[en] In this work we demonstrate how one can, in a generic approach, derive a set of N simple quadratic Bethe equations for integrable Richardson–Gaudin (RG) models built out of N spins-1/2. These equations depend only on the N eigenvalues of the various conserved charges so that any solution of these equations defines, indirectly through the corresponding set of eigenvalues, one particular eigenstate.

The proposed construction covers the full class of integrable RG models of the XYZ (including the subclasses of XXZ and XXX models) type realised in terms of spins-1/2, coupled with one another through , , terms, including, as well, magnetic field-like terms linear in the Pauli matrices.

The approach exclusively requires integrability, defined here only by the requirement that N conserved charges R _i (with ) such that exist. The result is therefore valid, and equally simple, for models with or without symmetry, with or without a properly defined pseudo-vacuum as well as for models with non-skew symmetric couplings. (paper)

[en] Published in summary form only

No abstract available

[en] The principle of basis set representation in terms of coordinate interchange matrices, of which the Pauli spin matrices are an example in two dimensions, are extended to three and four dimensions. The four-dimensional basis set of coordinate interchange matrices satisfies the usual conditions of completeness, but the three-dimensional basis set cannot be complete under any circumstances and an 'anticomplete' property is assigned to it. The coefficients of the basis set, when used to represent an arbitrary matrix, form a Hadamard transform of the cyclically interchanged arbitrary matrix. (author)

[en] Self-testing is a device-independent technique based on non-local correlations whose aim is to certify the effective uniqueness of the quantum state and measurements needed to produce these correlations. It is known that the maximal violation of some Bell inequalities suffices for this purpose. However, most of the existing self-testing protocols for two devices exploit the well-known Clauser–Horne–Shimony–Holt Bell inequality or modifications of it, and always with two measurements per party. Here, we generalize the previous results by demonstrating that one can construct self-testing protocols based on the chained Bell inequalities, defined for two devices implementing an arbitrary number of two-output measurements. On the one hand, this proves that the quantum state and measurements leading to the maximal violation of the chained Bell inequality are unique. On the other hand, in the limit of a large number of measurements, our approach allows one to self-test the entire plane of measurements spanned by the Pauli matrices X and Z. Our results also imply that the chained Bell inequalities can be used to certify two bits of perfect randomness. (paper)

No abstract available

[en] The work dwells on the generalization of approach to microscopic theory of the Fermi liquid for superfluid system. Appearance of the Cooper condensate is considered therefore in system with singlet coupling alongside with conventional density should be introduced. Non-local operator was introduced into consideration and equation for the calculation of anomalous component of mass operator via potential of two-particle interaction was plotted. The Belyaev isotopic formalism in which the problem is reduced to the spreading of the Fermi liquid microscopic theory for two-component systems with spontaneously violated isotopic symmetry was used

[en] A formula is derived that expresses the local spin and field operators of fundamental graded models in terms of the elements of the monodromy matrix. This formula may be understood as a quantum version of the classical inverse scattering transformation

No abstract available

[en] We present a quantum signature scheme for a participant attack using only Pauli operators. The arbitrator verifies the signature and serves to prevent the denial of participants as well as the existing arbitrated quantum signature. Conversely, Bob’s existential forgery and Alice’s disavowal, which are reported to be a shortcoming of Pauli operators, are not allowed. This simplifies the structure and increases the efficiency of communication.