Researchers at MIT and the University of Ferrara have devised a new framework aimed at improving the distinguishability of quantum states, a critical property for advancing sensing, communication, computing, and control technologies. A fundamental challenge in quantum system design is that no two Gaussian states are orthogonal, creating unavoidable errors when attempting to differentiate between them; this limitation is now being addressed with a novel mathematical approach. The team, including Moe Falb at MIT with Andrea Giani and Andrea Conti at the University of Ferrara, translated quantum states of light into algebraic varieties, simplifying analysis and reducing it to solvable equations. “Quantum systems can provide performance that is significantly better than classical counterparts,” says Win, “but this doesn’t come for free,” emphasizing the need for careful engineering of quantum states to encode information effectively, especially given that current quantum devices remain stable for a fraction of a second.
Quantum State Distinguishability Challenges in Sensing and Computing
The team, including Moe Falb, focused on moving beyond Gaussian states to non-Gaussian states achieved through operations like photon addition or subtraction, exciting or removing photons to alter the quantum state. Giani notes that the range of non-Gaussian states is quite large, but their focus is on states easier to implement with current technologies. The theoretical characterization developed by the team provides a blueprint for designing these non-Gaussian states, allowing for the creation of states with demonstrably higher distinguishability, as Win explains, and is based on solving polynomial equations that describe the orthogonality of the quantum states. Conti anticipates that experimentalists will quickly be able to implement these methods, as these kinds of photon-varied states have already been produced in the laboratory.
we have been studying how to design distinguishable quantum states, which translates directly into improved performance for sensing and communication.”
Translating Quantum States with Algebraic Varieties
The pursuit of stable, distinguishable quantum states, essential building blocks for future quantum technologies, is increasingly focused on moving beyond limitations inherent in widely studied Gaussian states. This approach doesn’t seek incremental improvements in existing systems, but rather a fundamental shift in how these states are designed and analyzed. The team, led by Moe Falb, translated the problem into mathematical equations, creating a more manageable system for analysis. This framework focuses on generating non-Gaussian states through photon addition and subtraction, altering the energy levels of photons.
Quantum systems can provide performance that is significantly better than classical counterparts,” Win says, “but this doesn’t come for free.”
Photon Variation Creates Useful Non-Gaussian States
Unlike traditional Gaussian states, which inherently lack perfect distinguishability, meaning no two are truly orthogonal, this approach leverages photon variation to generate states where differences are more readily detectable. Andrea Giani of the University of Ferrara explains this process involves either adding or subtracting photons, shifting their energy levels to transition from Gaussian to non-Gaussian states. This isn’t simply about theoretical advancement; the team specifically targeted non-Gaussian states that are easier to implement with current technologies, recognizing the need to bridge the gap between promising physics and practical engineering. The core of their innovation lies in translating the complexities of quantum states into the more manageable language of algebraic varieties, effectively reducing the problem to solvable mathematical equations. Moe Falb’s framework addresses a significant limitation of existing quantum devices, which tend to remain stable for a fraction of a second and require complex protocols to distinguish states.
The domain of non-Gaussian states is quite big,” Giani says, “but among them, we are looking into non-Gaussian states that are easier to implement with current technologies, because if we want to make the transition to the quantum world, we need to take into account realistic experimental challenges.”
Theoretical Framework Enables Design of Orthogonal States
A fundamental limitation in quantum system design has long been the inability to perfectly differentiate between Gaussian states; no two are truly orthogonal, introducing unavoidable errors. This new approach directly addresses this challenge by offering a method for generating states with demonstrably improved distinguishability. The team led by Moe Falb clarifies that this process, called photon variation, “can take two forms: photon addition, in which photons are excited to a higher energy state, or photon subtraction, in which photons are annihilated.” Crucially, these photon-varied states are not merely theoretical constructs; they have already been produced in the laboratory, making practical implementation more feasible. This connection between algebraic equations and underlying physics, Falb explains, “happened to be polynomial equations,” allowing for a solution where previously there was only trial and error.
The equations to be solved for determining the orthogonality” of the quantum states “happened to be polynomial equations,”
