Researchers worldwide are racing to develop new quantum-based systems for sensing, communication, computing, and control that promise to outperform traditional systems. Creating stable, measurable, and distinguishable quantum states, which are at the heart of any such system, is a daunting task. Quantum states have unique properties that can be exploited for novel information processing systems; however, achieving stability and distinguishability is challenging. Extracting information from a quantum system relies on the distinguishability of quantum states, an intrinsic property linked to orthogonality.
No two Gaussian states (a widely studied class of quantum states) are orthogonal, leading to unavoidable errors when attempting to distinguish them. Additionally, current quantum devices tend to remain stable only for a fraction of a second and require complex protocols to distinguish states. Researchers at MIT and the University of Ferrara have now found a new approach for creating easily distinguishable states that could facilitate the development of these new quantum-based devices.
This new approach is detailed in a paper published in Physical Review A by Moe Z. Win and Peter L. Falb at MIT, along with Andrea Giani and Andrea Conti from the University of Ferrara. The team discovered a method to translate between quantum states of light and algebraic varieties (a mathematical structure from abstract algebra), simplifying the analysis into solvable mathematical equations.
"Quantum systems can provide performance that is significantly better than classical counterparts," Win states, "but this doesn’t come for free." To develop practical devices for producing and detecting different states, "one needs to carefully engineer the quantum states in which they encode information." Traditional computers typically use different voltages in a solid-state device to encode ones and zeros, while optical systems may use the presence or absence of light pulses. In quantum devices, states might relate to the spin state of a single atom or the excitation level of a group of electrons.
The specific states studied in this analysis pertain to the energy levels of photons. Giani explains that they employed an operation called photon variation, which can take two forms: photon addition (exciting photons to a higher energy state) or photon subtraction (removing photons from the system). These operations transition the quantum state from Gaussian to non-Gaussian states, which the team concluded to be more useful. "The domain of non-Gaussian states is quite large," Giani notes, "but among them, we are looking into non-Gaussian states that are easier to implement with current technologies, because if we want to transition to the quantum world, we need to consider realistic experimental challenges."
Unlike some cutting-edge technologies being studied for potential quantum applications, Giani mentions that "these types of photon-varied states have already been produced in the laboratory, and there is much interest in this kind of operation." These states are relatively new, and Conti states, "there was a need for a theoretical characterization for these states." The theoretical characterization derived by the team, based on underlying mathematical properties, enables the design of states with higher levels of distinguishability. With this work, Win asserts, "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."
The findings arise from the connection between algebraic equations and underlying physics, Win remarks, "That was the important connection between different disciplines — bringing algebraic geometry to the table." Falb adds, "The equations to be solved for determining the orthogonality of the quantum states happened to be polynomial equations. It just happened that there was the appropriate mathematics to solve them."
Now that the principles have been established, implementation should be relatively straightforward, researchers say. There are already some optical setups that can be used to implement these kinds of 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 more advanced technology." Conti adds, "As soon as this paper is published, we hope that experimentalists can try these methods." But that’s just the beginning, Win emphasizes. "We are gaining momentum, and it’s very exciting," he says. "The approach 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 apply to one particular setup, but something significantly broader."
Blogger's Review: The research team’s innovative connection between quantum states and algebraic geometry provides a fresh perspective on the distinguishability issue in quantum systems. This approach could significantly advance practical applications of quantum technologies, laying a foundation for the future of quantum computing and communication, making it an exciting area to watch.