A single programmable photonic circuit for universal quantum measurements

Abstract

Programmable photonic quantum processors face a critical challenge: despite significant advances in quantum state preparation and manipulation, measurements remain limited to projective techniques. Here, we demonstrate a programmable measurement processor that overcomes this limitation by enabling arbitrary quantum measurements within a scalable circuit framework. Our large-scale integrated photonic architecture achieves precise coherent control of ancillary quantum systems, realizing a universal four-dimensional quantum measurement device. We benchmark the processor by performing measurement tomography on 100 randomly selected measurements, achieving an average fidelity of 97.7%. The processor's performance exceeds the theoretical limits of projective measurements in three key quantum information tasks: state discrimination (with 23 times lower error), state estimation (with 10.6% higher fidelity), and randomness generation (with 37% more randomness yield), demonstrating its high operational quality. This work establishes a fully programmable quantum measurement processor, advancing the development of universal quantum operations for photonic quantum information processing by providing the key missing component.

Figures (4)

• Figure 1: Universal quantum measurement circuit and its characterization. (A) Conceptual illustration. Specialized devices for implementing different types of quantum measurements can be replaced with a single programmable device capable of implementing any measurement. (B) Experimental setup. An input single photon is prepared in an arbitrary path-encoded four-dimensional state using three Mach-Zehnder interferometers (MZIs). The measurement circuit can implement an arbitrary measurement on it through a cascade of 15 periodic modules. Each module contains four MZIs tied to four two-dimensional unitary operators $C_i^j$ ($j=1,\dots,4$) and is configured to realize the outcome associated with the measurement operator $E_i$. The last three modules can be further simplified by removing the trivial MZIs. (C) Photograph of our chip alongside a coin. (D) Fidelities of 100 randomly sampled measurements determined by measurement tomography. Left: The average fidelity and its standard deviation for each set of 20 measurements with a specific number of outcomes. Right: all 100 individual fidelities. (E) Tomographic fidelities of the five measurements employed for the quantum information tasks. In each case, the device is re-calibrated to optimize the implementation. Each value is obtained by averaging over more than 10 million photon counts, and the error bar represents the standard deviation calculated from repeated experiments. PMs: projective measurements; USD: unambiguous state dicrimination; SE: state estimation; RNG: random number generation; MMI BS: multimode interference beam splitter.
• Figure 2: Experimental unambiguous state discrimination. (A) Schematic of unambiguously discriminating a set of four states by allowing an inconclusive measurement outcome. (B) Experimental measurement probabilities for three different sets of states. The values for the incorrect outcomes are labeled on the corresponding bars. (C) Experimental error rates compared with the theoretical limits of the minimum-error state discrimination protocol, and experimental probabilities of the inconclusive outcome compared with the theoretical optimal values. Each experimental value is the average over ten repeated experiments, with roughly $4\times4000$ photon counts collected in each, and the error bar indicates the standard deviation.
• Figure 3: Experimental two-copy state estimation. (A) Schematic of the optimal estimation protocol. Two copies of an unknown pure qubit state are collectively measured and an estimate is constructed depending on the measurement outcome. (B) Experimental estimation fidelities for the states with Bloch vectors on the $xz$ plane and $xy$ plane, respectively. Each data point is the average over ten repeated experiments, with roughly 4000 photon counts collected in each run, and the error bar indicates the standard deviation. (C) The average, minimum, and standard deviation of the experimental estimation fidelities across all input states studied, compared with the theoretical predictions and the corresponding results achieved by the projective measurement $\Pi^{\mathrm{proj}}$ proposed in Ref. MassP95.
• Figure 4: Experimental measurement-device-independent randomness certification. (A) Schematic of the protocol. 16 probe states are symmetric and informationally complete and one probe state is maximally mixed. The formers are used to ensure security and the latter is used to generate randomness from the output of the uncharacterised measurement. (B) Experimental measurement probabilities for the 17 input states. The results for inputs $x=1,\dots,16$ were obtained from roughly $16\times60000$ photon counts, while the results for the input $x=17$ were obtained from roughly 240000 photon counts. (C) Experimental success probability for the discrimination and lower bounds on min-entropy and Shannon entropy, compared with the optimal values and the corresponding bounds for projective measurements.