Abstract At the fundamental level, the dynamics of quantum fields is invariant under the combination of time reversal, charge conjugation, and parity inversion. This symmetry implies that a broad class of effective quantum evolutions are bidirectional, meaning that the exchange of their inputs and outputs gives rise to valid quantum evolutions. Recently, it has been observed that quantum theory is theoretically compatible with a family of operations in which the roles of the inputs and outputs is indefinite. However, such operations have not been demonstrated in the laboratory so far. Here we experimentally demonstrate input-output indefiniteness in a photonic setup, demonstrating an advantage in a quantum game and showing incompatibility with a definite input-output direction by more than 69 standard deviations. Our results establish input-output indefiniteness as a new resource for quantum information protocols, and enable the table-top simulation of hypothetical scenarios where the arrow of time could be in a quantum superposition.
Abstract At the fundamental level, the dynamics of quantum fields is invariant under the combination of time reversal, charge conjugation, and parity inversion. This symmetry implies that a broad class of effective quantum evolutions are bidirectional, meaning that the exchange of their inputs and outputs gives rise to valid quantum evolutions. Recently, it has been observed that quantum theory is theoretically compatible with a family of operations in which the roles of the inputs and outputs is indefinite. However, such operations have not been demonstrated in the laboratory so far. Here we experimentally demonstrate input-output indefiniteness in a photonic setup, demonstrating an advantage in a quantum game and showing incompatibility with a definite input-output direction by more than 69 standard deviations. Our results establish input-output indefiniteness as a new resource for quantum information protocols, and enable the table-top simulation of hypothetical scenarios where the arrow of time could be in a quantum superposition.
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.
In the macroscopic world, time is intrinsically asymmetric, flowing in a specific direction, from past to future. However, the same is not necessarily true for quantum systems, as some quantum processes produce valid quantum evolutions under time reversal. Supposing that such processes can be probed in both time directions, we can also consider quantum processes probed in a coherent superposition of forward and backward time directions. This yields a broader class of quantum processes than the ones considered so far in the literature, including those with indefinite causal order. In this work, we demonstrate an operation belonging to this class: the quantum time flip. Using a photonic realisation of this operation, we apply it to a game formulated as a discrimination task between two sets of operators. This game not only serves as a witness of an indefinite time direction, but also allows for a computational advantage over strategies using a fixed time direction, and even those with an indefinite causal order. Published by the American Physical Society 2024
In classical physics, events follow a definite causal order: the past influences the future, but not the reverse. Quantum theory, however, permits superpositions of causal orders—the so-called indefinite causal orders (ICOs)—which can provide operational advantages over classical scenarios. Verifying such phenomena has sparked significant interest, much like earlier efforts devoted to refuting local realism and confirming quantum entanglement. To date, demonstrations of ICO have all been based a process called the quantum switch and have relied on device-dependent or semi-device-independent protocols. Achieving a device-independent verification of ICO would imply that nature allows for correlations that do not respect causality, independent of any experimental assumptions or underlying theoretical description of the experiment. To this end, a recent theoretical development introduced a Bell-like inequality that allows for fully device-independent verification of ICO in a quantum switch. Here we implement this verification by experimentally violating this inequality. In particular, we measure a value of 1.8328 ± 0.0045 , which is 18 standard deviations above the definite causal order bound of 1.75 . Our work presents the first implementation of a device-independent protocol to verify ICO, albeit in the presence of experimental loopholes. This represents an important step toward the device-independent verification of an ICO and provides a context in which to identify loopholes specifically related to the verification of ICO.
Abstract The fundamental dynamics of quantum particles is neutral with respect to the arrow of time. And yet, our experiments are not: we observe quantum systems evolving from the past to the future, but not the other way round. A fundamental question is whether it is possible, at least in principle, to conceive a broader set of operations that probe quantum processes in the backward direction, from the future to the past, or more generally, in a combination of the forward and backward directions. Here we introduce a mathematical framework for operations that are not constrained to a definite time direction. More generally, we introduce a set of multipartite operations that include indefinite time direction as well as indefinite causal order, providing a framework for potential extensions of quantum theory.
Treating the arrow of time as a controllable quantum variable rather than a fixed external parameter is a central challenge in quantum physics. Recently, Bloch~\cite{Bloch2025} proposed the theoretical concept of a \emph{time qubit}, a two-level control space HT=span{∣+⟩,∣−⟩} that selects between opposite Hamiltonian evolutions H^±=H^0±V^, but this paradigm has remained experimentally unrealized. Here we formulate the quantum-optical theory of a single-photon time qubit---uncovering quantum-vacuum control and complementarity of the arrow of time---and experimentally probe and validate its predictions using phase-resolved single-photon interferometry from two coherently seeded entangled nonlinear biphoton sources~\cite{Lee2018,Yoon2021}. First, we show theoretically and verify experimentally that a controlled π pump--seed phase inversion during pair creation from the quantum vacuum flips the stimulated displacement generator V^→−V^ on top of the spontaneous two-mode squeezing background H^0, reversing the stimulated evolution time [U^stim,−(t)=U^stim,+(−t)] and enabling universal single-qubit SU(2) control and postselection-free first-order tomography on the temporal Bloch sphere. Second, we prove that spontaneous idler vacuum fluctuations record complete which-branch (temporal-direction) information whereas the shared coherent seed erases it without cascading or aligning the idler beams, establishing an exact wave--particle complementarity law ∣r∣=V=∣α∣2/(1+∣α∣2) for the purity of the arrow of time and enabling direct first-order measurement of the Loschmidt time-reversal echo.