IQC PhD thesis defence - Kohdai Kuroiwa

Candidate: Kohdai Kuroiwa
Supervisor: Debbie Leung
Location: QNC 2101
Date/Time: December 9, 2026, 9:00 a.m.

In this thesis, we study quantum information processing by revisiting several conventional assumptions in quantum Shannon theory and quantum resource theories. In quantum Shannon theory, we examine how the communication cost of quantum source compression depends on the error criterion. In quantum resource theories, we investigate operational advantages without assuming convexity, entanglement formation in infinite-dimensional systems under restricted communication, and unitary implementation using auxiliary resource states.

In quantum Shannon theory, we first develop quantum rate-distortion theory for mixed-state ensemble sources under local error criteria. For entanglement-assisted compression, we obtain a single-letter characterization in terms of quantum mutual information. Without entanglement assistance, the optimal compression rate for nonzero average local error is characterized by a regularized entanglement of purification. We examine the special cases of visible compression, in which the sender knows the label of the state, and blind compression, in which the sender does not have access to the label. We also characterize the joint achievable region of quantum communication and entanglement rates. Next, under a global error criterion, we prove exponential strong converses for visible ensemble-source state redistribution, a generalization of visible compression, and for blind compression. At rates strictly outside the respective achievable regions, the fidelity decays exponentially with block length. In particular, in the blind-compression strong-converse proof, we introduce a new quantity, the Koashi--Imoto overlap, to address instability in the structure of quantum ensembles. These results highlight the difference between local and global error criteria: local distortion permits rate reductions, whereas a global error criterion yields sharp thresholds for reliable compression.

In quantum resource theories, we first develop a theory of resource witnesses without imposing the conventional assumption of convexity. We introduce a multicopy witness based on a widely used resource measure, the generalized robustness. Using this witness, we prove that every resource state provides an advantage in a suitable channel discrimination task, even when the set of free states is nonconvex. We also relate the generalized robustness to the worst-case advantage in channel discrimination by expressing the set of free states as a union of convex subsets. Additionally, we show that our analysis extends to another resource measure, the weight of resource, as well as to resource theories of quantum channels and instruments. Next, we investigate quantum resource theories beyond finite-dimensional settings. For bipartite states on separable Hilbert spaces, we characterize the entanglement cost of formation using local operations and communication at asymptotically vanishing rates. The optimal cost is expressed by the regularized entanglement of purification, as in the finite-dimensional case, provided that at least one target marginal state has finite entropy. To prove achievability, we extend a finite-dimensional communication-efficient dilution protocol by developing refined typicality arguments. For the converse proof, we establish a one-sided asymptotic continuity property of the entanglement of purification. The optimal cost is achievable using classical communication at a vanishing rate, and allowing quantum communication does not reduce this cost. Finally, we study the implementation of resource-generating unitaries using an auxiliary system that may be infinite dimensional. Using the measured relative entropy of resource, we show that exact implementation requires an auxiliary state with infinite relative entropy of resource. This extends previous impossibility results beyond the assumption of additive resource measures. For finite-dimensional target systems, we also derive a quantitative resource--error trade-off in terms of the relative entropy of resource and its measured counterpart. As an example, we consider the resource theory of single-qubit magic and present explicit calculations for the T gate and a gate preparing the F state.

Taken together, these results clarify how error criteria and structural assumptions shape the capabilities and limitations of quantum information processing. By extending operational characterizations beyond conventional settings, this thesis identifies which conclusions remain valid when assumptions such as convexity, finite dimensionality, and additivity are relaxed, and where fundamental limitations persist. The resulting characterizations and proof techniques provide a foundation for studying quantum communication and resource manipulation in a broader range of settings.