Yoshifumi Nakata 교수

We introduce a new quantity, called pseudo-entropy, as a generalization of entanglement entropy via postselection. We expect this quantity to provide a new class of order parameters in quantum many-body systems. In the anti--de Sitter space (AdS)/conformal field theory (CFT) correspondence, this quantity is dual to areas of minimal area surfaces in time-dependent Euclidean spaces which are asymptotically AdS. We call this geometric computation of pseudo-entropy via the $\mathrm{AdS}/\mathrm{CFT}

Motivated by studies of typical properties of quantum states in statistical mechanics, we introduce phase-random states, an ensemble of pure states with fixed amplitudes and uniformly distributed phases in a fixed basis. We first give a sufficient condition for canonical states to typically appear in subsystems of phase-random states, which reveals a trade-off relation between the initial state in the bounded energy subspace and the energy eigenstates that define that subspace. We then investiga

We study the robustness of multipartite entanglement of the ground state of the one-dimensional spin-$\frac{1}{2}$ $XY$ model with a transverse magnetic field in the presence of thermal excitations by investigating a threshold temperature, below which the thermal state is guaranteed to be entangled. We obtain the threshold temperature based on the geometric measure of entanglement of the ground state. The threshold temperature reflects three characteristic lines in the phase diagram of the corre

The Hayden-Preskill protocol is a qubit-toy model of the black hole information paradox. Based on the assumption of scrambling, it was revealed that quantum information is instantly leaked out from the quantum many-body system that models a black hole. In this paper, we extend the protocol to the case where the system has symmetry and investigate how the symmetry affects the leakage of information. We especially focus on the conservation of the number of up-spins. Developing a partial decoupling

We investigate decoupling, one of the most important primitives in quantum Shannon theory, by replacing the uniformly distributed random unitaries commonly used to achieve the protocol, with repeated applications of random unitaries diagonal in the Pauli-Z and -X bases. This strategy was recently shown to achieve an approximate unitary 2-design after a number of repetitions of the process, which implies that the strategy gradually achieves decoupling. Here, we prove that even fewer repetitions o

Quantum error correction (QEC) is one of the central concepts in quantum information science and also has wide applications in fundamental physics. The capacity theorems provide solid foundations of QEC. We here provide a general and highly applicable form of capacity theorem for both classical and quantum information, i.e., hybrid information, with the assistance of a limited resource of entanglement in a one-shot scenario, which covers broader situations than the existing ones. Harnessing the

A distribution of thermal states given by random Hamiltonians with a local structure is studied and it is shown that the ensemble of these states monotonically approaches the unitarily invariant ensemble with decreasing temperature if all particles interact according to a single random interaction and achieves a state t-design at a temperature $O$(1/ log(t)).

Information scrambling refers to the unitary dynamics that quickly spreads and encodes localized quantum information over an entire many-body system and makes the information accessible from any small subsystem. While information scrambling is the key to understanding complex quantum many-body dynamics and is well-understood in random unitary models, it has been hardly explored in Hamiltonian systems. In this Letter, we investigate the information recovery in various time-independent Hamiltonian

Among various classes of quantum error correcting codes (QECCs), non-stabilizer codes have rich properties and are of theoretical and practical interest. Decoding non-stabilizer codes is, however, a highly non-trivial task. In this paper, we show that a decoding circuit for Calderbank-Shor-Steane (CSS) codes can be straightforwardly extended to handle general QECCs. The key to the extension lies in the use of a pair of classical-quantum (CQ) codes associated with the QECC to be decoded. The deco

Unitary 2-designs are random unitary matrices which, in contrast to their Haar-distributed counterparts, have been shown to be efficiently realized by quantum circuits. Most notably, unitary 2-designs are known to achieve decoupling, a fundamental primitive of paramount importance in quantum Shannon theory. Here we prove that unitary 2-designs can be implemented approximately using random diagonal-unitaries.

The black hole (BH) information paradox has been a central problem in fundamental physics, posing a question lying between macroscopic BH physics and microscopic descriptions of a BH. In recent years, quantum information theory has shed new light on the problem, where based on the information scrambling and entanglement, a microscopic process of how information leaks out from a quantum BH has been clarified. However, micro-macro correspondence in the information paradox has been yet to be reveal

Unitary 2-designs are random unitary matrices which, in contrast to their Haar-distributed counterparts, have been shown to be efficiently realized by quantum circuits. Most notably, unitary 2-designs are known to achieve decoupling, a fundamental primitive of paramount importance in quantum Shannon theory. Here we prove that unitary 2-designs can be implemented approximately using random diagonal-unitaries.

The major goal of quantum communication theory is to determine how much information can be protected from a given quantum noise by encoding operations. The capacity theorems provide answers to the question in various settings. We here provide a capacity theorem when the information to be protected is both classical and quantum, i.e., hybrid information, with assistance of a limited resource of entanglement in one-shot scenario. The theorem covers broad situations, and most capacity theorems in t