© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:0905.0158 · Physical Review Letters

Tomography and Entanglement in Coupled Josephson Junction Qubits

Niels Grønbech‐Jensen, Jeffrey E. Marchese, Matteo Cirillo, James A. Blackburn

Published Jun 29, 2010• 16 citations

Abstract

We provide an alternative interpretation of experimental results that were represented as demonstrating entanglement between two macroscopic quantum Josephson oscillators. We model the experimental system using the well-established classical equivalent circuit of a resistively and capacitively shunted Josephson junction. Simulation results are used to generate the corresponding density matrix which shows features quite similar to the previously published matrix generated from experimental data. Since our data are generated by a classical model, we therefore submit that state tomography cannot be used to determine absolutely whether or not quantum entanglement has taken place. Analytical arguments are given for why the classical analysis provides an adequate explanation of the experimental results.

DOI: 10.1103/physrevlett.105.010501

Related papers

Classical analysis of capacitively coupled superconducting qubits

James A. Blackburn, Jeffrey E. Marchese, Matteo Cirillo +1 more

An electrical circuit consisting of two capacitively coupled inductive loops, each interrupted by a Josephson junction, is analyzed through the classical resistively and capacitively shunted junction (RCSJ) model. The same circuit has recently been studied experimentally and the results were used to demonstrate quantum-mechanical entanglement in the system by observing the correlated states of the two inductive loops after initial microwave perturbations. Our classical analysis shows that the observed phenomenon exists entirely within the classical RCSJ model, and we provide a detailed intuitive description of the transient dynamics responsible for the observations.

arXiv:0810.4722•Physical Review B•Feb 17, 2009•12 citations

Quantumness of Josephson junctions reexamined

Robert Alicki

There exists an increasing evidence supporting the picture of the Josephson junction (JJ) as a "macroscopic quantum system". On the other hand the interpretation of experimental data strongly depends on the assumed theoretical model. We analyse the possible states of a Cooper pair box ("charge qubit") for the two types of models : two-mode Bose-Hubbard model with its large $N$ aproximations and the many-body description within the mean-field approximation (Gross-Pitaevski equation). While the first class of models supports the picture of JJ being a quantum subsystem of a single degree of freedom, the second approach yields an essentially classical structure of accessible quantum states which, in particular, implies the absence of entanglement for two coupled JJ's. The arguments in favor of the mean-field theory are presented and different experimental tests including a new proposal are briefly discussed.

arXiv:quant-ph/0610008•Oct 1, 2006•5 citations

False qubits II. Entanglement of Josephson junctions

Robert Alicki

The recent experimental evidence for entangled states of two Josephson junction qubits is briefly discussed. It is argued that the interpretation of the experimental data strongly depends on the assumed theoretical model. Namely, the qubit states are supposed to be the lowest lying eigenstates of a certain effective Hamiltonian and hence automatically orthogonal, while the simple analysis within a more fundamental many-particle model shows that those states should strongly overlap. This makes the standard interpretation of the measurement procedure questionable.

arXiv:quant-ph/0609122•Sep 16, 2006•2 citations

Cooper Pair Box Coupled to a Current-Biased Josephson Junction

F. W. J. Hekking, O. Buisson, Franck Balestro +1 more

We study the dynamics of a quantum superconducting circuit which consists of a Josephson charge qubit, coupled capacitively to a current biased Josephson junction. Under certain conditions, the eigenstates of the qubit and the junction become entangled. We obtain the time evolution of these states in the limit of weak coupling. Rabi oscillations occur, as a result of the spontaneous emission and re-absorption of a single oscillation quantum in the junction. We discuss a possible way to experimentally determine the quantum state of the junction and hence observe the Rabi oscillations.

arXiv:cond-mat/0201284•Jan 16, 2002•7 citations

Spectroscopy of capacitively coupled Josephson-junction qubits

Philip R. Johnson, Frederick W. Strauch, Alex J. Dragt +4 more

We show that two capacitively coupled Josephson junctions, in the quantum limit, form a simple coupled qubit system with effective coupling controlled by the junction bias currents. We compute numerically the energy levels and wave functions for the system, and show how these may be tuned to make optimal qubits. The dependence of the energy levels on the parameters can be measured spectroscopically, providing an important experimental test for the presence of entangled multiqubit states in Josephson-junction based circuits.

