High-Capacity Quantum Secure Direct Communication with Single Photons in Both Polarization and Spatial-Mode Degrees of Freedom

We present a high-capacity quantum secure direct communication (QSDC) protocol with single photons in both the polarization and the spatial-mode degrees of freedom. With a single photon traveling forth and back from the receiver to the sender, it can carry 2 bits of information as the sender can encode his message on both the polarization states and the spatial-mode states of single photons independently. Moreover, our QSDC protocol is feasible as the preparation and the measurement of a single-photon quantum state in both the polarization and the spatial-mode degrees of freedom is not difficult with current technology.     

Three-party Quantum Secure Direct Communication with Single Photons in both Polarization and Spatial-mode Degrees of Freedom

We present an efficient three-party quantum secure direct communication (QSDC) protocol with single photos in both polarization and spatial-mode degrees of freedom. The three legal parties’ messages can be encoded on the polarization and the spatial-mode states of single photons independently with desired unitary operations. A party can obtain the other two parties’ messages simultaneously through a quantum channel. Because no extra public information is transmitted in the classical channels, the drawback of information leakage or classical correlation does not exist in the proposed scheme. Moreover, the comprehensive security analysis shows that the presented QSDC network protocol can defend the outsider eavesdropper’s several sorts of attacks. Compared with the single photons with only one degree of freedom, our protocol based on the single photons in two degrees of freedom has higher capacity. Since the preparation and the measurement of single photon quantum states in both the polarization and the spatial-mode degrees of freedom are available with current quantum techniques, the proposed protocol is practical.     

Information Leakage Problem in Efficient Bidirectional Quantum Secure Direct Communication with Single Photons in Both Polarization and Spatial-Mode Degrees of Freedom

The information leakage problem in the efficient bidirectional quantum secure direct communication protocol with single photons in both polarization and spatial-mode degrees of freedom is pointed out. Next, a way to revise this protocol to a truly secure one is given. We hope people pay more attention to the information leakage problem in order to design truly secure quantum communication protocols.     

Deterministic nondestructive state analysis for polarization-spatial-time-bin hyperentanglement with cross-Kerr nonlinearity

We present a deterministic nondestructive hyperentangled Bell state analysis protocol for photons entangled in three degrees of freedom(DOFs),including polarization,spatial-mode,and time-bin DOFs.The polarization Bell state analyzer and spatial-mode Bell state analyzer are constructed by polarization parity-check quantum nondemolition detector(P-QND)and spatial-mode parity-check quantum nondemolition detector(S-QND)using cross-Kerr nonlinearity,respectively.The time-bin Bell state analyzer is constructed by the swap gate for polarization state and time-bin state of a photon(P-T swap gate)and P-QND.The Bell states analyzer for one DOF will not destruct the Bell states of other two DOFs,so the polarization-spatial-time-bin hyperentangled Bell states can be determinately distinguished without destruction.This deterministic nondestructive state analysis method has useful applications in quantum information protocols.     

High-Capacity Three-Party Quantum Secret Sharing with Single Photons in Both the Polarization and the Spatial-Mode Degrees of Freedom

We present a high-capacity three-party quantum secret sharing (QSS) protocol with a sequence of single photons in both the polarization and the spatial-mode degrees of freedom. By inserting the boss Alice into the middle position between the two agents Bob and Charlie, our QSS protocol is secure in theory. The boss Alice chooses some unitary operations to encode her information on the single photons. It is interesting to point out the fact that Alice does not change the bases of the single photons which are used to carry the useful information about the private key, which improves its success probability for obtaining a private key. Compared with the QSS protocol by Zhou et al. (Chin. Phys. Lett. 24, 2181 (2007)), our QSS protocol has a higher capacity without increasing the difficulty of its implementation in experiment as each correlated photon can carry two bits of useful information. Compared with those QSS protocols based on entangled photon pairs and Bell-state measurements, our QSS protocol is more feasible as it does not require the complete Bell-state analysis which is not easy with linear optics. We give out the setup for the implementation of our QSS protocol with linear optical elements.     

Three-step three-party quantum secure direct communication

We propose a three-party quantum secure direct communication(QSDC) protocol with hyperentanglement in both spatial-mode and polarization degrees of freedom. The secret message can be encoded independently with desired unitary operations in two degrees of freedom. In this protocol, a party can synchronously obtain the other two parties' messages. Compared with previous three-party QSDC protocols, our protocol has several advantages. First, the single photons in our protocol are only required to transmit for three times. This advantage makes this protocol simple and useful. Second, Alice and Bob can send different secret messages to Charlie, respectively. Finally, with hyperentanglement, this protocol has a higher information capacity than other protocols.     

