Remarks on a quantum state extension problem

Reinhard F. Werner

V. N. Ivanov

Sergio A Albeverio, L. Dąbrowski, Shao-Ming Fei

The integrability of one-dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) δ-function interaction there is another singular point interactions which gives rise to a new one-parameter family of integrable quantum mechanical many-body systems. The bound states and scattering matrices are calculated for both bosonic and fermionic statistics.

Edward B. Fel’dman, Alexander Ivanovich Zenchuk, Wentao Qi +1 more

In this paper, we solve three important problems that are revealed, in particular, to matrix-manipulation algorithms. The principal novelty is introducing the concept of quantumly controlled measurement that removes the post-selection problem by solving the problem of small access probability to the desired state of ancilla and possesses several remarkable properties. We also introduce separate encoding of the real and imaginary parts of a complex matrix that allows to include the Hermitian conjugation into the list of matrix manipulations. Finally, we weaken the constraints on the { modulus} of matrix elements unavoidably imposed by the normalization condition for a pure quantum state. The quantumly controlled measurement together with both other extensions are implemented into the matrix multiplication algorithm. The appropriate circuits are presented.

Z. I. Bezhaeva, Валерий Иустинович Оселедец

Kun Cao, Zheng-Wei Zhou, Guang‐Can Guo +1 more

We demonstrate an efficient numerical method to calculate the three-tangle of general mixed states. We construct an ``energy function'' (target function) for the three-tangle of the mixed state under certain constraints. The energy function (target function) is then optimized via the replica exchange Monte Carlo method. We have extensively tested the method for the examples with known analytical results, showing remarkable agreement. The method can be applied to other optimization problems in quantum information theory.