arXiv subjects

Yoshiyuki Tsuda

Publications and source records attributed to Yoshiyuki Tsuda.

8 recordsLinked to original sources

arXiv2019

A squeezing invariant measurement to test displacement of quantum Gaussian states

We consider a hypothesis testing problem for displacement parameters of n independent copies of an m-mode squeezed quantum Gaussian state whose mixture parameter is known. Given n>1, we construct a quantum measurement as a test using an observable which is invariant by n-fold tensor product of any m-mode squeezing operator. For a pure state case, we calculate the type II error probability of this test. We compare this test with a Hotelling's T-squared test which is based on heterodyne measurements.

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arXiv2006

Bhattacharyya inequality for quantum state estimation

Using higher-order derivative with respect to the parameter, we will give lower bounds for variance of unbiased estimators in quantum estimation problems. This is a quantum version of the Bhattacharyya inequality in the classical statistical estimation. Because of non-commutativity of operator multiplication, we obtain three different types of lower bounds; Type S, Type R and Type L. If the parameter is a real number, the Type S bound is useful. If the parameter is complex, the Type R and L bounds are useful. As an application, we will consider estimation of polynomials of the complex amplitude of the quantum Gaussian state. For the case where the amplitude lies in the real axis, a uniformly optimum estimator for the square of the amplitude will be derived using the Type S bound. It will be shown that there is no unbiased estimator uniformly optimum as a polynomial of annihilation and/or creation operators for the cube of the amplitude. For the case where the amplitude does not necessarily lie in the real axis, uniformly optimum estimators for holomorphic, antiholomorphic and real-valued polynomials of the amplitude will be derived. Those estimators for the holomorphic and real-valued cases attains the Type R bound, and those for the antiholomorphic and real-valued cases attains the Type L bound. This article clarifies what is the best method to measure energy of laser.

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arXiv2006

A study of LOCC-detection of a maximally entangled state using hypothesis testing

We study how well answer to the question ``Is the given quantum state equal to a certain maximally entangled state?'' using LOCC, in the context of hypothesis testing. Under several locality and invariance conditions, optimal tests will be derived for several special cases by using basic theory of group representations. Some optimal tests are realized by performing quantum teleportation and checking whether the state is teleported. We will also give a finite process for realizing some optimal tests. The performance of the tests will be numerically compared.

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arXiv2006

Hypothesis testing for an entangled state produced by spontaneous parametric down conversion

Generation and characterization of entanglement are crucial tasks in quantum information processing. A hypothesis testing scheme for entanglement has been formulated. Three designs were proposed to test the entangled photon states created by the spontaneous parametric down conversion. The time allocations between the measurement vectors were designed to consider the anisotropic deviation of the generated photon states from the maximally entangled states. The designs were evaluated in terms of the p-value based on the observed data. It has been experimentally demonstrated that the optimal time allocation between the coincidence and anti-coincidence measurement vectors improves the entanglement test. A further improvement is also experimentally demonstrated by optimizing the time allocation between the anti-coincidence vectors. Analysis on the data obtained in the experiment verified the advantage of the entanglement test designed by the optimal time allocation.

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arXiv2004

Quantum estimation for non-differentiable models

State estimation is a classical problem in quantum information. In optimization of estimation scheme, to find a lower bound to the error of the estimator is a very important step. So far, all the proposed tractable lower bounds use derivative of density matrix. However, sometimes, we are interested in quantities with singularity, e.g. concurrence etc. In the paper, lower bounds to a Mean Square Error (MSE) of an estimator are derived for a quantum estimation problem without smoothness assumptions. Our main idea is to replace the derivative by difference, as is done in classical estimation theory. We applied the inequalities to several examples, and derived optimal estimator for some of them.

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arXiv2003

Disturbance of operation in quantum estimation for the Gaussian P-function

For the quantum Gaussian state family, Hayashi proposed a quantum mechanical operation using beam splitters to estimate the location and scale parameters of the P-function, and he showed that it is asymptotically optimal. In this paper, we analyze the effect of disturbance of his operation caused by the randomness of the transparency of the beam splitters. It is shown that even if the variance of the random transparency is small, Hayashi's estimators are improper in a sense that they are biased and asymptotically inconsistent. In such a case, we propose to stop the operation and correct the biases of estimators.

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arXiv2002

Experimental investigation of pulsed entangled photons and photonic quantum channels

The development of key devices and systems in quantum information technology, such as entangled particle sources, quantum gates and quantum cryptographic systems, requires a reliable and well-established method for characterizing how well the devices or systems work. We report our recent work on experimental characterization of pulsed entangled photonic states and photonic quantum channels, using the methods of state and process tomography. By using state tomography, we could reliably evaluate the states generated from a two-photon source under development and develop a highly entangled pulsed photon source. We are also devoted to characterization of single-qubit and two-qubit photonic quantum channels. Characterization of typical single-qubit decoherence channels has been demonstrated using process tomography. Characterization of two-qubit channels, such as classically correlated channels and quantum mechanically correlated channels is under investigation. These characterization techniques for quantum states and quantum processes will be useful for developing photonic quantum devices and for improving their performances.

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arXiv2002

A New Strategy of Quantum-State Estimation for Achieving the Cramer-Rao Bound

We experimentally analyzed the statistical errors in quantum-state estimation and examined whether their lower bound, which is derived from the Cramer-Rao inequality, can be truly attained or not. In the experiments, polarization states of bi-photons produced via spontaneous parametric down-conversion were estimated employing tomographic measurements. Using a new estimation strategy based on Akaike's information criterion, we demonstrated that the errors actually approach the lower bound, while they fail to approach it using the conventional estimation strategy.

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