Characterization and optimized engineering of bosonic quantum interfaces under single-mode operational constraints

TL;DR

This paper fully characterizes linear bosonic quantum interfaces under single-mode operation constraints, introducing invariants and systematic engineering strategies to realize arbitrary interfaces with minimal components.

Contribution

It provides a complete characterization of two-mode bosonic interfaces under single-mode restrictions and develops optimal protocols for their engineering using cascading methods.

Findings

Invariant transmission strength characterizes all interfaces with arbitrary Gaussian operations.

Additional invariants, irreducible squeezing and shearing, emerge under squeezing restrictions.

Optimal protocols require at most three component interfaces without restrictions, extended to five with constraints.

Abstract

Controlling the quantum interface between two bosonic modes is essential in countless implementations of quantum information processing. However, full controllability is rarely achieved in most platforms due to specific physical limitations. In this work, we completely characterize the linear two-mode interfaces under the most pessimistic restriction that only single-mode operation is available. When arbitrary Gaussian single-mode operations can be applied to both modes, we find that every interface can be characterized by an invariant transmission strength. Moreover, in the practical situation that squeezing is restricted in one of the modes, we discover two additional quantities, irreducible squeezing and irreducible shearing, that are invariant under the allowable controls. By using this characterization, we develop systematic strategies to engineer an arbitrary linear interface through cascading multiple fixed component interfaces. Without squeezing restriction, our protocol is optimal and requires at most three component interfaces. Under the squeezing constraint, our protocol can be extended to engineer also the additional invariants by using no more than two more rounds of cascade. We also propose the remote squeezing scheme to tackle the squeezing restriction through interfacing with an active auxiliary mode.