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T. Hashimoto

Publications and source records attributed to T. Hashimoto.

At least 109 records · Page 6Linked to original sources
arXiv2008

Local Quantum Pure-state Identification without Classical Knowledge

Suppose we want to distinguish two quantum pure states. We consider the case in which no classical knowledge on the two states is given and only a pair of samples of the two states is available. This problem is called quantum pure-state identification problem. Our task is to optimize the mean identification success probability, which is averaged over an independent unitary invariant distribution of the two reference states. In this paper, the two states are assumed bipartite states which are generally entangled. The question is whether the maximum mean identification success probability can be attained by means of an LOCC (Local Operations and Classical Communication) measurement scheme. We will show that this is possible by constructing a POVM which respects the conditions of LOCC.

quant-ph↗
arXiv2007

Stationary quantum Markov process for the Wigner function

As a stochastic model for quantum mechanics we present a stationary quantum Markov process for the time evolution of the Wigner function on a lattice phase space Z_N x Z_N with N odd. By introducing a phase factor extension to the phase space, each particle can be treated independently. This is an improvement on earlier methods that require the whole distribution function to determine the evolution of a constituent particle. The process has branching and vanishing points, though a finite time interval can be maintained between the branchings. The procedure to perform a simulation using the process is presented.

quant-ph↗
arXiv2006

Optimal estimation of a physical observable's expectation value for pure states

We study the optimal way to estimate the quantum expectation value of a physical observable when a finite number of copies of a quantum pure state are presented. The optimal estimation is determined by minimizing the squared error averaged over all pure states distributed in a unitary invariant way. We find that the optimal estimation is "biased", though the optimal measurement is given by successive projective measurements of the observable. The optimal estimate is not the sample average of observed data, but the arithmetic average of observed and "default nonobserved" data, with the latter consisting of all eigenvalues of the observable.

quant-ph↗
arXiv2006

Unambiguous pure state identification without classical knowledge

We study how to unambiguously identify a given quantum pure state with one of the two reference pure states when no classical knowledge on the reference states is given but a certain number of copies of each reference quantum state are presented. By the unambiguous identification, we mean that we are not allowed to make a mistake but our measurement can produce an inconclusive result. Assuming the two reference states are independently distributed over the whole pure state space in a unitary invariant way, we determine the optimal mean success probability for an arbitrary number of copies of the reference states and a general dimension of the state space. It is explicitly shown that the obtained optimal mean success probability asymptotically approaches that of the unambiguous discrimination as the number of the copies of the reference states increases.

quant-ph↗
arXiv2005

Quantum pure-state identification

We address a problem of identifying a given pure state with one of two reference pure states, when no classical knowledge on the reference states is given, but a certain number of copies of them are available. We assume the input state is guaranteed to be either one of the two reference states. This problem, which we call quantum pure state identification, is a natural generalization of the standard state discrimination problem. The two reference states are assumed to be independently distributed in a unitary invariant way in the whole state space. We give a complete solution for the averaged maximal success probability of this problem for an arbitrary number of copies of the reference states in general dimension. It is explicitly shown that the obtained mean identification probability approaches the mean discrimination probability as the number of the reference copies goes to infinity.

quant-ph↗
arXiv2005

Reexamination of optimal quantum state estimation of pure states

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 M. Hayashi in terms of an infinite set of covariant positive operator valued measures (POVM's) and by Bruss 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 POVM 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(>N) copies is universal if it is used for N copies as input.

quant-ph↗
arXiv2005

Mean king's problem with mutually unbiased bases and orthogonal Latin squares

The mean king's problem with maximal mutually unbiased bases (MUB's) in general dimension d is investigated. It is shown that a solution of the problem exists if and only if the maximal number (d+1) of orthogonal Latin squares exists. This implies that there is no solution in d=6 or d=10 dimensions even if the maximal number of MUB's exists in these dimensions.

quant-ph↗
arXiv2004

Extended Quantum Color Coding

The quantum color coding scheme proposed by Korff and Kempe (quant-ph/0405086) is easily extended so that the color coding quantum system is allowed to be entangled with an extra auxiliary quantum system. It is shown that in the extended scheme we need only $\sim 2\sqrt{N}$ quantum colors to order $N$ objects in large $N$ limit, whereas $\sim N/e$ quantum colors are required in the original non-extended version. The maximum success probability has asymptotics expressed by the Tracy-Widom distribution of the largest eigenvalue of a random GUE matrix.

