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Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the…
We propose and demonstrate scheme for direct experimental testing of quantum commutation relations for Pauli operators. The implemented device is an advanced quantum processor that involves two programmable quantum gates. Depending on a…
Quantum mechanics is characterized by quantum coherence and entanglement. After having discovered how these fundamental concepts govern physical reality, scientists have been devoting intense efforts to harness them to shape future science…
Understanding the demarcation line between classical and quantum is an important issue in modern physics. The development of such an understanding requires a clear picture of the various concurrent notions of `classicality' in quantum…
The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In…
Linear response theory is concerned with the way in which a physical system reacts to a small change in the applied forces. Here we show that quantum mechanics in the Heisenberg representation can be understood as a linear response theory.…
We evaluate the degree of quantum correlation between two fermions (bosons) subject to continuous time quantum walks in a one-dimensional ring lattice with periodic boundary conditions. In our approach, no particle-particle interaction is…
Some predictions of quantum mechanics are in contrast with the macroscopic realm of everyday experience, in particular those originated by the Heisenberg uncertainty principle, encoded in the non-commutativity of some measurable operators.…
The uncertainty principle sets limit on our ability to predict the values of two incompatible observables measured on a quantum particle simultaneously. This principle can be stated in various forms. In quantum information theory, it is…
Photon indistinguishability is an essential concept to understanding mysterious quantum features from the viewpoint of the wave-particle duality in quantum mechanics. The physics of indistinguishability lies in the manipulation of quantum…
In the present paper, in terms of the measurability concept introduced in the previous works of the author, a quantum theory is studied. Within the framework of this concept, several examples are considered using the Schrodinger picture;…
We describe realizations of the color analogue of the Heisenberg Lie algebra by power series in non-commuting indeterminates satisfying Heisenberg's canonical commutation relations of quantum mechanics. The obtained formulas are used to…
We study the quantum-mechanical uncertainty relation originating from the successive measurement of two observables $\hat{A}$ and $\hat{B}$, with eigenvalues $a_n$ and $b_m$, respectively, performed on the same system. We use an extension…
Quantum information is a common topic of research in many areas of quantum physics, such as quantum communication and quantum computation, as well as quantum thermodynamics. It can be encoded in discrete or continuous variable systems, with…
Although non-commutativity of a certain set of quantum operators (e.g., creation/annihilation operators and Pauli spin operators) has been shown experimentally in recent years, the commu- tation relation for the position and the momentum…
The mathematical methods that have been used to analyze the statistical properties of boson fields, and in particular the coherence of photons in quantum optics, have their counterparts for Fermi fields. The coherent states, the…
Gaussian quantum systems exhibit many explicitly quantum effects but can be simulated classically. Using both the Hilbert space (Koopman) and the phase-space (Moyal) formalisms we investigate how robust this classicality is. We find…
Bell-type experiments that test correlated observables typically involve measurements of spin or polarization on multi-particle systems in singlet states. These observables are all non-commuting and satisfy an uncertainty relation.…
The process of measuring a two-level quantum system was examined by applying Hamiltonian formalism. For the measurement of an observable that does not commute with the system Hamiltonian, a non-trivial relationship among the strength of…
In this paper we analyze the quantum uncertainties and the photon statistics in the interaction between the two modes of radiation by treating them as coupled harmonic oscillator with the motivation of controlling quantum properties of one…