Ryuji Takagi

Evaluating the maximum amount of work extractable from a nanoscale quantum system is one of the central problems in quantum thermodynamics. Previous works identified the free energy of the input state as the optimal rate of extractable work under the crucial assumption: experimenters know the description of the given quantum state, which restricts the applicability to significantly limited settings. Here, we show that this optimal extractable work can be achieved without knowing the input states at all, removing the aforementioned fundamental operational restrictions. We achieve this by presenting a universal work extraction protocol, whose description does not depend on input states but nevertheless extracts work quantified by the free energy of the unknown input state. Remarkably, our result partially encompasses the case of infinite-dimensional systems, for which optimal extractable work has not been known even for the standard state-aware setting. Our results clarify that, in spite of the crucial difference between the state-aware and state-agnostic scenarios in accomplishing information-theoretic tasks, whether we are in possession of information on the given state does not influence the optimal performance of the asymptotic work extraction.

Uhlmann's theorem is a central result in quantum information theory, associating the closeness of two quantum states with that of their purifications. This theorem well characterizes the fundamental task of transforming a quantum state into another state via local operations on its subsystem. The optimal transformation for this task is called the Uhlmann transformation, which has broad applications in various fields; however, its quantum circuit implementation and computational cost have remained unclear. In this work, we fill this gap by proposing quantum query and sample algorithms that realize the Uhlmann transformation in the form of quantum circuits. These algorithms achieve exponential improvements in computational costs, including query and sample complexities, over naive approaches based on state measurements such as quantum state tomography, under certain computational models. We apply our algorithms to the square root fidelity estimation task and particularly show that our approach attains a better query complexity than the prior state-of-the-art. Furthermore, we discuss applications to several information-theoretic tasks, specifically, entanglement transmission, quantum state merging, and algorithmic implementation of the Petz recovery map, providing a comprehensive evaluation of the computational costs.

Quantum technologies offer exceptional---sometimes almost magical---speed and performance, yet every quantum process costs physical resources. Designing next-generation quantum devices, therefore, depends on solving the following question: which resources, and in what amount, are required to implement a desired quantum process? Casting the problem in the language of quantum resource theories, we prove a universal cost-irreversibility tradeoff: the lower the irreversibility of a quantum process, the greater the required resource cost for its realization. The trade-off law holds for a broad range of resources---energy, magic, asymmetry, coherence, athermality, and others---yielding lower bounds on resource cost of any quantum channel. Its broad scope positions this result as a foundation for deriving the following key results: (1) we show a universal relation between the energetic cost and the irreversibility for arbitrary channels, encompassing the energy-error tradeoff for any measurement or unitary gate; (2) we extend the energy-error tradeoff to free energy and work costs; (3) we extend the Wigner-Araki-Yanase theorem, which is the universal limitation on measurements under conservation laws, to a wide class of resource theories: the probability of failure in distinguishing resourceful states via a measurement is inversely proportional to its resource cost; (4) we prove that infinitely many resource-non-increasing operations in fact require an infinite implementation cost. These findings reveal a universal relationship between quantumness and irreversibility, providing a first step toward a general theory that explains when---and how---quantumness can suppress irreversibility.

We establish universal limitations on the manipulation of quantum channel resources under the most general transformation protocols. Focusing in particular on the class of distillation tasks -- which can be understood either as the purification of noisy channels into unitary ones, or the extraction of state-based resources from channels -- we develop fundamental restrictions on the error necessarily incurred in such transformations. Our results are applicable to the study of general quantum resources under any physical manipulation scheme, which includes general adaptive protocols with or without a definite causal order. We introduce comprehensive lower bounds for the overhead of any distillation protocol in terms of required channel uses, imposing strong limitations on the practical efficiency and cost of channel resource manipulation. In the asymptotic setting, our results yield broadly applicable strong converse bounds for the rates of distillation. As a special case, our methods apply to the manipulation of quantum states, in which case they significantly improve on and extend previous approaches. We demonstrate our results through explicit applications to quantum communication, where we recover in particular a number of strong converse bounds for the quantum capacity of channels assisted by different classes of operations, as well as to fault-tolerant quantum computation, where we obtain improved bounds for the overhead cost of magic state distillation and gate synthesis.