Power of sequential protocols in hidden channel discrimination

Any physical operation on a quantum system can be described as a quantum channel. Identification of quantum channels, referred to as quantum channel discrimination (QCD), is a fundamental task in experiments. A central achievement in QCD is unraveling the bounds of error probability in discrimination and the protocols used to achieve it.



However, quantum coherent measurements are often made under much stricter restrictions than those typically assumed in QCD. For example, in quantum non-demolition measurements, a physical system H is not directly measured by positive operator-valued measurement. Instead, the measurement is done by a measurement system that has limited unitary interaction with H. Here, the physical system is hidden in the sense that it cannot be measured directly, and it is not clear whether the same error probability limits and optimal protocols applicable to conventional QCD are achievable on hidden systems.



In this talk, we propose Hidden QCD, a QCD problem in which the queries involving initial state, quantum operations, and measurements to the hidden system are all subject to experimentally-relevant restrictions. By studying parallel, 1-qubit sequential, and multi-shot protocols, we show that the sequential use of channels is essential in Hidden QCD. For the parallel and multishot protocols of depth one, it is impossible to succeed in channel discrimination. In the sequential protocol, by contrast, the error probability can be reduced to zero for a sufficient number of queries N to the channel. Moreover, we can accomplish Hidden QCD with a number of queries N that scales with the desired error probability at the Heisenberg limit (faster than the standard quantum limit). Our results are surprising in that the 1-qubit sequential protocol is superior to parallel protocol under experimentally-relevant restrictions and can even saturate quantum limits.