An efficient protocol for the private comparison of equal information based on the triplet entangled state and single-particle measurement

The central theme of this paper is that we propose an efficient protocol for comparing the equal information with the help of a third party (TP). We assume that TP is semi-honest, i.e., TP executes the protocol loyally, keeps a record of all its intermediate computations and might try to steal the players’ private inputs from the record, but he cannot be corrupted by the adversary. The security of this protocol with respect to various kinds of attacks is discussed. Our protocol utilizes the triplet entangled states and the simple single-particle measurement. The particles carried the secret messages do not be repeatedly transmitted. The players’ messages are divided into many groups. Sometimes, the protocol is already successfully completed, but all data are not compared. Thus, many time and huge quantum resources can be saved.     

Nonlocal hyperconcentration on entangled photons using photonic module system

Entanglement distribution will inevitably be affected by the channel and environment noise. Thus distillation of maximal entanglement nonlocally becomes a crucial goal in quantum information. Here we illustrate that maximal hyperentanglement on nonlocal photons could be distilled using the photonic module and cavity quantum electrodynamics, where the photons are simultaneously entangled in polarization and spatial-mode degrees of freedom. The construction of the photonic module in a photonic band-gap structure is presented, and the operation of the module is utilized to implement the photonic nondestructive parity checks on the two degrees of freedom. We first propose a hyperconcentration protocol using two identical partially hyperentangled initial states with unknown coefficients to distill a maximally hyperentangled state probabilistically, and further propose a protocol by the assistance of an ancillary single photon prepared according to the known coefficients of the initial state. In the two protocols, the total success probability can be improved greatly by introducing the iteration mechanism, and only one of the remote parties is required to perform the parity checks in each round of iteration. Estimates on the system requirements and recent experimental results indicate that our proposal is realizable with existing or near-further technologies.     

A two-step quantum secure direct communication protocol with hyperentanglement

We propose a two-step quantum secure direct communication (QSDC) protocol with hyperentanglement in both the spatial-mode and the polarization degrees of freedom of photon pairs which can in principle be produced with a beta barium borate crystal. The secret message can be encoded on the photon pairs with unitary operations in these two degrees of freedom independently. This QSDC protocol has a higher capacity than the original two-step QSDC protocol as each photon pair can carry 4 bits of information. Compared with the QSDC protocol based on hyperdense coding, this QSDC protocol has the immunity to Trojan horse attack strategies with the process for determining the number of the photons in each quantum signal as it is a one-way quantum communication protocol.     

Dynamic Multi-Party Quantum Private Comparison Protocol with Single Photons in Both Polarization and Spatial-Mode Degrees of Freedom

A dynamic quantum private comparison protocol based on the single photons in both polarization and spatial-mode degrees of freedom is proposed. In this protocol, any two parties of n(n ≥ 4) parties can compare their private information with the help of others n ? 2 parties. And any party can join in the protocol to take part in the comparison of n parties. Correctness analysis shows that the proposed protocol can be used to compare their information correctly. Security analysis shows that the proposed protocol can resist the general active attacks from an outside eavesdropper. And it can overcomes the problem of information leakage.     

A New Multi-Party Quantum Private Comparison Protocol Based on Circle Model

Recently multi-party quantum private comparison (MQPC) has attracted more and more attentions in the research of quantum cryptography. In our paper, a new MQPC protocol has been proposed by encoding the compared secrets on the phase of n-level single photons. From the proposed protocol, a generic model named circle model can be summarized. With the help of a semi-honest third party (TP), it can be proved that our protocol is immune to the outside attack and dishonest participants’ (including TP) attack.

     

Cryptanalysis and Improvement of Quantum Private Comparison Protocol Based on Bell Entangled States

Recently, Liu et al. [Commun. Theor. Phys. 57 (2012) 583] proposed a quantum private comparison protocol based on entanglement swapping of Bell states, which aims to securely compare the equality of two participants' information with the help of a semi-honest third party (TP). However, the present study points out there is a fatal loophole in Liu et al.'s protocol, and TP can make Bell-basis measurement to know all the participants' secret inputs without being detected. To fix the problem, a simple solution, which uses one-time eavesdropper checking with decoy photons instead of twice eavesdropper checking with Bell states, is demonstrated. Compared with the original protocol, it not only reduces the Bell states consumption but also simplifies the protocol steps.     

Quantum private comparison of arbitrary single qubit states based on swap test

By using swap test, a quantum private comparison (QPC) protocol of arbitrary single qubit states with a semi-honest third party is proposed. The semi-honest third party (TP) is required to help two participants perform the comparison. She can record intermediate results and do some calculations in the whole process of the protocol execution, but she cannot conspire with any of participants. In the process of comparison, the TP cannot get two participants' private information except the comparison results. According to the security analysis, the proposed protocol can resist both outsider attacks and participants' attacks. Compared with the existing QPC protocols, the proposed one does not require any entanglement swapping technology, but it can compare two participants' qubits by performing swap test, which is easier to implement with current technology. Meanwhile, the proposed protocol can compare secret integers. It encodes secret integers into the amplitude of quantum state rather than transfer them as binary representations, and the encoded quantum state is compared by performing the swap test. Additionally, the proposed QPC protocol is extended to the QPC of arbitrary single qubit states by using multi-qubit swap test.     

