We propose a decoy-pulse method to overcome the photon-number-splitting attack for Bennett-Brassard 1984 quantum key distribution protocol in the presence of high loss: A legitimate user intentionally and randomly replaces signal pulses by multiphoton pulses (decoy pulses). Then they check the loss of the decoy pulses. If the loss of the decoy pulses is abnormally less than that of signal pulses, the whole protocol is aborted. Otherwise, to continue the protocol, they estimate the loss of signal multiphoton pulses based on that of decoy pulses. This estimation can be done with an assumption that the two losses have similar values. We justify that assumption.

We show a geometric formulation for minimum-error discrimination of qubit states, that can be applied to arbitrary sets of qubit states given with arbitrary a priori probabilities. In particular, when qubit states are given with equal a priori probabilities, we provide a systematic way of finding optimal discrimination and the complete solution in a closed form. This generally gives a bound to cases when prior probabilities are unequal. Then, it is shown that the guessing probability does not depend on detailed relations among given states, such as angles between them, but on a property that can be assigned by the set of given states itself. This also shows how a set of quantum states can be modified such that the guessing probability remains the same. Optimal measurements are also characterized accordingly, and a general method of finding them is provided. . The process of distinguishing quantum states is generally a building block when quantum systems are applied to information processing, in particular for communication tasks [1]. Its usefulness as a theoretical tool to investigate quantum information theory has also been shown, according to the recent progress along the line, in secure communication, randomness extraction in classical-quantum correlations [3], and semi-device independent quantum information tasks [4].

This paper provides a simple variation of the basic ideas of the BB84 quantum cryptographic scheme leading to a method of key expansion. A secure random sequence ( the bases sequence ) determines the encoding bases in a proposed scheme. Using the bases sequence repeatedly is proven to be safe by quantum mechanical laws. *

Light emission from pale blue to greenish blue is successfully obtained from the diodes made of the trimethylsilyl-, monoalkoxy-, and dialkoxy-substituted polymers with welldefined conjugation length containing phenylenevinylene units. The conjugation length is adjusted by incorporating the nonconjugated spacer group in the backbone. The polymers are organic soluble and allow the fabrication of the light-emitting diode by spinning without further thermal processes. The fabricated devices show typical diode characteristics with operation voltages of 15-20 V, and the light is visible at the current density of about less than 0.5 mA/cm* 12 345for all three devices. The electroluminescence spectra are similar to the photoluminescence spectra and show the red shift as the electron-donation effects of the substituents become stronger. The bluest color of light emission corresponds to 470 nm for the polymer with trimethylsilyl substituent.

We provide a general framework of utilizing the no-signaling principle in derivation of the guessing probability in the minimum-error quantum state discrimination. We show that, remarkably, the guessing probability can be determined by the no-signaling principle. This is shown by proving that, in the semidefinite programing for the discrimination, the optimality condition corresponds to the constraint that quantum theory cannot be used for a superluminal communication. Finally, a general bound to the guessing probability is presented in a closed form.

We prove a special case of Helstrom theorem by using no-signaling condition in the special theory of relativity that faster-than-light communication is impossible. 03.65.Wj Quantum bits (qubits) are fundamentally different from classical bits in that unknown qubits cannot be copied with unit efficiency [1,2,3] (no-cloning theorem). Another related property of qubits is that nonorthogonal qubits cannot be distinguished with certainty [4].Interestingly, however, it has been found that the nosignaling condition is entangled with other impossibility proofs [5,6,7,8]. In particular, it has been shown that no-signaling condition gives the same tight bound on probability of conclusive measurement as obtained by quantum mechanical formula [7].In this paper, we add one in the list of theorems that can be proven by the no-signaling condition. We prove a special case of Helstrom theorem [9]. Result in this paper is closely related to other's works but different. In particular, our argument is quite similar to the one in Ref.[5]. Our contribution is an observation that violation of Helstrom theorem implies that two appropriately chosen (different) decompositions of the same density operator can be discriminated. This paper is organized as follows. We describe the proposition that we will prove. We prove it by no-signaling condition and then we conclude.Roughly speaking, Helstrom theorem means that the more non-orthogonal two qubits are, the more difficult it is to discriminate them by positive-operator-valuedmeasurement [4]. Let us consider a special case of Helstrom theorem.Proposition-1: Consider two non-orthogonal qubits, |α and |β , whose overlap, | α|β | 2 , is between 0 and 1. We are given a qubit that is either |α or |β with equal a priori probability, 1/2. We want to identify the qubit quantum mechanically. Identifier of the qubit gives either an output, 0, or the other output, 1. P E is the probability of making error in the identification. Minimal value of P E is given by. ♦ (Proposition-1 has interesting applications in quantum cryptography. For example, Bennett 1992 quantum key distribution protocol [10] and quantum remote gambling protocol [11].) Before we prove Proposition-1, let us introduce the followings. Any pure qubit |i i| can be represented by a three-dimensional Euclidean Bloch vector r i as |i i| = (1/2)(1 +r i · σ) [12]. Here 1 is identity operator, σ = (σ x , σ y , σ z ), and σ x , σ y , σ z are Pauli operators. Two Bloch vectors corresponding to |α and |β arer α andr β , respectively. We define an angle between r α andr β to be 2θ. That is, | α|β | 2 = cos 2 θ. A pure state |γ is defined as that its Bloch vectorr γ bisects the two Bloch vectorsr α andr β in the same plane, namelŷ r γ = C(r α +r β ) where C is a constant for normalization.A pure state |δ is defined as its Bloch vectorr δ makes an angle π/2 and π/2 + θ with the Bloch vectorr γ and r α , in the same plane, respectively. A pure state | − δ is defined as its Bloch vectorr −δ is the negative of that of |δ , namely −r δ . Note that al...

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We propose an improved bound for the difference between phase and bit error rate in measurementdevice-independent quantum key distribution with uncharacterized qubits. We show by simulations that the bound considerably increases the final key rates.