research

Quantum supermaps The notion of quantum supermaps provides a framework for going beyond standard quantum theory, potentially offering new insights into the long-standing problem of reconciling quantum mechanics with Einstein’s theory of relativity. Mathematically, a quantum supermap is a higher-order transformation acting on a set of quantum channels, which may not necessarily admit a realization as a causally ordered quantum circuit.

Bistochastic quantum theory In Ref. ¹, we characterize the set of bistochastic channels as the largest class of operations that admit input–output inversion, and we formulate operations without a definite input–output direction as supermaps on bistochastic channels. An explicit example of such an operation is the quantum time flip, which we show can outperform standard quantum circuits. In Ref. ², we report the first experimental realization of the quantum time flip in a photonic platform, demonstrating its advantages both via witness observables and through a unitary-gate discrimination game.

We further investigate the advantage provided by quantum supermaps on bistochastic communication resources in both classical and quantum communication scenarios (Ref. ³).

Quantum violation of causal inequalities Assuming that quantum theory holds locally and that local devices are connected via a quantum supermap leads to an analogue of Bell nonlocality in a causally indefinite setting. Remarkably, some quantum supermaps generate correlations that defy any causal explanation. In Ref. ⁴, we introduce a general method to bound quantum signaling correlations between local events, deriving Tsirelson-like bounds for a broad class of causal inequalities. This offers a powerful approach for understanding the capabilities and limitations of quantum mechanics in causally indefinite frameworks.

Research in progress Understanding the limits of quantum information processing from foundational principles of quantum mechanics.