arXiv:cond-mat/0210278•Physical review. B, Condensed matter•Jan 22, 2003•51 citations

Controllable manipulation and entanglement of macroscopic quantum states in coupled charge qubits

J. Q. You, J. S. Tsai, Franco Nori

We present an experimentally implementable method to couple Josephson charge qubits and to generate and detect macroscopic entangled states. A large-junction superconducting quantum interference device is used in the qubit circuit for both coupling qubits and implementing the readout. Also, we explicitly show how to achieve a microwave-assisted macroscopic entanglement in the coupled-qubit system.

arXiv:cond-mat/0306363•Physical review. B, Condensed matter•Jul 22, 2003•129 citations

We provide an alternative interpretation of experimental results that were represented as demonstrating entanglement between two macroscopic quantum Josephson oscillators. We model the experimental system using the well-established classical equivalent circuit of a resistively and capacitively shunted Josephson junction. Simulation results are used to generate the corresponding density matrix which shows features quite similar to the previously published matrix generated from experimental data. Since our data are generated by a classical model, we therefore submit that state tomography cannot be used to determine absolutely whether or not quantum entanglement has taken place. Analytical arguments are given for why the classical analysis provides an adequate explanation of the experimental results.

An electrical circuit consisting of two capacitively coupled inductive loops, each interrupted by a Josephson junction, is analyzed through the classical resistively and capacitively shunted junction (RCSJ) model. The same circuit has recently been studied experimentally and the results were used to demonstrate quantum-mechanical entanglement in the system by observing the correlated states of the two inductive loops after initial microwave perturbations. Our classical analysis shows that the observed phenomenon exists entirely within the classical RCSJ model, and we provide a detailed intuitive description of the transient dynamics responsible for the observations.

There exists an increasing evidence supporting the picture of the Josephson junction (JJ) as a "macroscopic quantum system". On the other hand the interpretation of experimental data strongly depends on the assumed theoretical model. We analyse the possible states of a Cooper pair box ("charge qubit") for the two types of models : two-mode Bose-Hubbard model with its large

N

aproximations and the many-body description within the mean-field approximation (Gross-Pitaevski equation). While the first class of models supports the picture of JJ being a quantum subsystem of a single degree of freedom, the second approach yields an essentially classical structure of accessible quantum states which, in particular, implies the absence of entanglement for two coupled JJ's. The arguments in favor of the mean-field theory are presented and different experimental tests including a new proposal are briefly discussed.

The recent experimental evidence for entangled states of two Josephson junction qubits is briefly discussed. It is argued that the interpretation of the experimental data strongly depends on the assumed theoretical model. Namely, the qubit states are supposed to be the lowest lying eigenstates of a certain effective Hamiltonian and hence automatically orthogonal, while the simple analysis within a more fundamental many-particle model shows that those states should strongly overlap. This makes the standard interpretation of the measurement procedure questionable.

We study the dynamics of a quantum superconducting circuit which consists of a Josephson charge qubit, coupled capacitively to a current biased Josephson junction. Under certain conditions, the eigenstates of the qubit and the junction become entangled. We obtain the time evolution of these states in the limit of weak coupling. Rabi oscillations occur, as a result of the spontaneous emission and re-absorption of a single oscillation quantum in the junction. We discuss a possible way to experimentally determine the quantum state of the junction and hence observe the Rabi oscillations.

We show that two capacitively coupled Josephson junctions, in the quantum limit, form a simple coupled qubit system with effective coupling controlled by the junction bias currents. We compute numerically the energy levels and wave functions for the system, and show how these may be tuned to make optimal qubits. The dependence of the energy levels on the parameters can be measured spectroscopically, providing an important experimental test for the presence of entangled multiqubit states in Josephson-junction based circuits.