Quantum Information Transfer In Cavity Systems For Quantum Money Transaction

Quantum information is a product of quantum mechanics and information theory. Thereare many topics worthy to be explored in the quantum information. Quantum entanglement,which is an important part in quantum information, is contributed to many branches. As a newresearch field, quantum money is also need quantum entanglement to finish its significantprocedures.Based on the study of quantum mechanic, the analysis about the properties ofentanglement are applied to the transmission of quantum states. Therefore, the quantummoney system are completed. The main jobs are presented as follows:(1) Entanglement transfer in a double-cavity optomechanical system is given.We give a theoretical study of a double-cavity system in which a mechanical resonatorbeam is coupled to two cavity fields on both side through radiation pressures. The indirectcoupling between the cavities via the resonator sets up a correlation between optomechanicalentanglements in the two cavities to the common resonator. This correlation translates into anentanglement transfer from one side of the cavities to the other, initiating an indirectentanglement of the cavities.(2)Aconcrete quantum money protocol based on quantum one-way function is proposed.The security of this protocol relies on the existence of quantum one-way function andno-cloning theory of fundamental quantum principles. Our protocol involves a new method todistinguish quantum money. That is, using quantum swap test circuit, to compare the stateannounced by bank with the state computed by user. In the generation procedure, one-onecorresponding states are created by a new code word and quantum one-way function to finishthe verification of quantum money states. The property of quantum one-way function preventsthe counterfeiter from obtaining the quantum money state based on the corresponding state.The accurate limit of the number of quantum money states makes the protocol satisfy thesecurity requirement.(3) A verification algorithm of quantum bill-checking machine based on induced trapdoorone-way transformation is presented.The role of the induced trapdoor one-way transformation is encrypting the quantummoney state in the bank and decrypting it in the verification algorithm. When the owner’s IDand private key are all added into the encryption quantum state through quantum fingerprinting function in the encryption of quantum money, the quantum money state isconverted from encryption quantum state by using trapdoor one-way transformation. Anyonewithout trapdoor cannot invert the trapdoor one-way transformation and such that thequantum money cannot be obtained by counterfeiter. In addition, the designed verificationalgorithm can decrypt the mixed state contained in the quantum money into two parts: thestate that contains owner’s information and quantum money state. As a result, the quantumbill-checking machine can not only verify quantum money but also authenticate the owner ofmoney.