Classification of three-body quantum halos

The different kinds of behaviour of three-body systems in the weak binding limit are classified with specific attention to the transition from a true three-body system to an effective two-body system. For weakly bound Borromean systems approaching the limit of binding we show that the size-binding energy relation is an almost universal function of the three s-wave scattering lengths measured in units of a hyperradial scaling parameter defined as a mass weighted average of two-body equivalent square well radii. We explain why three-body halos follow this curve and why systems appearing above reveal two-body substructures. Three-body quantum halos 2-3 times larger than the limit set by zero hypermoment are possible

Bidirectional imperfect quantum teleportation with a single Bell state

We present a bidirectional modification of the standard one-qubit teleportation protocol, where both Alice and Bob transfer noisy versions of their qubit states to each other by using single Bell state and auxiliary (trigger) qubits. Three schemes are considered: the first where the actions of parties are governed by two independent quantum random triggers, the second with single random trigger, and the third as a mixture of the first two. We calculate the fidelities of teleportation for all schemes and find a condition on correlation between trigger qubits in the mixed scheme which allows us to overcome the classical fidelity boundary of 2/3. We apply the Choi-Jamiolkowski isomorphism to the quantum channels obtained in order to investigate an interplay between their ability to transfer the information, entanglement-breaking property, and auxiliary classical communication needed to form correlations between trigger qubits. The suggested scheme for bidirectional teleportation can be realized by using current experimental tools.Comment: 8 pages, 4 figures; published versio

Symmetric blind information reconciliation and hash-function-based verification for quantum key distribution

We consider an information reconciliation protocol for quantum key distribution (QKD). In order to correct down the error rate, we suggest a method, which is based on symmetric blind information reconciliation for the low-density parity-check (LDPC) codes. We develop a subsequent verification protocol with the use of $\epsilon$-universal hash functions, which allows verifying the identity between the keys with a certain probability.Comment: 4 pages; 1 figure; published versio

Teleportation in an indivisible quantum system

Teleportation protocol is conventionally treated as a method for quantum state transfer between two spatially separated physical carriers. Recent experimental progress in manipulation with high-dimensional quantum systems opens a new framework for implementation of teleportation protocols. We show that the one-qubit teleportation can be considered as a state transfer between subspaces of the whole Hilbert space of an indivisible eight-dimensional system. We explicitly show all corresponding operations and discuss an alternative way of implementation of similar tasks.Comment: 4 pages, 1 figure, 1 tabl

Superfluidity of identical fermions in an optical lattice: atoms and polar molecules

In this work, we discuss the emergence of $p$-wave superfluids of identical fermions in 2D lattices. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices, for short-range interacting atoms, the scattering amplitude is strongly reduced compared to free space due to a small overlap of wavefunctions of fermions sitting in the neighboring lattice sites, which suppresses the $p$-wave superfluidity. However, we show that for a moderate lattice depth there is still a possibility to create atomic $p$-wave superfluids with sizable transition temperatures. The situation is drastically different for fermionic polar molecules. Being dressed with a microwave field, they acquire a dipole-dipole attractive tail in the interaction potential. Then, due to a long-range character of the dipole-dipole interaction, the effect of the suppression of the scattering amplitude in 2D lattices is absent. This leads to the emergence of a stable topological $p_x+ip_y$ superfluid of identical microwave-dressed polar molecules.Comment: 14 pages, 4 figures; prepared for proceedings of the IV International Conference on Quantum Technologies (Moscow, July 12-16, 2017); the present paper summarizes the results of our studies arXiv:1601.03026 and arXiv:1701.0852