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 sequence of quantum channels, which may not necessarily admit a realization as a causally ordered quantum circuit.

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 with no causal order. In Ref. ¹, we introduce a general method to bound quantum signaling correlations between 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 theory with indefinite causal order.

Parity erasure as a foundational principle for indefinite causal order. In Ref. ², we identify an information-theoretic principle, termed parity erasure, that completely characterizes quantum supermaps with indefinite causal order. Our characterization does not rely on the formalism of quantum theory itself, but instead is derived from a set of axioms for general operational probabilistic theories, and thus holds also for a large class of theories beyond quantum theory. This informational approach reveals a fundamental property of information exchange in scenarios with indefinite causal structure.

Bistochastic quantum theory. In Ref. ³, 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. ⁴, 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. ⁵).

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