand-alone single-core quantum computers, in many distributed scenarios, quantum information might have to be passed on from one quantum information processing system to another one, possibly via noisy quantum communication channels with noise levels above fault-tolerant thresholds. In such situations, quantum information processing devices will have quantum inputs, quantum outputs or even both, which pass qubits among each other. Working in the fault-tolerant framework of [Kitaev, 1997], we show that any quantum circuit with quantum input and output can be transformed into a fault-tolerant circuit that produces the ideal circuit with some controlled noise applied at the input and output. The framework allows the direct composition of the statements, enabling versatile future applications. We illustrate this with a concrete application, namely, communication over a noisy channel with faulty encoding and decoding operations [Christandl and M{ü}ller-Hermes, 2024]. For communication codes with linear minimum distance, we construct fault-tolerant encoders and decoders for general noise (including coherent errors). For the weaker, but standard, model of local stochastic noise, we obtain fault-tolerant encoders and decoders for any communication code that can correct a constant fraction random errors.
A completely depolarising quantum channel always outputs a fully mixed state and thus cannot transmit any information. In a recent Letter\cite{ebler18}, it was however shown that if a quantum state passes through two such channels in a quantum superposition of different orders---a setup known as the ``quantum switch''---then information can nevertheless be transmitted through the channels. Here, we show that a similar effect can be obtained when one coherently controls between sending a target system through one of two identical depolarising channels. Whereas it is tempting to attribute this effect in the quantum switch to the indefinite causal order between the channels, causal indefiniteness plays no role in this new scenario. This raises questions about its role in the corresponding effect in the quantum switch. We study this new scenario in detail and we see that, when quantum channels are controlled coherently, information about their specific implementation is accessible in the output state of the joint control-target system. This allows two different implementations of what is usually considered to be the same channel to therefore be differentiated. More generally, we find that to completely describe the action of a coherently controlled quantum channel, one needs to specify not only a description of the channel (e.g., in terms of Kraus operators), but an additional ``transformation matrix'' depending on its implementation.
Usual scenarios of fault-tolerant computation are concerned with the fault-tolerant realization of quantum algorithms that compute classical functions, such as Shor’s algorithm for factoring. In particular, this means that input and output to the quantum algorithm are classical. In contrast to stand-alone single-core quantum computers, in many distributed scenarios, quantum information might have to be passed on from one quantum information processing system to another one, possibly via noisy quantum communication channels with noise levels above fault-tolerant thresholds. In such situations, quantum information processing devices will have quantum inputs, quantum outputs or even both, which pass qubits among each other. Working in the fault-tolerant framework of [Kitaev, 1997], we show that any quantum circuit with quantum input and output can be transformed into a fault-tolerant circuit that produces the ideal circuit with some controlled noise applied at the input and output. The framework allows the direct composition of the statements, enabling versatile future applications. We illustrate this with a concrete application, namely, communication over a noisy channel with faulty encoding and decoding operations [Christandl and Müller-Hermes, 2024]. For communication codes with linear minimum distance, we construct fault-tolerant encoders and decoders for general noise (including coherent errors). For the weaker, but standard model of local stochastic noise, we obtain fault-tolerant encoders and decoders for any communication code that can correct a constant fraction of random errors.
A completely depolarising quantum channel always outputs a fully mixed state and thus cannot transmit any information. In a recent Letter\cite{ebler18}, it was however shown that if a quantum state passes through two such channels in a quantum superposition of different orders---a setup known as the ``quantum switch''---then information can nevertheless be transmitted through the channels. Here, we show that a similar effect can be obtained when one coherently controls between sending a target system through one of two identical depolarising channels. Whereas it is tempting to attribute this effect in the quantum switch to the indefinite causal order between the channels, causal indefiniteness plays no role in this new scenario. This raises questions about its role in the corresponding effect in the quantum switch. We study this new scenario in detail and we see that, when quantum channels are controlled coherently, information about their specific implementation is accessible in the output state of the joint control-target system. This allows two different implementations of what is usually considered to be the same channel to therefore be differentiated. More generally, we find that to completely describe the action of a coherently controlled quantum channel, one needs to specify not only a description of the channel (e.g., in terms of Kraus operators), but an additional ``transformation matrix'' depending on its implementation.