MIT-Ferrara Team Creates a Mathematical Blueprint for More Distinguishable Quantum States

Researchers at MIT and the University of Ferrara have developed a mathematical blueprint for designing quantum states of light that can be made more easily distinguishable from one another, a property that is foundational to any practical quantum device. The work 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.

Recovering information from a quantum system depends on how well its quantum states can be distinguished, a property tied to their orthogonality. Because no two Gaussian states, a widely studied class of quantum states, are ever orthogonal, some error is unavoidable when trying to tell them apart, and current quantum devices remain stable for only fractions of a second. "Quantum systems can provide performance that is significantly better than classical counterparts," Win said, "but this doesn't come for free" — researchers must carefully engineer the quantum states used to encode information.

The team focused on "photon variation," a process of adding or removing photons that transforms Gaussian states into non-Gaussian states, which Giani said are especially promising because "these kinds of photon-varied states have already been produced in the laboratory." The researchers found a way to translate these quantum states of light into algebraic varieties, a structure from abstract algebra, turning the problem of determining orthogonality into polynomial equations that can be solved more easily. "That was the important connection between different disciplines — bringing algebraic geometry to the table," Win said.

The researchers said existing optical setups can already be adapted to produce the states their equations describe, without requiring more advanced technology, and that they hope experimentalists will test the methods now that the paper has been published.