Secure NN-dimensional Simultaneous Dense Coding and Applications

Simultaneous dense coding 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 simultaneous dense coding: (1) We propose three simultaneous dense coding 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 finalise 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 simultaneous dense coding against the intercept-resend attack. (5) We show that simultaneous dense coding 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.Comment: 22 pages, comments are welcom

Fair and optimistic quantum contract signing

We present a fair and optimistic quantum contract signing protocol between two clients that requires no communication with the third trusted party during the exchange phase. We discuss its fairness and show that it is possible to design such a protocol for which the probability of a dishonest client to cheat becomes negligible, and scales as N^{-1/2}, where N is the number of messages exchanged between the clients. Our protocol is not based on the exchange of signed messages: its fairness is based on the laws of quantum mechanics. Thus, it is abuse-free, and the clients do not have to generate new keys for each message during the Exchange phase. We discuss a real-life scenario when the measurement errors and qubit state corruption due to noisy channels occur and argue that for real, good enough measurement apparatus and transmission channels, our protocol would still be fair. Our protocol could be implemented by today's technology, as it requires in essence the same type of apparatus as the one needed for BB84 cryptographic protocol. Finally, we briefly discuss two alternative versions of the protocol, one that uses only two states (based on B92 protocol) and the other that uses entangled pairs, and show that it is possible to generalize our protocol to an arbitrary number of clients.Comment: 11 pages, 2 figure

Identical particles are indistinguishable but..

It is shown that quantum systems of identical particles can be treated as if they were different when they are in well differentiated states. This simplifying assumption allows the consideration of quantum systems isolated from the rest of the universe and justifies many intuitive statements about identical systems. However, it is shown that this simplification may lead to wrong results in the calculation of the entropy. Keywords: quantum mechanics, identical systems, entrop

Fidelity Between Partial States as Signature of Quantum Phase Transitions

We introduce a partial state fidelity approach to quantum phase transitions. We consider a superconducting lattice with a magnetic impurity inserted at its centre, and look at the fidelity between partial (either one-site or two-site) quantum states. In the vicinity of the point of the quantum phase transition, we observe a sudden drop of the fidelity between two one-site partial states corresponding to the impurity location and its close vicinity. In the case of two-site states, the fidelity reveals the transition point as long as one of the two electron sites is located at the impurity, while the other lies elsewhere in the lattice. We also determine the Uhlmann mixed state geometric phase, recently introduced in the study of the structural change of the system state eigenvectors in the vicinity of the lines of thermal phase transitions, and find it to be trivial, both for one- and two-site partial states, except when an electron site is at the impurity. This means that the system partial state eigenvectors do not contribute significantly to the enhanced state distinguishability around the point of this quantum phase transition. Finally, we use the fidelity to analyze the total amount of correlations contained within a composite system, showing that, even for the smallest two-site states, it features an abrupt quantitative change in the vicinity of the point of the quantum phase transition.Comment: 11 pages, 5 figure

Entanglement Concentration Using Quantum Statistics

We propose an entanglement concentration scheme which uses only the effects of quantum statistics of indistinguishable particles. This establishes the fact that useful quantum information processing can be accomplished by quantum statistics alone. Due to the basis independence of statistical effects, our protocol requires less knowledge of the initial state than most entanglement concentration schemes. Moreover, no explicit controlled operation is required at any stage.Comment: 2 figure