Quasi-Bell entangled coherent states and its quantum discrimination problem in the presence of thermal noise

The so-called quasi-Bell entangled coherent states in a thermal environment are studied. In the analysis, we assume thermal noise affects only one of the two modes of each state. First the matrix representation of the density operators of the quasi-Bell entangled coherent states in a thermal environment is derived. Secondly we investigate the entanglement property of one of the quasi-Bell entangled coherent states with thermal noise. At that time a lower bound of the entanglement of formation for the state is computed. Thirdly the minimax discrimination problem for two cases of the binary set of the quasi-Bell entangled coherent states with thermal noise is considered, and the error probabilities of the minimax discrimination for the two cases are computed with the help of Helstrom's algorithm for finding the Bayes optimal error probability of binary states.Comment: 10 pages, 3 figures, submitted to Proceedings of Quantum Communications and Quantum Imaging XIII Conference at SPIE 2015 Optics + Photonics, San Diego, 9-12 August 201

Coupling Lemma and Its Application to The Security Analysis of Quantum Key Distribution

It is known that the coupling lemma provides a useful tool in the study of probability theory and its related areas. It describes the relation between the variational distance of two probability distributions and the probability that outcomes from the two random experiments associated with each distribution are not identical. In this paper, the failure probability interpretation problem that has been presented by Yuen and Hirota is discussed from the viewpoint of the application of the coupling lemma. First, we introduce the coupling lemma, and investigate properties of it. Next, it is shown that the claims for this problem in the literatures are justified by using the coupling lemma. Consequently, we see that the failure probability interpretation is not adequate in the security analysis of quantum key distribution

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

Upper and Lower Bounds on Optimal Success Probability of Quantum State Discrimination with and without Inconclusive Results

We propose upper and lower bounds on the maximum success probability for discriminating given quantum states. The proposed upper bound is obtained from a suboptimal solution to the dual problem of the corresponding optimal state discrimination problem. We also give a necessary and sufficient condition for the upper bound to achieve the maximum success probability; the proposed lower bound can be obtained from this condition. It is derived that a slightly modified version of the proposed upper bound is tighter than that proposed by Qiu et al. [Phys. Rev. A 81, 042329 (2010)]. Moreover, we propose upper and lower bounds on the maximum success probability with a fixed rate of inconclusive results. The performance of the proposed bounds are evaluated through numerical experiments

Finding optimal solutions for generalized quantum state discrimination problems

We try to find an optimal quantum measurement for generalized quantum state discrimination problems, which include the problem of finding an optimal measurement maximizing the average correct probability with and without a fixed rate of inconclusive results and the problem of finding an optimal measurement in the Neyman-Pearson strategy. We propose an approach in which the optimal measurement is obtained by solving a modified version of the original problem. In particular, the modified problem can be reduced to one of finding a minimum error measurement for a certain state set, which is relatively easy to solve. We clarify the relationship between optimal solutions to the original and modified 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

Generalized bipartite quantum state discrimination problems with sequential measurements

We investigate an optimization problem of finding quantum sequential measurements, which forms a wide class of state discrimination problems with the restriction that only sequential measurements are allowed. Sequential measurements from Alice to Bob on a bipartite system are considered. Using the fact that the optimization problem can be formulated as a problem with only Alice's measurement and is convex programming, we derive its dual problem and necessary and sufficient conditions for an optimal solution. In the problem we address, the output of Alice's measurement can be infinite or continuous, while sequential measurements with a finite number of outcomes are considered. It is shown that there exists an optimal sequential measurement in which Alice's measurement with a finite number of outcomes as long as a solution exists. We also show that if the problem has a certain symmetry, then there exists an optimal solution with the same type of symmetry. A minimax version of the problem is considered, and necessary and sufficient conditions for a minimax solution are derived. An example in which our results can be used to obtain an analytical expression for an optimal sequential measurement is finally provided

Optimal discrimination of optical coherent states cannot always be realized by interfering with coherent light, photon counting, and feedback

It is well known that a minimum error quantum measurement for arbitrary binary optical coherent states can be realized by a receiver that comprises interfering with a coherent reference light, photon counting, and feedback control. We show that, for ternary optical coherent states, a minimum error measurement cannot always be realized by such a receiver. The problem of finding an upper bound on the maximum success probability of such a receiver can be formulated as a convex programming. We derive its dual problem and numerically find the upper bound. At least for ternary phase-shift keyed coherent states, this bound does not reach that of a minimum error measurement

A simple quantum channel having superadditivity of channel capacity

When classical information is sent through a quantum channel of nonorthogonal states, there is a possibility that transmittable classical information exceeds a channel capacity in a single use of the initial channel by extending it into multi-product channel. In this paper, it is shown that this remarkable feature of a quantum channel, so-called superadditivity, appears even in as low as the third extended coding of the simplest binary input channel. A physical implementation of this channel is indicated based on cavity QED techniques.Comment: 5 pages, LaTeX, 3 eps figure

Quantum stream cipher by Yuen 2000 protocol: Design and experiment by intensity modulation scheme

This paper shall investigate Yuen protocol, so called Y-00, which can realize a randomized stream cipher with high bit rate(Gbps) for long distance(several hundreds km). The randomized stream cipher with randomization by quantum noise based on Y-00 is called quantum stream cipher in this paper, and it may have security against known plaintext attacks which has no analog with any conventional symmetric key ciphers. We present a simple cryptanalysis based on an attacker's heterodyne measurement and the quantum unambiguous measurement to make clear the strength of Y-00 in real communication. In addition, we give a design for the implementation of an intensity modulation scheme and report the experimental demonstration of 1 Gbps quantum stream cipher through 20 km long transmission line.Comment: This paper will appear in Phys. Rev.

Quantum key distribution with unconditional security for all optical fiber network

In this paper, 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.Comment: SPIE conference on quantum commun. Proc. SPIE no-516