We compare the entropy-energy inequality and the von Neumann entropic inequality for three level atom implemented on superconducting circuits with Josephson junction. The positivityof entropy and energy relations for the qutrit system are used for verification of state tomography of qudit systems. The results obtained are valid for generic quantum states (qudits) and are illustrated on the example of the temperature density matrix of the single qutrit state.
We discuss the known construction of two interacting superconducting circuits, based on Josephson junctions, that can be precisely engineered and easily controlled. In particular, weuse the parametric excitation of two circuits, realized by an instant change of the qubit coupling, to study entropic and information properties of the density matrix of the composite system. The density matrix is obtained from the initial thermal state and is then analyzed in the approximation of small perturbation parameter and sufficiently low temperature. We also check the subadditivity condition for this system both for von Neumann and deformed entropies and look at the dependance of mutual information on the temperature of the system. Finally, we discuss the applicability of this approach to describe such system of two coupled superconducting qubits as harmonic oscillators with limited Hilbert space.
The aim of this work is to verify the new entropic and information inequalities for non-composite systems using experimental 5×5 density matrix of the qudit state, measured by thetomographic method in a multi-level superconducting circuit. These inequalities are well-known for bipartite and tripartite systems, but have never been tested for superconducting qudits. Entropic inequalities can also be used to evaluate the accuracy of experimental data and the value of mutual information, deduced from them, may charachterize correlations between different degrees of freedom in a noncomposite system.
Design of a large-scale quantum computer has paramount importance for science and technologies. We investigate a scheme for realization of quantum algorithms using noncomposite quantumsystems, i.e., systems without subsystems. In this framework, n artificially allocated „subsystems“ play a role of qubits in n-qubits quantum algorithms. With focus on two-qubit quantum algorithms, we demonstrate a realization of the universal set of gates using a d=5 single qudit state. Manipulation for an ancillary level in the systems allows effective implementation of operators from U(4) group via operators from SU(5) group. Using a possible experimental realization of such systems through anharmonic superconducting many-level quantum circuits, we present a blueprint for a single qudit realization of the Deutsch algorithm, which generalizes previously studied realization based on the virtual spin representation [A.R. Kessel et al., Phys. Rev. A 66, 062322 (2002)].
We study a class of entropic inequalities obtained for noncomposite quantum systems realized by a superconducting circuit with the Josephson junction. By using a mapping on a bipartitequantum state, we discuss possible realizations of various quantum logic gates for noncomposite quantum systems. In this framework, we consider logN entropic inequalities for Shannon and R\’eniy entropies based on the quantum Fourier transform. Implementation of the quantum Fourier transform algorithm on a quantum processor based on superconducting circuits opens a way for experimental verification of these inequalities.