이석형 교수

Masking quantum information, which is impossible without randomness as a resource, is a task that encodes quantum information into the bipartite quantum state while forbidding local parties from accessing that information. In this paper, we disprove the geometric conjecture about unitarily maskable states [Modi, Pati, Sen, and Sen, Phys. Rev. Lett. 120, 230501 (2018)], and make an algebraic analysis of quantum masking. First, we show a general result of quantum channel mixing that a subchannel's

We give an operational meaning to the min-entropy of a quantum state as a resource measure for various interconnected tasks. In particular, we show that the min-entropy without smoothing measures the amount of quantum information that can be hidden or encoded perfectly in the one-shot setting when the quantum state is used as a randomness or correlation source. First, we show that the min-entropy of entanglement of a pure bipartite state is the maximum number of qubits privately transferable whe

The conventional framework of quantum theory treats space and time in vastly different ways by representing temporal correlations via quantum channels and spatial correlations via multipartite quantum states—an imbalance absent in classical probability theory. Since Leifer and Spekkens [] called for a causally neutral formulation of quantum theory in their seminal work, numerous attempts have been made to rectify this asymmetry by proposing a dynamical description of a quantum system encapsulate

Recently, a teleportation scheme using a two-mode squeezed state to teleport a photonic qubit, so called a “hybrid” approach, has been suggested and experimentally demonstrated as a candidate to overcome the limitations of all-optical quantum information processing. We find, however, that there exists the upper bound of fidelity when teleporting a photonic qubit via a two-mode squeezed channel under a lossy environment. The increase of photon loss decreases this bound, and teleportation better t

Catalysts are substances that assist transformation of other resourceful objects without being consumed in the process. However, the fact that their ``catalytic power'' is limited and can be depleted is often overlooked, especially in the recently developing theories on catalysis of quantum randomness utilizing building correlation with catalyst. In this work, we establish a resource theory of one-shot catalytic randomness in which uncorrelatedness is consumed in catalysis of randomness. We do s

A commitment scheme allows one to commit to hidden information while keeping its value recoverable when needed. Despite considerable efforts, an unconditionally and perfectly secure bit commitment has been proven impossible both classically and quantum-mechanically. The situation is similar when committing to qubits instead of classical bits as implied in the no-masking theorem [K. Modi et al., Phys. Rev. Lett. {\bf 120}, 230501 (2018)]. In this Letter, we find that circumvention of the no-maski

Catalysts used in quantum resource theories need not be in isolation and, therefore, are possibly correlated with external systems, which the agent does not have access to. Do such correlations help or hinder catalysis, and does the classicality or quantumness of such correlations matter? To answer this question, we first focus on the existence of a noninvasively measurable observable that yields the same outcomes for repeated measurements since this signifies macrorealism, a key property distin

A system-ancilla bipartite state capable of containing the complete information of an unknown quantum channel acting on the system is called faithful. In this work, we extend the applicability and generality of faithfulness significantly by introducing its local variant and examining their relationship when applied to various classes of quantum channels. In doing so, we discovered that, in the original proof by D'Ariano and Presti, only sufficiency was shown, not the full equivalence between fai

Randomness can help one to implement quantum maps that cannot be realized in a deterministic fashion. Recently, it was discovered that explicitly treating a randomness source as a quantum system could double the efficiency as a catalyst for some tasks. In this work, we generalize this result to general randomness-utilizing processes and show that the gap between the efficiencies of classical and quantum catalytic randomness is generic. To explore the achievability of catalysis of quantum randomn

We generalize the theory of catalytic quantum randomness to distributed and dynamical settings. First, we expand the theory of catalytic quantum randomness by calculating the amount of (R\'enyi) entropy catalytically extractable from a distributed or dynamical randomness source. We show that no entropy can be catalytically extracted when one cannot implement local projective measurement on randomness source without altering its state. As an application, we prove that quantum operation cannot be

The theory of quantum states over time extends the density operator formalism into the temporal domain, providing a unified treatment of timelike and spacelike separated systems in quantum theory. Although recent results have characterized quantum states over time involving two timelike separated systems, it remains unclear how to consistently extend the notion of quantum states over time to multipartite temporal scenarios, such as those considered in studies of Leggett-Garg inequalities. In thi

We introduce and study the problem of scrambler hacking, which is the procedure of quantum information extraction from and installation on a quantum scrambler given only partial access. This problem necessarily emerges from a central topic in contemporary physics - information recovery from systems undergoing scrambling dynamics, such as the Hayden-Preskill protocol in black hole studies - because one must replace quantum data with another when extracting it due to the no-cloning theorem. For la

Catalysts are substances that assist transformation of other resourceful objects without being consumed in the process. However, the fact that their `catalytic power' is limited and can be depleted is often overlooked, especially in the recently developing theories on catalysis of quantum randomness utilizing building correlation with catalyst. In this work, we establish a resource theory of one-shot catalytic randomness in which uncorrelatedness is consumed in catalysis of randomness. We do so

Catalysts used in quantum resource theories need not be in isolation and therefore are possibly correlated with external systems, which the agent does not have access to. Do such correlations help or hinder catalysis, and does the classicality or quantumness of such correlations matter? To answer this question, we first focus on the existence of a non-invasively measurable observable that yields the same outcomes for repeated measurements, since this signifies macro-realism, a key property disti

In the quantum theory, it has been shown that one can see if a process has the time reversal symmetry by applying the matrix transposition and examining if it remains physical. However, recent discoveries regarding the indefinite causal order of quantum processes suggest that there may be other, more general symmetry transformations of time besides the complete reversal. In this work, we introduce an expanded concept of matrix transposition, the generalized transposition, that takes into account