Akihisa Hayashi

Bio: Akihisa Hayashi is an academic researcher from University of Fukui. The author has contributed to research in topics: Wigner distribution function & Phase space. The author has an hindex of 17, co-authored 52 publications receiving 1065 citations. Previous affiliations of Akihisa Hayashi include University of Siegen & Folkwang University of the Arts.

An uncertainty principle for quaternion Fourier transform

Abstract: We review the quaternionic Fourier transform (QFT). Using the properties of the QFT we establish an uncertainty principle for the right-sided QFT. This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains. It is shown that only a Gaussian quaternion signal minimizes the uncertainty.

Remote state preparation without oblivious conditions

Abstract: In quantum teleportation, neither Alice nor Bob acquires any classical knowledge on teleported states. The teleportation protocol is said to be oblivious to both parties. In remote state preparation (RSP), it is assumed that Alice is given complete classical knowledge on the state that is to be prepared by Bob. Recently, Leung and Shor [e-print quant-ph/0201008] showed that the same amount of classical information as that in teleportation needs to be transmitted in any exact and deterministic RSP protocol that is oblivious to Bob. Assuming that the dimension of subsystems in the prior-entangled state is the same as the dimension of the input space, we study similar RSP protocols, but not necessarily oblivious to Bob. We show that in this case Bob's quantum operation can be safely assumed to be a unitary transformation. We then derive an equation that is a necessary and sufficient condition for such a protocol to exist. By studying this equation, we show that one-qubit RSP requires two classical bits of communication, which is the same amount as in teleportation, even if the protocol is not assumed oblivious to Bob. For higher dimensions, it is still an open question whether the amount of classical communication can be reduced by abandoning oblivious conditions.

Reexamination of optimal quantum state estimation of pure states

Abstract: A direct derivation is given for the optimal mean fidelity of quantum state estimation of a $d$-dimensional unknown pure state with its $N$ copies given as input, which was first obtained by Hayashi in terms of an infinite set of covariant positive operator valued measures (POVM's) and by Bru\ss{} and Macchiavello establishing a connection to optimal quantum cloning. An explicit condition for POVM measurement operators for optimal estimators is obtained, by which we construct optimal estimators with finite POVMs using exact quadratures on a hypersphere. These finite optimal estimators are not generally universal, where universality means the fidelity is independent of input states. However, any optimal estimator with finite POVM for $M(gN)$ copies is universal if it is used for $N$ copies as input.

Self-consistent mean-field models for nuclear structure

Abstract: The authors review the present status of self-consistent mean-field (SCMF) models for describing nuclear structure and low-energy dynamics. These models are presented as effective energy-density functionals. The three most widely used variants of SCMF's based on a Skyrme energy functional, a Gogny force, and a relativistic mean-field Lagrangian are considered side by side. The crucial role of the treatment of pairing correlations is pointed out in each case. The authors discuss other related nuclear structure models and present several extensions beyond the mean-field model which are currently used. Phenomenological adjustment of the model parameters is discussed in detail. The performance quality of the SCMF model is demonstrated for a broad range of typical applications.

Multiphoton entanglement and interferometry

Abstract: Multiphoton interference reveals strictly nonclassical phenomena. Its applications range from fundamental tests of quantum mechanics to photonic quantum information processing, where a significant fraction of key experiments achieved so far comes from multiphoton state manipulation. The progress, both theoretical and experimental, of this rapidly advancing research is reviewed. The emphasis is given to the creation of photonic entanglement of various forms, tests of the completeness of quantum mechanics (in particular, violations of local realism), quantum information protocols for quantum communication (e.g., quantum teleportation, entanglement purification, and quantum repeater), and quantum computation with linear optics. The scope of the review is limited to ``few-photon'' phenomena involving measurements of discrete observables.

Machine learning & artificial intelligence in the quantum domain: a review of recent progress.

