Global coherence identified as the genuine quantum resource behind discord

Quantum discord has long been treated as a measure of the specifically quantum part of the correlations between two quantum systems, because it can remain nonzero even for mixed states that are separable, meaning they are not entangled. Yet a new theoretical study argues that discord itself does not, in general, capture genuinely quantum correlations. The work, published in Quantum Information Processing, introduces a concept the authors call global coherence and builds a resource theory around it to identify what actually powers discord-based quantum information protocols.

The central idea is precise. In a bipartite system, global coherence is defined as bipartite coherence that cannot be attributed to local coherence in either subsystem alone. In other words, if all the coherent superposition behavior of the joint state can be explained by coherence present separately in subsystem A or subsystem B, then the state has no global coherence. The researchers give this abstract definition an operational handle: global coherence is characterized by discordant states whose correlation matrix rank exceeds the minimum subsystem dimension. That rank condition provides a concrete mathematical test for when a discordant state carries correlations that are genuinely quantum rather than merely locally coherent.

To turn this idea into a usable framework, the authors construct the resource theory of global coherence. Resource theories are a standard tool in quantum information science: they specify which states are free, which operations can be performed at no cost, and which states count as valuable resources for tasks. In this theory, the free operations are any local operations of the form Φ_A ⊗ Φ_B, meaning arbitrary operations applied independently to each subsystem. Crucially, classical randomness is not freely available. This choice distinguishes global coherence from frameworks in which adding classical noise costs nothing, and it sharpens the claim that the resource being quantified is specifically quantum.

The framework yields a striking structural result. The authors establish that global coherence is necessary for semi-device-independent steerability. Steering is the phenomenon in which measurements on one quantum system allow an observer to prepare, or steer, the state of a distant partner system, and semi-device-independent protocols assume less about the devices than fully trusted settings. The analogy drawn in the paper is direct: just as entanglement is necessary for standard steering, global coherence is necessary for steering in this semi-device-independent setting. This gives global coherence an operational meaning tied to a certified quantum information task rather than remaining a purely abstract quantity.

The study also resolves a resource-identification question for a specific protocol. For remote state preparation using two-qubit states, the researchers identify a necessary and sufficient quantum resource by introducing a global coherence quantifier. A quantifier of this kind assigns a number to each state, measuring how much of the resource it contains, and the necessary-and-sufficient status means that a two-qubit state can support the protocol exactly when this quantifier is nonzero. This moves the analysis beyond qualitative statements and provides a sharp criterion for when remote state preparation succeeds.

Finally, the work establishes a hierarchy of correlations in bipartite quantum states and clarifies the relationship between coherence, discord, and entanglement. These three notions have often been discussed in parallel, and the new hierarchy organizes them into a single structure. The upshot is that discord, entanglement, and coherence are not interchangeable labels for quantumness; global coherence emerges as the resource that captures genuinely quantum correlation where entanglement measures alone fall short, since discord can be nonzero for separable mixed states.

The practical significance lies in demonstrating that genuinely quantum correlation, as captured by global coherence, enables operational advantages beyond those achievable with locally coherent states. Locally coherent states may look quantum in each subsystem individually, yet they lack the joint, nonlocal coherence that the theory identifies as the true asset. For discord-based quantum information protocols, this reframing suggests that past debates over whether discord is a useful resource can be settled by asking a sharper question: does the state possess global coherence?

As a theoretical contribution, the paper does not report an experiment; its claims concern definitions, resource-theoretic axioms, and mathematical characterizations of bipartite states. Even so, the operational anchors are concrete. The correlation-matrix-rank condition gives experimenters a state-dependent test, the semi-device-independent steering connection ties the resource to certification tasks that tolerate untrusted devices, and the two-qubit quantifier supplies a necessary-and-sufficient criterion for remote state preparation. Together these results indicate that the specifically quantum component of correlations, present even without entanglement, is best understood through global coherence, offering researchers a refined tool for designing and certifying quantum information tasks built on discordant states.

Subject of Research: Global coherence as the genuine quantum resource in quantum discord for quantum information tasks

Article Title: Global coherence: the genuine quantum resource in discord for quantum information tasks

Article References: Jebarathinam, C., Ku, H.-Y., Cheng, H.-C., & Goan, H.-S. (2026). Global coherence: the genuine quantum resource in discord for quantum information tasks. Quantum Information Processing, 25(11), Article 355. https://doi.org/10.1007/s11128-026-05379-8

Image Credits: AI Generated

DOI: 10.1007/s11128-026-05379-8

Keywords: quantum discord, global coherence, resource theory, entanglement, steering, remote state preparation, bipartite states, quantum information, separable states, correlation matrix rank, semi-device-independent protocols, quantum coherence