MIT and University of Ferrara researchers created a mathematical blueprint for designing distinguishable non-Gaussian quantum states.
Researchers worldwide are working to develop quantum systems for sensing, communications, computing, and control that could outperform today’s technologies. A major challenge is creating quantum states that are stable, measurable, and easy to distinguish, since these states are the foundation of any practical quantum device.
Quantum states have unique characteristics that make them attractive for advanced information processing. However, achieving both stability and distinguishability remains difficult. Recovering information from a quantum system depends on how well its quantum states can be distinguished, a property tied to orthogonality. Because no two Gaussian states (a widely studied class of quantum states) are orthogonal, some level of error is unavoidable when trying to tell them apart.
Current quantum devices also remain stable for only fractions of a second and often rely on complicated methods to distinguish between quantum states. Researchers at MIT and the University of Ferrara have now developed a new technique for creating more easily distinguishable states, a step that could support the next generation of quantum technologies.
The approach is detailed in a paper published in Physical Review A by Moe Z. Win and Peter L. Falb of MIT, together with Andrea Giani and Andrea Conti of the University of Ferrara. The researchers discovered a way to translate quantum states of light into algebraic varieties (a mathematical structure from abstract algebra), allowing the problem to be expressed as mathematical equations that can be solved more easily.
Designing More Distinguishable Quantum States
“Quantum systems can provide performance that is significantly better than classical counterparts,” Win says, “but this doesn’t come for free.” To build practical devices that generate and detect different quantum states, “one needs to carefully engineer the quantum states in which they encode information.”
Conventional computers typically represent ones and zeros using different voltage levels in solid-state devices, while optical systems may rely on the presence or absence of a pulse of light. In quantum technologies, information can instead be encoded in properties such as the spin of a single atom or the excitation level of a group of electrons.
Win says that “we have been studying how to design distinguishable quantum states, which translates directly into improved performance for sensing and communication.” In technical terms, the research focuses on increasing the orthogonality, or distinguishability, of different quantum states.
Photon-Varied Non-Gaussian States Offer New Possibilities
The team’s theoretical work focused on photon energy levels. Giani explains that the researchers used a process called photon variation, which includes either photon addition, where photons are raised to a higher energy state, or photon subtraction, where photons are annihilated (i.e., removed from the system). These operations transform Gaussian states into non-Gaussian states, which the researchers found to be especially promising.
“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.”
Unlike some emerging quantum technologies that remain largely experimental, Giani notes that “these kinds of photon-varied states have already been produced in the laboratory, and there is much interest in this kind of operation.”
Algebraic Geometry Enables Quantum State Design
Because these quantum states are relatively new, Conti says, “there was a need for a theoretical characterization for these states.” The mathematical framework developed by the researchers provides that characterization and makes it possible to design states with greater distinguishability.
Win says, “We have a theory that gives us a blueprint to go design these non-Gaussian states, rather than just, ‘Try this and that, and let’s hope they’re somewhat distinguishable.’ Our theory tells us exactly how to go about designing orthogonal non-Gaussian states.”
According to Win, the breakthrough came from linking algebraic equations with the underlying physics. “That was the important connection between different disciplines—bringing algebraic geometry to the table.”
“The equations to be solved for determining the orthogonality of the quantum states happened to be polynomial equations,” Falb says. “It just happened that there was the appropriate mathematics to solve them.”
From Mathematical Theory to Quantum Device Implementation
With the underlying principles now established, the researchers believe putting the method into practice should be relatively straightforward. Existing optical setups can already be adapted to create these quantum states.
“In principle,” Giani notes, “you can just put the parameters that you find by solving these equations directly into your physical apparatuses and produce these kinds of states. I don’t think this requires some more advanced technology.”
Conti adds that “as soon as this paper is published, we hope that experimentalists can try these methods.”
Win says the work represents only the beginning. “We are getting momentum, and it’s very exciting,” he says. “The approach that we are taking here is to ask more general questions than just, ‘Here’s a particular setup, how do you tune it to get a performance gain?’ Rather, we’re looking at a class of signal design problems and then finding keys that really unlock these so that hopefully the answer will not just be applied to only one particular setup but something significantly broader.”
Reference: “Unveiling distinguishable non-Gaussian quantum states” by Andrea Giani, Moe Z. Win, Peter L. Falb and Andrea Conti, 15 June 2026, Physical Review A.
DOI: 10.1103/ffbg-4897
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