Abstract: Quantum information technologies, on the one hand, and intelligent learning systems, on the other, are both emergent technologies that are likely to have a transformative impact on our society in the future. The respective underlying fields of basic research-quantum information versus machine learning (ML) and artificial intelligence (AI)-have their own specific questions and challenges, which have hitherto been investigated largely independently. However, in a growing body of recent work, researchers have been probing the question of the extent to which these fields can indeed learn and benefit from each other. Quantum ML explores the interaction between quantum computing and ML, investigating how results and techniques from one field can be used to solve the problems of the other. Recently we have witnessed significant breakthroughs in both directions of influence. For instance, quantum computing is finding a vital application in providing speed-ups for ML problems, critical in our 'big data' world. Conversely, ML already permeates many cutting-edge technologies and may become instrumental in advanced quantum technologies. Aside from quantum speed-up in data analysis, or classical ML optimization used in quantum experiments, quantum enhancements have also been (theoretically) demonstrated for interactive learning tasks, highlighting the potential of quantum-enhanced learning agents. Finally, works exploring the use of AI for the very design of quantum experiments and for performing parts of genuine research autonomously, have reported their first successes. Beyond the topics of mutual enhancement-exploring what ML/AI can do for quantum physics and vice versa-researchers have also broached the fundamental issue of quantum generalizations of learning and AI concepts. This deals with questions of the very meaning of learning and intelligence in a world that is fully described by quantum mechanics. In this review, we describe the main ideas, recent developments and progress in a broad spectrum of research investigating ML and AI in the quantum domain.

Quantum teleportation of multiple degrees of freedom of a single photon

Abstract: The quantum teleportation of composite quantum states of a single photon encoded in both spin and orbital angular momentum is achieved, with a teleportation fidelity above the classical limit, by quantum non-demolition measurement assisted discrimination of the Bell states describing the entanglement of the two degrees of freedom. In the process known as quantum teleportation, quantum information encoded in a quantum particle, for example a photon, is transferred from one place to the other without ever moving the photon. Although quantum teleportation has been demonstrated with a variety of different systems, all have so far been limited in one crucial aspect: they only allow teleporting one degree of freedom. Here, Nai-Le Liu and colleagues demonstrate quantum teleportation of two degrees of freedom — spin and orbital angular momentum — in a single photon. Their experimental implementation is very complex and entails various innovative techniques, most notably a hybrid Bell-state measurement scheme. The intricacy of this scheme illustrates how difficult it will be to implement quantum teleportation of more complex quantum systems with more degrees of freedom. But this work represents a first and significant step in this direction. Quantum teleportation1 provides a ‘disembodied’ way to transfer quantum states from one object to another at a distant location, assisted by previously shared entangled states and a classical communication channel. As well as being of fundamental interest, teleportation has been recognized as an important element in long-distance quantum communication2, distributed quantum networks3 and measurement-based quantum computation4,5. There have been numerous demonstrations of teleportation in different physical systems such as photons6,7,8, atoms9, ions10,11, electrons12 and superconducting circuits13. All the previous experiments were limited to the teleportation of one degree of freedom only. However, a single quantum particle can naturally possess various degrees of freedom—internal and external—and with coherent coupling among them. A fundamental open challenge is to teleport multiple degrees of freedom simultaneously, which is necessary to describe a quantum particle fully and, therefore, to teleport it intact. Here we demonstrate quantum teleportation of the composite quantum states of a single photon encoded in both spin and orbital angular momentum. We use photon pairs entangled in both degrees of freedom (that is, hyper-entangled) as the quantum channel for teleportation, and develop a method to project and discriminate hyper-entangled Bell states by exploiting probabilistic quantum non-demolition measurement, which can be extended to more degrees of freedom. We verify the teleportation for both spin–orbit product states and hybrid entangled states, and achieve a teleportation fidelity ranging from 0.57 to 0.68, above the classical limit. Our work is a step towards the teleportation of more complex quantum systems, and demonstrates an increase in our technical control of scalable quantum technologies.