September 2022

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.

The questions we raise in this letter are as follows: What is the most general representation of a quantum state at a single time? Can we adapt the current representations to the scenarios in which the order of quantum operations are coherently or incoherently superposed? If so, what is the relation between the state at a given time and the uncertainty in the order of events before and after it? By establishing the relationship of two-state vector formalism with pseudo-density operators, we introduce the notion of single-time pseudo-state which can be constructed by either ideal or weak measurements. We show that the eigenspectrum in the latter case enables us to discriminate between the coherent and incoherent superpositions of causal orders in which the pre- and post-selection measurements are interchanged with a non-zero probability. Finally, we discuss some of the possible experimental realizations in existing photonic setups.

We extend the circuit model of quantum computation so that the wiring between gates is soft-coded within registers inside the gates. The addresses in these registers can be manipulated and put into superpositions. This aims at capturing indefinite causal orders and making their geometrical layout explicit: we express the quantum switch and the polarizing beam-splitter within the model. In this context, our main contribution is a full characterization of the anonymity constraints. Indeed, the names used as addresses should not matter beyond the wiring they describe, i.e. quantum evolutions should commute with “renamings”. We show that these quantum evolutions can still act non-trivially upon the names. We specify the structure of “nameblind” matrices.

The `Wigner’s friend’ thought experiment illustrates the puzzling nature of quantum measurement. Časlav Brukner discusses how recent results suggest that in quantum theory the objectivity of measurement outcomes is relative to observation and observer.