Quantum State Discrimination via Partial Measurement Offers No Average Gain.

The accurate identification of quantum states represents a fundamental challenge in quantum information science, with implications for secure communication and computation. Recent research explores whether strategically limiting information gained through measurement – a process termed partial post-selection – can enhance the ability to distinguish between quantum states. Qipeng Qian, from the Program in Applied Mathematics at the University of Arizona, and Christos N. Gagatsos, affiliated with both the Department of Electrical and Computer Engineering and the Wyant College of Optical Sciences at the same institution, investigate this question in their work, “The effect of partial post-selection on quantum discrimination”. Their analysis, utilising a framework involving local operations and classical communication (LOCC), demonstrates that, on average, employing partial measurements to manipulate states before attempting discrimination does not yield improved performance compared to directly discriminating the original states. This conclusion holds even when allowing for classical communication between measurement outcomes, suggesting inherent limitations to this state engineering approach.

Recent research investigates the efficacy of utilising pre-measurement strategies, involving partial measurements and subsequent classical communication, to enhance the discrimination of two unknown quantum states. The study demonstrates that, on average, employing these techniques does not improve the probability of correctly distinguishing between the states, maintaining the same minimum error probability as direct discrimination without pre-measurement.

The research establishes a general analytical framework for scenarios where an unknown quantum state interacts with an environment before undergoing a partial measurement on one component of the system. This partial measurement, unlike a complete measurement which definitively determines the state, yields probabilistic outcomes. These probabilities are then communicated classically to an observer, who uses this information to attempt to distinguish between the initial states. The framework utilises Positive Operator-Valued Measures (POVMs), a mathematical formalism describing measurements in quantum mechanics where outcomes are associated with probabilities, to model these partial measurements.

The analysis operates within the constraints of Local Operations and Classical Communication (LOCC), a fundamental principle in quantum information theory. LOCC dictates that information can only be exchanged through classical channels and local operations on quantum systems, precluding instantaneous communication or entanglement-assisted strategies that might otherwise improve discrimination. The researchers rigorously demonstrate that no LOCC strategy can outperform direct discrimination in this specific setup. This means that even with the added flexibility of pre-measurement and classical communication, the fundamental limits on distinguishing between quantum states remain unchanged.

While this research establishes a negative result, indicating the limitations of this particular approach, it also opens avenues for future investigation. The researchers suggest exploring scenarios involving more complex environmental interactions or the inclusion of unitary transformations, which preserve the norm of quantum states, to determine if improvements are possible under different conditions. Potential applications of this work extend to areas such as quantum cryptography, where secure communication relies on the ability to distinguish between quantum states, and quantum sensing, where precise measurements are crucial for detecting weak signals.