One of the consequences in the distribution of quantum states over a long distance is that, since resulting quantum states are noisy due to the intervention of an environment, a measurement setting should be re-aligned to optimize detection events, for which additional experimental resources such as quantum tomography of a channel or resulting states is necessary. In this work, we present a protocol for protecting an optimal measurement setup without verifying a channel. A receiver does not have to revise the measurement prepared in a noiseless scenario since it would remain optimal for quantum states resulting from an unknown and noisy channel. The measurement protection protocol realizes a supermap describing transformations over quantum channels and is experimentally feasible as it only applies local unitary transformations before and after the transmission. We present experimental proof-of-principle demonstrations of the measurement protection protocol. We also apply the measurement protection to a prepare-and-measure protocol, the Bennett-Brassard 1984 (BB84) protocol, and find that preserving an optimal measurement can suppress quantum-bit error rates, allowing the protocol to tolerate an even higher noise during transmission. The BB84 protocol with the measurement protection is experimentally demonstrated with the polarization encoding on photonic qubits.

In this work, we consider the preservation of a measurement for quantum systems interacting with an environment. Namely, a method of preserving an optimal measurement over a channel is devised, what we call channel coding of a quantum measurement in that operations are applied before and after a channel in order to protect a measurement. A protocol that preserves a quantum measurement over an arbitrary channel is shown only with local operations and classical communication without the use of a larger Hilbert space. Therefore, the protocol is readily feasible with present day's technologies. Channel coding of qubit measurements is presented, and it is shown that a measurement can be preserved for an arbitrary channel for both i) pairs of qubit states and ii) ensembles of equally probable states. The protocol of preserving a quantum measurement is demonstrated with IBM quantum computers.

In the above-named work, the corresponding author should have been identified as Joonwoo Bae.