New Quantum Yardsticks Rank the Nonclassicality of Light More Precisely Than Ever

Light is the workhorse of the quantum technology revolution. Squeezed states of light sharpen the sensitivity of gravitational-wave detectors, single photons carry quantum keys across continental fiber networks, and entangled optical fields drive the boson-sampling machines that race against classical supercomputers. Yet a deceptively simple question still occupies theorists: given a beam of light, exactly how nonclassical is it? A new theoretical study by Qing-Long Tian and You-Neng Guo of Changsha University, published in Quantum Information Processing, offers a sharper answer than before by building two closely related measures of nonclassicality and proving a rigorous hierarchy between them.

The question matters because classical physics, through the framework of electromagnetic waves and coherent states, can mimic a surprising amount of quantum optical behavior. Since the pioneering work of Roy Glauber and E. C. G. Sudarshan in the 1960s, physicists have known that some optical states can be fully described by classical probability distributions over field amplitudes, while others cannot. States in the second category, the genuinely nonclassical ones, are precisely the resources that enable quantum-enhanced sensing, secure communication, and photonic quantum computing. Quantifying the depth of that nonclassicality, however, has spawned a zoo of competing measures: Wigner function negativity, sub-Poissonian statistics, quadrature squeezing, entropic criteria, and distances to the nearest classical state, each capturing a different facet of the phenomenon.

Tian and Guo approach the problem from a direction inspired by so-called entanglement potentials. The idea, developed over the past decade by researchers including Adam Miranowicz, Karol Bartkiewicz, and their collaborators, is elegant: a single-mode optical state can be mixed with an auxiliary qubit, and the resulting two-qubit system can be tested for quantum correlations. The amount of entanglement, steering, or Bell nonlocality that can be generated this way serves as a certificate of how nonclassical the original light was. In effect, the optical state is interrogated by asking how much quantum correlation it can unlock, and experimental groups in Olomouc have recently demonstrated these potentials for single-photon states in the laboratory.

The new work extends this program beyond entanglement to two subtler correlation quantifiers. The first is local quantum uncertainty, introduced by Davide Girolami and colleagues in 2013, which measures the minimum uncertainty, in the Wigner-Yanase skew information sense, that a local measurement can have about a quantum system. The second is local quantum Fisher information, a related quantity built from the quantum Fisher information that underlies the ultimate precision limits of quantum metrology. Both quantifiers detect quantum correlations that entanglement measures miss, and both have been extensively studied in spin chains, nitrogen-vacancy centers, and axially symmetric qubit-qutrit systems. Tian and Guo now transplant them into quantum optics, defining the local quantum uncertainty potential, or LQUP, and the local quantum Fisher information potential, or LQFIP, as the maximum of these quantities extractable when a single-mode optical field is coupled to a probe qubit.

The central result of the paper is a set of exact mathematical bounds connecting the two potentials. For a specific class of nonclassical states, the authors derive both the lower and the upper bound of the LQFIP as a function of the LQUP, and they identify precisely which states saturate each bound. This is more than a technical curiosity. It means that knowing one potential pins down the range of the other, so the two measures cannot disagree arbitrarily. The relationship establishes a strong hierarchy of nonclassicality for single-qubit optical states, one that maps directly onto the well-studied hierarchy of quantum correlations in two-qubit systems.

The proof of the upper bound, laid out in an appendix of the paper, is a compact exercise in linear algebra and inequalities. Writing the potential in terms of the eigenvalues and eigenvectors of the joint state, the authors decompose the Fisher-information-based quantity into a term proportional to the uncertainty-based one plus a remainder. The Cauchy-Schwarz inequality then shows that the remainder is always nonnegative, which forces the Fisher potential to fall below the parabolic bound given by the product of the uncertainty potential and its complement. The normalization of the measurement Hamiltonian, a Pauli operator along an arbitrary direction, guarantees that the auxiliary sum appearing in the inequality never exceeds two, closing the argument. The result is a tight, state-independent constraint that any physical system must obey.

Why should a hierarchy of this kind matter outside the pages of a mathematics-heavy journal? The answer lies in resource theories, the framework in which modern quantum information treats entanglement, coherence, and nonclassicality as fuels to be budgeted and spent. If two proposed measures of the same resource can be ordered by a proven inequality, experimenters can choose whichever is easier to measure without losing the ability to rank states consistently. The LQUP and LQFIP, being defined through local measurements on an appended qubit, are in principle accessible with the same interferometric techniques already used to estimate entanglement potentials, and the LQFIP carries a direct metrological interpretation through its connection to parameter-estimation precision.

That metrological connection runs deep. The quantum Fisher information sets the ceiling on how well a phase, frequency, or field strength can be estimated with a given state, a bound that underlies the advantage of squeezed light in the LIGO interferometers and of entangled probes in quantum-enhanced microscopy. By proving that the local quantum Fisher information potential is bounded above and below by functions of the local quantum uncertainty potential, the Changsha team effectively links a general-purpose nonclassicality certificate to a quantity with immediate operational meaning for sensing. An optical state that scores high on the uncertainty potential is guaranteed a corresponding level of interferometric power, and the saturating states tell metrologists exactly which light achieves the optimum.

The study also fits into a broader and sometimes counterintuitive lesson from the past decade: mixtures of quantum states can be more quantum, by certain measures, than their pure superpositions, and dissipation or unbalanced beam splitting can increase relative nonclassicality rather than destroy it. A hierarchy that holds for all states in a class provides the organizing principle needed to make sense of such surprises. It tells researchers when a comparison between two optical states is meaningful and when an apparent contradiction between measures merely reflects the fact that they probe different facets of the same underlying resource.

For the field of quantum optics, the new potentials join an expanding toolkit that ranges from Hillery’s nonclassical distance of 1987 to computable measures based on the Hilbert-Schmidt distance and the negativity of the Wigner function. What distinguishes the entanglement-potential family, and now its uncertainty- and Fisher-based extensions, is its operational character: the measures are defined by what a laboratory can actually extract from a state rather than by abstract distances in an infinite-dimensional space. As photonic platforms mature toward fault-tolerant quantum computing and networked quantum sensors, having a rigorously ordered set of nonclassicality quantifiers, with proven bounds and characterized extremal states, turns a conceptual debate into an engineering decision. Tian and Guo’s hierarchy is a step toward that kind of quantitative discipline in the quantum light that will power the next generation of technologies.

Subject of Research: Hierarchy between local quantum uncertainty and local quantum Fisher information potentials as measures of nonclassicality in single-mode optical states

Article Title: Stronger hierarchy between local quantum uncertainty and local quantum fisher information potentials

Article References: Tian, Q.-L., & Guo, Y.-N. (2026). Stronger hierarchy between local quantum uncertainty and local quantum fisher information potentials. Quantum Information Processing, 25(10), Article 327. https://doi.org/10.1007/s11128-026-05349-0

Image Credits: AI Generated

DOI: 10.1007/s11128-026-05349-0

Keywords: quantum optics, nonclassicality, local quantum uncertainty, quantum Fisher information, entanglement potential, quantum correlations, single-mode optical states, quantum metrology, quantum information, squeezed light, Wigner-Yanase skew information, Quantum Information Processing