Quantum cryptography with 3-state systems

We consider quantum cryptographic schemes where the carriers of information are 3-state particles. One protocol uses four mutually unbiased bases and appears to provide better security than obtainable with 2-state carriers. Another possible method allows quantum states to belong to more than one basis. The security is not better, but many curious features arise.Comment: 11 pages Revte

The Security of Practical Quantum Key Distribution

Quantum key distribution (QKD) is the first quantum information task to reach the level of mature technology, already fit for commercialization. It aims at the creation of a secret key between authorized partners connected by a quantum channel and a classical authenticated channel. The security of the key can in principle be guaranteed without putting any restriction on the eavesdropper's power. The first two sections provide a concise up-to-date review of QKD, biased toward the practical side. The rest of the paper presents the essential theoretical tools that have been developed to assess the security of the main experimental platforms (discrete variables, continuous variables and distributed-phase-reference protocols).Comment: Identical to the published version, up to cosmetic editorial change

Bell inequality for quNits with binary measurements

We present a generalized Bell inequality for two entangled quNits. On one quNit the choice is between two standard von Neumann measurements, whereas for the other quNit there are N2 different binary measurements. These binary measurements are related to the intermediate states known from eavesdropping in quantum cryptography. The maximum violation by √N is reached for the maximally entangled state. Moreover, for N=2 it coincides with the familiar CHSH-inequalit

Graphical Classification of Entangled Qutrits

A multipartite quantum state is entangled if it is not separable. Quantum entanglement plays a fundamental role in many applications of quantum information theory, such as quantum teleportation. Stochastic local quantum operations and classical communication (SLOCC) cannot essentially change quantum entanglement without destroying it. Therefore, entanglement can be classified by dividing quantum states into equivalence classes, where two states are equivalent if each can be converted into the other by SLOCC. Properties of this classification, especially in the case of non two-dimensional quantum systems, have not been well studied. Graphical representation is sometimes used to clarify the nature and structural features of entangled states. SLOCC equivalence of quantum bits (qubits) has been described graphically via a connection between tripartite entangled qubit states and commutative Frobenius algebras (CFAs) in monoidal categories. In this paper, we extend this method to qutrits, i.e., systems that have three basis states. We examine the correspondence between CFAs and tripartite entangled qutrits. Using the symmetry property, which is required by the definition of a CFA, we find that there are only three equivalence classes that correspond to CFAs. We represent qutrits graphically, using the connection to CFAs. We derive equations that characterize the three equivalence classes. Moreover, we show that any qutrit can be represented as a composite of three graphs that correspond to the three classes