quant-ph↗
arXiv2003

Quantum Markov Process on a Lattice

We develop a systematic description of Weyl and Fano operators on a lattice phase space. Introducing the so-called ghost variable even on an odd lattice, odd and even lattices can be treated in a symmetric way. The Wigner function is defined using these operators on the quantum phase space, which can be interpreted as a spin phase space. If we extend the space with a dichotomic variable, a positive distribution function can be defined on the new space. It is shown that there exits a quantum Markov process on the extended space which describes the time evolution of the distribution function.

hep-lat↗
arXiv2002

Renormalization group flow of SU(3) lattice gauge theory - Numerical studies in a two coupling space

We investigate the renormalization group (RG) flow of SU(3) lattice gauge theory in a two coupling space with couplings $β_{11}$ and $β_{12}$ corresponding to $1\times 1$ and $1\times 2$ loops respectively. Extensive numerical calculations of the RG flow are made in the fourth quadrant of this coupling space, i.e., $β_{11}>0$ and $β_{12}<0$. Swendsen's factor two blocking and the Schwinger-Dyson method are used to find an effective action for the blocked gauge field. The resulting renormalization group flow runs quickly towards an attractive stream which has an approximate line shape. This is numerical evidence of a renormalized trajectory which locates close to the two coupling space. A model flow equation which incorporates a marginal coupling (asymptotic scaling term), an irrelevant coupling and a non-perturbative attraction towards the strong coupling limit reproduces qualitatively the observed features. We further examine the scaling properties of an action which is closer to the attractive stream than the currently used improved actions. It is found that this action shows excellent restoration of rotational symmetry even for coarse lattices with $a \sim 0.3$ fm.

hep-lat↗
arXiv2002

Remote State Preparation without Oblivious Conditions

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 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. We study similar RSP protocols, but not necessarily oblivious to Bob. First it is shown that 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 2 cbits of classical 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 open whether the amount of classical communication can be reduced by abandoning oblivious conditions.

quant-ph↗
arXiv2001

Wigner Functions on a Lattice

The Wigner functions on the one dimensional lattice are studied. Contrary to the previous claim in literature, Wigner functions exist on the lattice with any number of sites, whether it is even or odd. There are infinitely many solutions satisfying the conditions which reasonable Wigner functions should respect. After presenting a heuristic method to obtain Wigner functions, we give the general form of the solutions. Quantum mechanical expectation values in terms of Wigner functions are also discussed.

hep-lat↗
arXiv2001

Determinant of a new fermionic action on a lattice - (I)

We investigate, analytically and numerically, the fermion determinant of a new action on a (1+1)-dimensional Euclidean lattice. In this formulation the discrete chiral symmetry is preserved and the number of fermion components is a half of that of Kogut-Susskind. In particular, we show that our fermion determinant is real and positive for U(1) gauge group under specific conditions, which correspond to gauge conditions on the infinite lattice. It is also shown that the determinant is real and positive for SU(N) gauge group without any condition.

hep-lat↗
arXiv2001

Determinant of a new fermionic action on a lattice - (II)

We investigate the fermion determinant of a new action on a $(1+D)$-dimensional lattice for SU(2) gauge groups. This action possesses the discrete chiral symmetry and provides $2^D$-component fermions. We also comment on the numerical results on fermion determinants in the $(1+D)$-dimensional SU(3) gauge fields.

hep-lat↗
arXiv2000

Chemical potential response of meson masses at finite temperature

We study the response of meson masses to the chemical potential ($\partial{m}/\partialμ$) at high temperature and at zero chemical potential on $N_f=2$ lattice with staggered fermions. Preliminary results for the meson composed of different quarks show that $\partial{m}/\partialμ|_{μ=0}$ is negative in the confinement phase and positive in the deconfinement phase.

hep-lat↗
arXiv2000

Meson Correlators in Finite Temperature Lattice QCD

We analyze temporal and spatial meson correlators in quenched lattice QCD at T>0. Below T_c we observe little change in the meson properties as compared with T=0. Above T_c we observe new features: chiral symmetry restoration and signals of plasma formation, but also indication of persisting mesonic (metastable) states and different temporal and spatial masses in the mesonic channels. This suggests a complex picture of QGP in the region 1 - 1.5 T_c.

hep-lat↗