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Minoru Horibe

Publications and source records attributed to Minoru Horibe.

7 recordsLinked to original sources
arXiv2013

Sp(2,$\mathbb{Z}$) invariant Wigner function on even dimensional vector space

We construct the quasi probability distribution $W(p,q)$ on even dimensional vector space with marginality and invariance under the transformation induced by projective representation of the group ${\rm Sp}(2,\mathbb{Z})$ whose elements correspond to linear canonical transformation. On even dimensional vector space, non-existence of such a quasi probability distribution whose arguments take physical values was shown in our previous paper(Phys.Rev.A{\bf 65} 032105(2002)). For this reason we study a quasi probability distribution $W(p,q)$ whose arguments $q$ and $p$ take not only $N$ physical values but also $N$ unphysical values, where $N$ is dimension of vector space. It is shown that there are two quasi probability distributions on even dimensional vector space. The one is equivalent to the Wigner function proposed by Leonhardt, and the other is a new one.

math-ph↗
arXiv2006

Optimal estimation of an observable's expectation value for pure states for general measure of deviation

We investigate the optimal estimation of quantum expectation value of a physical observable, which minimizes a mean error with respect to general measure of deviation, when a finite number of copies of a pure state are prepared. If pure sates are uniformly distributed, the minimum value of mean error for any measure of deviation is achieved by projective measurement on each copy.

quant-ph↗
arXiv2004

Solution to the King's problem with observables being not mutually complementary

We investigate the King's problem of the measurement of operators $\vec{n}_k \nobreak \cdot \nobreak \vecσ (k=1,2,3)$ instead of the three Cartesian components $σ_x$, $σ_y$ and $σ_z$ of the spin operator $\vecσ$. Here, $\vec{n}_k$ are three-dimensional real unit vectors. We show the condition over three vectors $\vec{n}_k$ to ascertain the result for measurement of any one of these operators.

quant-ph↗
arXiv2001

Existence of the Wigner function with correct marginal distributions along tilted lines on a lattice

In order to determine the Wigner function uniquely, we introduce a new condition which ensures that the Wigner function has correct marginal distributions along tilted lines. For a system in $N$ dimensional Hilbert space, whose "phase space" is a lattice with $N^2$ sites, we get different results depending on whether $N$ is odd or even. Under the new condition, the Wigner function is determined if $N$ is an odd number, but it does not exist if $N$ is even.

quant-ph↗
arXiv1994

Relation between Yang-Baxter and Pair Propagation Equations in 16-Vertex Models

We study a relation between two integrability conditions, namely the Yang-Baxter and the pair propagation equations, in 2D lattice models. While the two are equivalent in the 8-vertex models, discrepancies appear in the 16-vertex models. As explicit examples, we find the exactly solvable 16-vertex models which do not satisfy the Yang-Baxter equations.

hep-th↗
arXiv1993

Towards a Canonical Formalism of Field Theory on Discrete Spacetime

It is shown that the difficulties in formulating the quantum field theory on discrete spacetime appear already in classical dynamics of one degree of freedom on discrete time. The difference equation of motion which maintains a conserved quantity like energy has a very restricted form that is not probably derived by the least action principle. On the other hand, the classical dynamics is possible to be canonically formulated and quantized, if the equation is derived from an action. The difficulties come mainly from this incompatibility of the conserved quantity and the action principle. We formulate a quantum field theory canonically on discrete spacetime in the case where the field equation is derived from an action, though there may be no exactly conserved quantity. It may, however, be expected that a conserved quantity exists for a low "energy" region.

hep-th↗