Abstract:
True tripartite entanglement of the state of a system of three qubits can be classified on the basis of stochastic local operations and classical communications (SLOCC). Such states can be classified in two categories: GHZ states and W-states. It is known that GHZ states can be used for teleportation and superdense coding, but the prototype W-state cannot be. However, we show that there is a class of W-states that can be used for perfect teleportation and superdense coding.

Abstract:
We prove that the ZX-calculus is incomplete for quantum mechanics. We suggest the addition of a new 'color-swap' rule, of which currently no analytical formulation is known and which we suspect may be necessary, but not sufficient to make the ZX-calculus complete.

Abstract:
We show that pivoting property of graph states cannot be derived from the axioms of the ZX-calculus, and that pivoting does not imply local complementation of graph states. Therefore the ZX-calculus augmented with pivoting is strictly weaker than the calculus augmented with the Euler decomposition of the Hadamard gate. We derive an angle-free version of the ZX-calculus and show that it is complete for real stabilizer quantum mechanics.

Abstract:
As we know, the states of triqubit systems have two important classes: GHZ-class and W-class. In this paper, the states of W-class are considered for teleportation and superdense coding, and are generalized to multi-particle systems. First we describe two transformations of the shared resources for teleportation and superdense coding, which allow many new protocols from some known ones for that. As an application of these transformations, we obtain a sufficient and necessary condition for a state of W-class being suitable for perfect teleportation and superdense coding. As another application, we find that state $|W>_{123}={1/2}(|100>_{123}+|010>_{123}+\sqrt{2}|001>_{123})$ can be used to transmit three classical bits by sending two qubits, which was considered to be impossible by P. Agrawal and A. Pati [Phys. Rev. A to be published]. We generalize the states of W-class to multi-qubit systems and multi-particle systems with higher dimension. We propose two protocols for teleportation and superdense coding by using W-states of multi-qubit systems that generalize the protocols by using $|W>_{123}$ proposed by P. Agrawal and A. Pati. We obtain an optimal way to partition some W-states of multi-qubit systems into two subsystems, such that the entanglement between them achieves maximum value.

Abstract:
Classical communication through quantum channels may be enhanced by sharing entanglement. Superdense coding allows the encoding, and transmission, of up to two classical bits of information in a single qubit. In this paper, the maximum classical channel capacity for states that are not maximally entangled is derived. Particular schemes are then shown to attain this capacity, firstly for pairs of qubits, and secondly for pairs of qutrits.

Abstract:
We present a protocol for multi-party superdense coding by using multi-atom in cavity quantum electrodynamics (QED). It is shown that, with a highly detuned cavity mode and a strong driving field, the protocol is insensitive to both cavity decay and thermal field. It is even certain to identify GHZ states via detecting the atomic states. Therefore we can realize the quantum dense coding in a simple way in the multiparty system.

Abstract:
We show that with the fourpartite quantum channel used to teleport an arbitrary two qubit state, we can construct a superdense coding protocol where it is possible to transmit 4 bits of classical information sending only 2 qubits. Alice and Bob initially share a four qubit maximally entangled state and by locally manipulating her two qubits Alice can generate 16 orthogonal maximally entangled states, which are used to encode the message transmitted to Bob. He reads the 4 bit message by a generalized Bell state measurement. A generalized protocol in which 2N bits of classical information is transmitted via N qubits is also presented. We also show that this four(2N-)partite channel is equivalent to two(N) Bell states, which proves that we need two(N) Bell states to teleport a two(N) qubit system.

Abstract:
We present a one-shot method for preparing pure entangled states between a sender and a receiver at a minimal cost of entanglement and quantum communication. In the case of preparing unentangled states, an earlier paper showed that a 2n-qubit quantum state could be communicated to a receiver by physically transmitting only n+o(n) qubits in addition to consuming n ebits of entanglement and some shared randomness. When the states to be prepared are entangled, we find that there is a reduction in the number of qubits that need to be transmitted, interpolating between no communication at all for maximally entangled states and the earlier two-for-one result of the unentangled case, all without the use of any shared randomness. We also present two applications of our result: a direct proof of the achievability of the optimal superdense coding protocol for entangled states produced by a memoryless source, and a demonstration that the quantum identification capacity of an ebit is two qubits.

Abstract:
We investigate the usefulness of different classes of genuine quadripartite entangled states as quantum resources for teleportation and superdense coding. We examine the possibility of teleporting unknown one, two and three qubit states. We show that one can use the teleportation protocol to send any general one and two qubit states. A restricted class of three qubit states can also be faithfully teleported. We also explore superdense coding protocol in single-receiver and multi-receiver scenarios. We show that there exist genuine quadripartite entangled states that can be used to transmit four cbits by sending two qubits. We also discuss some interesting features of multi-receiver scenario under LOCC paradigm.

Abstract:
Recently Liu, Long, Tong and Li [Phys. Rev. A 65, 022304 (2002)] have proposed a scheme for superdense coding between multiparties. This scheme seems to be highly asymmetric in the sense that only one sender effectively exploits entanglement. We show that this scheme can be modified in order to allow more senders to benefit of the entanglement enhanced information transmission.