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Making quantum measurement useful: Quantum State Discrimination beyond classical limits


Using single-photon detection and an adaptive measurement strategy, we determine the state of an optical pulse with errors below what is possible with even the best possible classical receiver, a limit often referred to as the "standard quantum limit (SQL)" or "shot-noise limit (SNL)."


Quantum receivers are one of the outstanding examples of useful quantum measurements, i.e., the measurements that yield the accuracy beyond the classically accessible means in a practical setting.

Displacement quantum receiver graph
*The Displacement quantum receiver* Consider an optical signal pulse. Color represents different letters of the alphabet. The receiver decides which alphabet letter this pulse is based on a measurement. Here we use a reference pulse (Local Oscillator) which can cancel the signal by displacing it at a 99:1 beam splitter. If no photons are detected, it is because the LO likely completely extinguished the signal. If the LO doesn’t match the signal pulse, then photons can be detected. The receiver then adjusts the LO to match the input to a different alphabet letter.

In digital optical communications a set of coherent pulses of faint light in any of M previously defined states forms a communication alphabet, where each symbol encodes log2M bits of information. Various sets of states or modulation protocols and corresponding measurement methods are well known in classical digital communications. Here we develop practical quantum-enabled methods and new alphabets that allow us to distinguish such “letters”, but better than any classical measurement can do.

Quantum receivers with legacy modulation schemes

We have developed quantum measurement that allows discrimination of 4 coherent states encoded with different phases (Quadrature Phase-Shift Keying  (QPSK) communication alphabet) beyond the classical SQL limit. We have achieved unconditional advantage over an ideal classical measurement of more than 6 dB, and more than 13 dB in comparison to the classical measurement with the same system efficiency. This is the first demonstration of unconditional advantage of quantum measurement for discrimination of more than two states.

Quantum state discrimination measurement graph
*Quantum state discrimination measurement that beats an ideal classical measurement.* The experimental error probability (blue dots) for the discrimination of four nonorthogonal states in the QPSK format, the ideal SQL (red line), the SQL adjusted for the 72% system efficiency of the receiver (dashed line), and the quantum limit, known as the Helstrom bound (black line).

The time resolving quantum receiver and the novel modulation schemes

Further, we investigate modulation schemes that can improve “quantum advantage” of a quantum measurement. We have developed and experimentally implemented a new quantum-enhanced communication system that features both the adaptive quantum measurement beyond the classical limit and the novel, “most suitable” modulation protocol numerically optimized to minimize discrimination error probability of the quantum receiver. 

We experimentally “unlock” the unforeseen advantages of the quantum measurement enabled by the first modulation scheme specifically designed and optimized for the time-resolved feedback receiver. We achieve record energy sensitivities and demonstrate successful discrimination of large alphabets of optical states (4≤M≤16) beyond the ideal classical shot-noise limit. Thus, we demonstrate the scalability of quantum measurement-enabled communication for the first time.

PRJC: “Time-Resolving Quantum Measurement Enables Energy-Efficient, Large-Alphabet Communication.”
PRJC: “Time-Resolving Quantum Measurement Enables Energy-Efficient, Large-Alphabet Communication.”
The Physical Review Journal Club returns with an exclusive conversation with authors I.A. Burenkov, M.V. Jabir, A. Battou, and S.V. Polyakov on their recently-published PRX Quantum paper: “Time-Resolving Quantum Measurement Enables Energy-Efficient, Large-Alphabet Communication”
time-resolved receiver’s scalability graph
*The time-resolved receiver’s scalability with alphabet length* The experimentally measured symbol error rate of the novel coherent frequency shift keying (CFSK) quantum receiver with the input of 1 photon/bit for protocols optimized for maximal energy sensitivity vs the alphabet length (green filled circles) together with the SNL (red solid line), an SNL adjusted for the 74.5% detection efficiency of the receiver (red dashed line) and Helstrom Bound (black line). Theoretical limits for the legacy phase shift keying (PSK) are shown with blue lines: Helstrom Bound (solid) and SNL (dashed).

Shot-by-shot estimation of quantum measurement confidence

The probabilistic nature of quantum measurement outcomes results in inconclusive and sometimes misleading results. Generally, because quantum measurements are probabilistic, prior experimental and most theoretical efforts describe ensemble probabilities for experimental outcomes, not what will occur in each measurement. Yet, specifically because most quantum measurements are probabilistic, the assessment of individual measurements has important implications. Thus, such quantum measurements can provide both the result and the “accuracy” of that result, i.e., shot by shot accuracy. Here we investigate this unique property of the quantum measurement applied to a state identification problem.

We, for the first time, experimentally obtain confidence levels for individual quantum measurements. To do so, we built a quantum-enabled communication link that can send and receive arbitrary user-defined data, also for the first time. In our experiment, the quantum measurement outperforms the idealized classical measurement in several aspects. First, the overall error rate of the quantum measurement is lower. Second, we identify states with higher single-shot certainty (fidelity) more often. Third, our ensemble-averaged certainty (fidelity) turns out to be higher. 

CMYK illustration
*Quantum measurement confidence estimation* A visual comparison of single-shot confidence estimates in an experimental quantum and idealized classical measurements. Left: the original 128x128 pixel image, where four primary (CMYK) colors correspond to the alphabet symbols. Middle: the same image experimentally obtained from continuous quantum measurement record. Right: the same image reconstructed from the simulated ideal homodyne measurement. The color for each pixel is calculated as a sum of primary colors weighted with the measured/simulated confidences of corresponding symbols.

The confidence estimation generalizes the quantum state identification problem and enhances the sensitivity and the specificity of the measurement at the same time, beyond classical means. It can be used in many applications where faint light is characterized. Particularly for low-energy telecommunication, the shot-by-shot confidence information can be directly fed into error-correcting algorithms.

Quantum Measurement Animated Video
Quantum Measurement Animated Video
Quantum measurement confidence estimation in the process of quantum state identification. This video shows the measurement principle, how the unique measurement record is experimentally acquired for each state identification, and explains how confidence values seen in are obtained. Video credits: Alexandra Semionov/NIST

Major Accomplishments

Created September 30, 2015, Updated February 16, 2022