We propose a universal measure of efficiency associated with a quantum-optical state and show that this efficiency cannot be improved by any linear-optical processing combined with destructive conditional measurements.
We propose a measure of quantum efficiency of a multimode state of light that quantifies the amount of optical loss this state has experienced, and prove that this efficiency cannot increase in any linear-optical processing with destructive conditional measurements. Any loss that has affected a state can neither be removed nor redistributed so as to further increase the efficiency in higher-efficiency modes at the expense of lower-efficiency modes. This result eliminates the possibility of catalytically improving photon sources.
We analyze the problem of increasing the efficiency of single-photon sources or single-rail photonic qubits via linear optical processing and destructive conditional measurements. We allow for the use of coherent states and do not limit to photon-counting measurements. We conjecture that, with the limitation that multiphoton components in the output are not permitted, it is not possible to increase the efficiency. We prove this conjecture for several important special cases, and provide extensive numerical results for the general case.
Probabilistic and destructive Bell-measurements, also known as fusions, constitute a fundamental primitive for photonic quantum technologies. These operations rely only on pairwise photonic interference, whereas the computational power of photonic quantum systems originates from many-body interference. Here, we introduce a family of high-efficiency linear-optical GHZ measurements based on four-mode interferometers and show that incorporating many-body interference into this ubiquitous primitive leads to more efficient entangling operations. For the four-photon case, the success probability is 9/32, and adaptive variants ensure that unsuccessful events project onto useful stabilizer states. We further show that the approach naturally generalizes to larger GHZ measurements, yielding an exponentially higher success probability than previous linear-optical schemes. Finally, we demonstrate practical advantages for graph-state resource generation, entanglement distribution between remote spin-photon interfaces, and fusion-based quantum computing. Our results establish high-efficiency many-body measurements as a new primitive for scalable photonic quantum information processing.