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arXiv:0909.3613 · Journal of Physics A Mathematical and Theoretical

Simultaneous dense coding

Haozhen Situ, Daowen Qiu

Published Jan 12, 2010• 26 citations
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Abstract

We present a dense coding scheme between one sender and two receivers, which guarantees that the receivers simultaneously achieve their respective information. In our scheme, the sender first performs a locking operation to entangle the particles from two independent quantum entanglement channels, so that the receivers cannot achieve their information unless they collaborate to perform the unlocking operation. We also show that the quantum Fourier transform can act as the locking operator both in simultaneous dense coding and teleportation. Finally we compare simultaneous dense coding with quantum secret sharing of classical messages.

DOI
10.1088/1751-8113/43/5/055301

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We present a dense coding scheme between one sender and two receivers, which guarantees that the receivers simultaneously achieve their respective information. In our scheme, the sender first performs a locking operation to entangle the particles from two independent quantum entanglement channels, so that the receivers cannot achieve their information unless they collaborate to perform the unlocking operation. We also show that the quantum Fourier transform can act as the locking operator both in simultaneous dense coding and teleportation. Finally we compare simultaneous dense coding with quantum secret sharing of classical messages.
Simultaneous dense coding (SDC) guarantees that Bob and Charlie simultaneously receive their respective information from Alice in their respective processes of dense coding. The idea is to use the so-called locking operation to “lock” the entanglement channels, thus requiring a joint unlocking operation by Bob and Charlie in order to simultaneously obtain the information sent by Alice. We present some new results on SDC: (1) We propose three SDC protocols, which use different N-dimensional entanglement (Bell state, W state and GHZ state). (2) Besides the quantum Fourier transform, two new locking operators are introduced (the double controlled-NOT operator and the SWAP operator). (3) In the case that spatially distant Bob and Charlie have to finalize the protocol by implementing the unlocking operation through communication, we improve our protocol’s fairness, with respect to Bob and Charlie, by implementing the unlocking operation in series of steps. (4) We improve the security of SDC against the intercept–resend attack. (5) We show that SDC can be used to implement a fair contract signing protocol. (6) We also show that the N-dimensional quantum Fourier transform can act as the locking operator in simultaneous teleportation of N-level quantum systems.
We firstly propose a simultaneous dense coding protocol with two-photon four-qubit cluster states in which two receivers can simultaneously get their respective classical information sent by a sender. Because each photon has two degrees of freedom, the protocol will achieve a high transmittance. The security of the simultaneous dense coding protocol has also been analyzed. Secondly, we investigate how to simultaneously teleport two different quantum states with polarization and path degree of freedom using cluster states to two receivers, respectively, and discuss its security. The preparation and transmission of two-photon four-qubit cluster states is less difficult than that of four-photon entangled states, and it has been experimentally generated with nearly perfect fidelity and high generation rate. Thus, our protocols are feasible with current quantum techniques.
We introduce the notion of distributed quantum dense coding, i.e., the generalization of quantum dense coding to more than one sender and more than one receiver. We show that global operations (as compared to local operations) of the senders do not increase the information transfer capacity, in the case of a single receiver. For the case of two receivers, using local operations and classical communication, a nontrivial upper bound for the capacity is derived. We propose a general classification scheme of quantum states according to their usefulness for dense coding. In the bipartite case (for any dimensions), bound entanglement is not useful for this task.
A scheme is proposed to realize the controlled dense coding by using a four-particle entangled state as the quantum channel. In this scheme, A and B are the sides of sender and receiver, C and D are used as the controlling particles. A, C and D should perform appropriate quantum operations on the particles that they own respectively, then they must transfer the particles to B. After a series of quantum operations, quantum transformations and quantum measurements, B would get the quantum state which can represent classical field information. By using this scheme, A and B realize the information teleportation of classical field 0～15 in the quantum channel.