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Physical Review A

Detecting highly entangled states with a joint qubit readout

Jerry M. Chow, L. DiCarlo, Jay Gambetta, Andreas Nunnenkamp, Lev S. Bishop, Luigi Frunzio, Michel Devoret, S. M. Girvin, Robert J. Schoelkopf

Published Jun 17, 2010• 118 citations
Publisher

Abstract

A single-channel joint readout is used to analyze highly entangled two-qubit states in a circuit quantum electrodynamics architecture. The measurement model for the readout is fully characterized, demonstrating a large sensitivity to two-qubit correlations. We quantify the high degree of entanglement by measuring a violation of the Clauser-Horne-Shimony-Holt inequality with a value of $2.61\ifmmode\pm\else\textpm\fi{}0.04$, without optimizing the preparation of the two-qubit state. In its present form, this joint readout can resolve improvements to the fidelity of two-qubit operations and be extended to three or four qubits.

DOI
10.1103/physreva.81.062325

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A single-channel joint readout is used to analyze highly entangled two-qubit states in a circuit quantum electrodynamics architecture. The measurement model for the readout is fully characterized, demonstrating a large sensitivity to two-qubit correlations. We quantify the high degree of entanglement by measuring a violation of the Clauser-Horne-Shimony-Holt inequality with a value of 2.61\ifmmode±\else\textpm\fi0.042.61\ifmmode\pm\else\textpm\fi{}0.042.61\ifmmode±\else\textpm\fi0.04, without optimizing the preparation of the two-qubit state. In its present form, this joint readout can resolve improvements to the fidelity of two-qubit operations and be extended to three or four qubits.
Accurate and precise detection of multi-qubit entanglement is key for the experimental development of quantum computation. Traditionally, non-classical correlations between entangled qubits are measured by counting coincidences between single-shot readouts of individual qubits. We report entanglement metrology using a single detection channel with direct access to ensemble-averaged correlations between two superconducting qubits. Following validation and calibration of this joint readout, we demonstrate full quantum tomography on both separable and highly-entangled two-qubit states produced on demand. Using a subset of the measurements required for full tomography, we perform entanglement metrology with ~95% accuracy and ~98% precision despite ~10% fidelity of single measurements. For the highly entangled states, measured Clauser-Horne-Shimony-Holt operators reach a maximum value of 2.61+/-0.04 and entanglement witnesses give a lower bound of ~88% on concurrence. In its present form, this detector will be able to resolve future improvements in the production of two-qubit entanglement and is immediately extendable to 3 or 4 qubits.
Maximally entangled states should maximally violate the Bell inequality. It is proved that all two-qubit states that maximally violate the Bell-Clauser-Horne-Shimony-Holt inequality are exactly Bell states and the states obtained from them by local transformations. The proof is obtained by using the certain algebraic properties that Pauli's matrices satisfy. The argument is extended to the three-qubit system. Since all states obtained by local transformations of a maximally entangled state are equally valid entangled states, we thus give the characterizations of maximally entangled states in both the two-qubit and three-qubit systems in terms of the Bell inequality.
We propose methods for the preparation and entanglement detection of multi-qubit Greenberger–Horne–Zeilinger (GHZ) states in circuit quantum electrodynamics. Using quantum trajectory simulations appropriate for the situation of a weak continuous measurement, we show that the joint dispersive readout of several qubits can be utilized for the probabilistic production of high-fidelity GHZ states. When employing a nonlinear filter on the recorded homodyne signal, the selected states are found to exhibit values of the Bell–Mermin operator exceeding 2 under realistic conditions. We discuss the potential of the dispersive readout to demonstrate a violation of the Mermin bound, and present a measurement scheme avoiding the necessity for full detector tomography.
We propose a new method for detecting entanglement of two qubits and discuss its relation with the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality. Without the need for full quantum tomography for the density matrix we can experimentally detect the entanglement by measuring less than 9 local observables for any given state. We show that this test is stronger than the CHSH-Bell inequality and also gives an estimation for the degree of entanglement. If prior knowledge is available we can further greatly reduce the number of required local observables. The test is convenient and feasible with present experimental technology.
An entangled state of a two-particle system is a quantum state that cannot be separated-it cannot be written as the product of states of the individual particles.One way to tell if a system is entangled is to use it to violate a Bell inequality (such as the Clauser-Horne-Shimony-Holt, CHSH, inequality), because entanglement is necessary to violate these inequalities.However, there are other, more efficient measurements that determine whether or not a system is entangled; an operator that corresponds to such a measurement is referred to as an entanglement witness.We present the theory of witness operators, and an undergraduate experiment that measures an entanglement witness for the joint polarization state of two photons.We are able to produce states for which the expectation value of the witness operator is entangled by more than 160 standard deviations.
The Schrodinger's cat thought experiment highlights the counterintuitive concept of entanglement in macroscopically distinguishable systems. The hallmark of entanglement is the detection of strong correlations between systems, most starkly demonstrated by the violation of a Bell inequality. No violation of a Bell inequality has been observed for a system entangled with a superposition of coherent states, known as a cat state. Here we use the Clauser-Horne-Shimony-Holt formulation of a Bell test to characterize entanglement between an artificial atom and a cat state, or a Bell-cat. Using superconducting circuits with high-fidelity measurements and real-time feedback, we detect correlations that surpass the classical maximum of the Bell inequality. We investigate the influence of decoherence with states up to 16 photons in size and characterize the system by introducing joint Wigner tomography. Such techniques demonstrate that information stored in superpositions of coherent states can be extracted efficiently, a crucial requirement for quantum computing with resonators.