Cryptanalysis and Improvement of Quantum Private Comparison Protocol Based on Bell Entangled States

Recently, Liu et al. [Commun. Theor. Phys. 57(2012) 583] proposed a quantum private comparison protocol based on entanglement swapping of Bell states, which aims to securely compare the equality of two participants' information with the help of a semi-honest third party(TP). However, the present study points out there is a fatal loophole in Liu et al.'s protocol, and TP can make Bell-basis measurement to know all the participants' secret inputs without being detected. To fix the problem, a simple solution, which uses one-time eavesdropper checking with decoy photons instead of twice eavesdropper checking with Bell states, is demonstrated. Compared with the original protocol,it not only reduces the Bell states consumption but also simplifies the protocol steps.     

Bidirectional Quantum Secure Direct Communication Network Protocol with Hyperentanglement

We propose a bidirectional quantum secure direct communication (QSDC) network protocol with the hyperentanglment in both the spatial-mode ad the polarization degrees of freedom of photon pairs which can in principle be produced with a beta barium borate crystal. The secret message can be encoded on the photon pairs with unitary operations in these two degrees of freedom independently. Compared with other QSDC network protocols, our QSDC network protocol has a higher capacity as each photon pair can carry 4 bits of information. Also, we discuss the security of our QSDC network protocol and its feasibility with current techniques.     

High-Capacity Quantum Secret Sharing with Hyperdense Coding Assisted by Hyperentangled Photon Pairs

We presents a high-capacity three-party quantum secret sharing (QSS) protocol with a sequence of photon pairs in hyperentangled Bell states in both the polarization and the spatial-mode degrees of freedom. In our scheme, the boss Alice prepares a sequence of photon pairs in hyperentangled Bell states and divides them into two photon sequences which are sent the two agents, respectively. Alice exploits four subsets of decoy photons to assure the security of the photon transmission between her and her agents. The present QSS scheme has the advantage of having a high channel capacity as each photon pair can carry 4 bits of secret message in principle, two times of that by Deng et al. (Phys. Lett. A 372: 1957, 2008). We give out the setups for the preparation of the photon pairs in hyperentangled Bell states with a beta barium borate crystal and the manipulation of the photons with linear optical elements. It will be shown that our QSS protocol is feasible with current experimental technology.     

Secure Quantum Private Comparison Protocol Based on the Entanglement Swapping Between Three-Particle W-Class State and Bell State

We propose a new quantum private comparison protocol with the help of a semi-honest third party (TP), enabling two participants to compare the equality of their private inputs without exposing any information about their respective private inputs. Different from previous protocols, our protocol utilizes the properties of entanglement swapping between three-particle W-Class state and Bell state. The presented protocol can ensure correctness, fairness and security. Meanwhile, all the quantum particles undergo a one-way transmission, and all the participants including TP are just required having the ability to perform Bell-state measurement and exclusive-or operation which make our protocol more feasible and efficient. At last, the security of this protocol with respect to various kinds of attacks is analyzed in detail.     

Improving the Security of ‘High-Capacity Quantum Summation with Single Photons in both Polarization and Spatial-Mode Degrees of Freedom’

In 2014, Zhang et al. (Int J Theor Phys:53:933–941, 2014) proposed a secure multi-party quantum summation protocol based on single photons in both polarization and spatial-mode degrees of freedom. They claimed that the proposed protocol can efficiently help the involved participants to sum their secrets, and at the same time, each participant’s secret can be kept from being known by others. However, this study shows that Zhang et al.’s protocol suffers from the intercept-resend attack. To solve this problem, a modification is proposed here.

     

General hyperentanglement concentration for polarizationspatial- time-bin multi-photon systems with linear optics

Hyperentanglement has attracted considerable attention recently because of its high-capacity for longdistance quantum communication. In this study, we present a hyperentanglement concentration protocol (hyper-ECP) for nonlocal three-photon systems in the polarization, spatial-mode, and timebin partially hyperentangled Greenberger–Horne–Zeilinger (GHZ) states using the Schmidt projection method. In our hyper-ECP, the three distant parties must perform the parity-check measurements on the polarization, spatial-mode, and time-bin degrees of freedom, respectively, using linear optical elements and Pockels cells, and only two identical nonlocal photon systems are required. This hyper-ECP can be directly extended to the N-photon hyperentangled GHZ states, and the success probability of this general hyper-ECP for a nonlocal N-photon system is the optimal one, regardless of the photon number N.     

High-Capacity Three-Party Quantum Secret Sharing With Hyperentanglement

We presents a novel scheme for high-capacity three-party quantum secret sharing (QSS) with the hyperentanglement in both the polarization and the spatial-mode degrees of freedom of photon pairs. The boss Alice need only prepare a sequence of photon pairs and some decoy photons. Her two agents measure their photons received from the boss Alice with two bases by choosing two unsymmetrical probabilities. The present QSS scheme has a high capacity as each pair can carry 2 bits of information, several times as other QSS schemes. Moreover, our setups with linear optical elements show that our QSS scheme does not increase the difficulty of its implementation in experiment and it is feasible with current techniques.