Secure multiparty quantum key agreement against collusive attacks.

Quantum key agreement enables remote participants to fairly establish a secure shared key based on their private inputs. In the circular-type multiparty quantum key agreement mode, two or more malicious participants can collude together to steal private inputs of honest participants or to generate the final key alone. In this work, we focus on a powerful collusive attack strategy in which two or more malicious participants in particular positions, can learn sensitive information or generate the final key alone without revealing their malicious behaviour. Many of the current circular-type multiparty quantum key agreement protocols are not secure against this collusive attack strategy. As an example, we analyze the security of a recently proposed multiparty key agreement protocol to show the vulnerability of existing circular-type multiparty quantum key agreement protocols against this collusive attack. Moreover, we design a general secure multiparty key agreement model that would remove this vulnerability from such circular-type key agreement protocols and describe the necessary steps to implement this model. The proposed model is general and does not depend on the specific physical implementation of the quantum key agreement.

Secure dynamic multiparty quantum private comparison.

We propose a feasible and efficient dynamic multiparty quantum private comparison protocol that is fully secure against participant attacks. In the proposed scheme, two almost-dishonest third parties generate two random keys and send them to all participants. Every participant independently encrypts their private information with the encryption keys and sends it to the third parties. The third parties can analyze the equality of all or some participants' secrets without gaining access to the secret information. New participants can dynamically join the protocol without the need for any additional conditions in the protocol. We provide detailed correctness and security analysis of the proposed protocol. Our security analysis of the proposed protocol against both inside and outside attacks proves that attackers cannot extract any secret information.

Quantum-classical correspondence in the vicinity of periodic orbits.

Quantum-classical correspondence in chaotic systems is a long-standing problem. We describe a method to quantify Bohr's correspondence principle and calculate the size of quantum numbers for which we can expect to observe quantum-classical correspondence near periodic orbits of Floquet systems. Our method shows how the stability of classical periodic orbits affects quantum dynamics. We demonstrate our method by analyzing quantum-classical correspondence in the quantum kicked top (QKT), which exhibits both regular and chaotic behavior. We use our correspondence conditions to identify signatures of classical bifurcations even in a deep quantum regime. Our method can be used to explain the breakdown of quantum-classical correspondence in chaotic systems.

Complete hyperentangled Bell state analysis for polarization and time-bin hyperentanglement.

We present a complete hyperentangled Bell state analysis protocol for two-photon four-qubit states that are simultaneously entangled in the polarization and time-bin degrees of freedom. The 16 hyperentangled states can be unambiguously distinguished via two steps. In the first step, the polarization entangled state is distinguished deterministically and nondestructively with the help of the cross-Kerr nonlinearity. Then, in the second step, the time-bin state is analyzed with the aid of the polarization entanglement. We also discuss the applications of our protocol for quantum information processing. Compared with hyperentanglement in polarization and spatial-mode degrees of freedom, the polarization and time-bin hyperentangled states provide savings in quantum resources since there is no requirement for two spatial modes for each photon. This is the first complete hyperentangled Bell state analysis scheme for polarization and time-bin hyperentangled states, and it can provide new avenues for high-capacity, long-distance quantum communication.

Efficient hyperconcentration of nonlocal multipartite entanglement via the cross-Kerr nonlinearity.

We propose two schemes for concentration of hyperentanglement of nonlocal multipartite states which are simultaneously entangled in the polarization and spatial modes. One scheme uses an auxiliary single-photon state prepared according to the parameters of the less-entangled states. The other scheme uses two less-entangled states with unknown parameters to distill the maximal hyperentanglement. The procrustean concentration is realized by two parity check measurements in both the two degrees of freedom. Nondestructive quantum nondemolition detectors based on cross-Kerr nonlinearity are used to implement the parity check, which makes the unsuccessful instances reusable in the next concentration round. The success probabilities in both schemes can be made to approach unity by iteration. Moreover, in both schemes only one of the N parties has to perform the parity check measurements. Our schemes are efficient and useful for quantum information processing involving hyperentanglement.

Signatures of chaos in the dynamics of quantum discord.

We identify signatures of chaos in the dynamics of discord in a multiqubit system collectively modelled as a quantum kicked top. The evolution of discord between any two qubits is quasiperiodic in regular regions, while in chaotic regions the quasiperiodicity is lost. As the initial wave function is varied from the regular regions to the chaotic sea, a contour plot of the time-averaged discord remarkably reproduces the structures of the classical stroboscopic map. We also find surprisingly opposite behavior of two-qubit discord versus entanglement of the two qubits as measured by the concurrence. Our results provide evidence of signatures of chaos in dynamically generated discord.

Information gain in tomography--a quantum signature of chaos.

We find quantum signatures of chaos in various metrics of information gain in quantum tomography. We employ a quantum state estimator based on weak collective measurements of an ensemble of identically prepared systems. The tomographic measurement record consists of a sequence of expectation values of a Hermitian operator that evolves under repeated application of the Floquet map of the quantum kicked top. We find an increase in information gain and, hence, higher fidelities in the reconstruction algorithm when the chaoticity parameter map increases. The results are well predicted by random matrix theory.

Entanglement as a signature of quantum chaos.

We explore the dynamics of entanglement in classically chaotic systems by considering a multiqubit system that behaves collectively as a spin system obeying the dynamics of the quantum kicked top. In the classical limit, the kicked top exhibits both regular and chaotic dynamics depending on the strength of the chaoticity parameter kappa in the Hamiltonian. We show that the entanglement of the multiqubit system, considered for both the bipartite and the pairwise entanglement, yields a signature of quantum chaos. Whereas bipartite entanglement is enhanced in the chaotic region, pairwise entanglement is suppressed. Furthermore, we define a time-averaged entangling power and show that this entangling power changes markedly as kappa moves the system from being predominantly regular to being predominantly chaotic, thus sharply identifying the edge of chaos. When this entangling power is averaged over all states, it yields a signature of global chaos. The qualitative behavior of this global entangling power is similar to that of the classical Lyapunov exponent.