Tsuyoshi Sasaki Usuda

Minimum error detection of classical linear code sending through a quantum channel

Abstract It is shown that group covariant signals with respect to a specific group with the operation “Exclusive OR”, which include binary linear codes as examples, satisfy the condition of the theorem 1 in [Phys. Rev. A 58 (1998) 146] and the minimum error detection is so-called square-root measurement.

Quantum stream cipher based on optical communications

In 2000, an attractive new quantum cryptography was discovered by H.P.Yuen based on quantum communication theory. It is applicable to direct encryption, for example quantum stream cipher based on Yuen protocol(Y-00), with high speeds and for long distance by sophisticated optical devices which can work under the average photon number per signal light pulse: = 1000 ~ 10000. In addition, it may provide information-theoretic security against known/chosen plaintext attack, which has no classical analogue. That is, one can provide secure communication, even the system has H(K)< SPIE Optics + Photonics OP 40 2004-08-02|2004-08-06 Optical Science and Technology, the SPIE 49th Annual Meeting AM04 516823 Denver, Colorado, United States Quantum Communications and Quantum Imaging II 5551 Quantum Communications and Quantum Information 9

Generalized quantum state discrimination problems

We address a broad class of optimization problems of finding quantum measurements, which includes the problems of finding an optimal measurement in the Bayes criterion and a measurement maximizing the average success probability with a fixed rate of inconclusive results. Our approach can deal with any problem in which each of the objective and constraint functions is formulated by the sum of the traces of the multiplication of a Hermitian operator and a detection operator. We first derive dual problems and necessary and sufficient conditions for an optimal measurement. We also consider the minimax version of these problems and provide necessary and sufficient conditions for a minimax solution. Finally, for optimization problem having a certain symmetry, there exists an optimal solution with the same symmetry. Examples are shown to illustrate how our results can be used.

Superadditivity in capacity of quantum channel for q-ary linearly dependent real symmetric-state signals

An analytical expression for the mutual information is derived for q-ary pseudo-cyclic codes. We compute mutual information for 3- and 5-ary linearly dependent signals. It is shown that higher quantum gain can be achieved by 3-ary codes and 50 percent of full quantum gain is achieved even for the codeword length n=16.

The multiple coding gain with two criteria in an attenuated quantum channel

Recently, the capacity of an attenuated quantum channel which is a model of a long distance optical fiber channel was derived. This capacity is in principle achieved by a continuous modulation and a random coding. However, a continuous modulation and a random coding are not practical. Therefore, we need discussion about capacity used for more practical modulation and coding. In this paper, we show characteristics of both information and error probability criteria for an attenuated channel using M-ary PSK modulation and pseudo-cyclic codes.

Group Covariant Signals in Quantum Information Theory

Necessary and sufficient condition for group covariant signals is given. This condition shows what kind of signals correspond to “group covariant signals.” We show by applying this condition that many signals, such as arbitrary binary signals, PPM, FSK, and PSK coherent-state signals, equidistant codes, and binary linear codes, are all group covariant.

Finding Optimal Solutions for Generalized Quantum State Discrimination Problems

We study an optimal quantum measurement for generalized quantum state discrimination problems, which include the problem of finding an optimal measurement maximizing the average success probability with and without a fixed rate of inconclusive results and the problem of finding an optimal measurement in the Neyman–Pearson strategy. We show that for any generalized quantum state discrimination problem, there is a corresponding minimum error discrimination problem sharing the same optimal measurement. We propose an approach in which the optimal measurement is obtained by solving the corresponding minimum error discrimination problem, and clarify the relationship between optimal solutions to the original and the corresponding problems, with which one can obtain an optimal solution to the original problem in some cases. Moreover, as an example of application of our approach, we present an algorithm for numerically obtaining optimal solutions to generalized quantum state discrimination problems.

On attainment of the capacity of broadband quantum channel by wavelength division multiplexing

Recently, the exact solution of the capacity of an attenuated quantum channel which is a model of a long distance optical fiber channel was derived [V. Giovannetti, et al., Phys. Rev. Lett. 90, 027902, (2004)]. In particular, the capacity of a broadband quantum channel, which is the ultimate limit of quantum communications, was shown. In this paper, we consider wavelength division multiplexing in order to attain the capacity of a broadband quantum channel.

Quantum key disribution with unconditional security for all-optical fiber network

Previously the present protocol was referred as Yuen-Kim second version in our papers. In this paper, it is called Yuen protocol (Y-00) and we present an efficient implementation method of physical layer of Y-00 which can support a secure communication and a quantum key distribution (more generally key expansion) by IMDD (intensity modulation/direct detection) or FSK (frequency shift keying) optical fiber communication network. Although the general proof of the security is not yet given, a brief sketch of security analysis is shown, which involve an entanglement attack.

Realizing a Two-Dimensional Positive Operator-Valued Measure by Local Operations and Classical Communication

We study the discrimination of multipartite quantum states by local operations and classical communication. We derive that any optimal discrimination of quantum states spanning a twodimensional Hilbert space in which each party’s space is finite dimensional is possible by local operations and one-way classical communication, regardless of the optimality criterion used and how entangled the states are.We study the realization of a 2-D positive operator-valued measure (POVM) by local operations and classical communication (LOCC). We derive that any POVM on a 2-D Hilbert space in which each party’s space is finite dimensional can be realized by one-way LOCC. This implies that any optimal discrimination of quantum states spanning such a 2-D Hilbert space is possible by one-way LOCC, regardless of the optimality criterion used and how entangled the states are.