[Paper Review] Violating Bell's inequality with an artificial atom and a cat state in a cavity

Brian Vlastakis, Andrei Petrenko+12 more|arXiv (Cornell University)|Apr 9, 2015

Quantum Information and Cryptography31 references3 citations

TL;DR

This paper demonstrates the first violation of Bell's inequality using an artificial atom entangled with a macroscopic cat state in a superconducting cavity, leveraging circuit QED, high-fidelity measurements, and real-time feedback to achieve post-selection-free Bell testing. The experiment reveals quantum nonlocality in a hybrid qubit–continuous-variable system and quantifies decoherence effects by tuning the cat state amplitude, confirming robust entanglement up to a critical size before decoherence suppresses nonclassical correlations.

ABSTRACT

The `Schrödinger's cat' thought experiment highlights the counterintuitive facet of quantum theory that entanglement can exist between microscopic and macroscopic systems, producing a superposition of distinguishable states like the fictitious cat that is both alive and dead. The hallmark of entanglement is the detection of strong correlations between systems, for example by the violation of Bell's inequality. Using the CHSH variant of the Bell test, this violation has been observed with photons, atoms, solid state spins, and artificial atoms in superconducting circuits. For larger, more distinguishable states, the conflict between quantum predictions and our classical expectations is typically resolved due to the rapid onset of decoherence. To investigate this reconciliation, one can employ a superposition of coherent states in an oscillator, known as a cat state. In contrast to discrete systems, one can continuously vary the size of the prepared cat state and therefore its dependence on decoherence. Here we demonstrate and quantify entanglement between an artificial atom and a cat state in a cavity, which we call a `Bell-cat' state. We use a circuit QED architecture, high-fidelity measurements, and real-time feedback control to violate Bell's inequality without post-selection or corrections for measurement inefficiencies. Furthermore, we investigate the influence of decoherence by continuously varying the size of created Bell-cat states and characterize the entangled system by joint Wigner tomography. These techniques provide a toolset for quantum information processing with entangled qubits and resonators. While recent results have demonstrated a high level of control of such systems, this experiment demonstrates that information can be extracted efficiently and with high fidelity, a crucial requirement for quantum computing with resonators.

Motivation & Objective

• To demonstrate quantum nonlocality in a hybrid system combining a microscopic artificial atom and a macroscopic cat state in a cavity.
• To overcome limitations of post-selection and measurement inefficiency in Bell tests by employing real-time feedback and high-fidelity detection.
• To investigate the role of decoherence in macroscopic superpositions by continuously varying the cat state amplitude.
• To develop and validate a joint Wigner representation for characterizing qubit–cavity entanglement in a reduced measurement basis.

Proposed method

• Utilizes circuit QED architecture with a transmon qubit coupled to a superconducting cavity to generate and measure entanglement.
• Employs sequential quantum non-demolition (QND) measurements: first qubit state, then cavity state via displaced photon number parity.
• Applies real-time feedback and pre-rotations to measure qubit observables along X, Y, and Z axes for CHSH Bell test settings.
• Constructs a joint Wigner representation using sixteen correlations derived from logical qubit encoding in coherent states |β⟩ and |−β⟩.
• Uses direct fidelity estimation and CHSH Bell test witnesses in the logical basis to quantify entanglement without full state tomography.
• Varies the cat state amplitude |β| to systematically probe the transition from quantum to classical behavior due to decoherence.

Experimental results

Research questions

• RQ1 Can Bell's inequality be violated using an artificial atom entangled with a macroscopic cat state in a cavity, without post-selection or corrections for measurement inefficiencies?
• RQ2 How does the degree of Bell violation depend on the size of the cat state, and what role does decoherence play in suppressing nonlocal correlations?
• RQ3 To what extent can the joint Wigner representation accurately characterize entangled qubit–cavity states using a minimal set of measurements?
• RQ4 Can high-fidelity, real-time measurement and feedback control enable robust detection of nonclassical correlations in hybrid quantum systems?
• RQ5 What is the maximum cat state amplitude for which quantum nonlocality remains detectable before decoherence dominates?

Key findings

• The experiment achieves a Bell inequality violation exceeding three standard deviations, confirming quantum nonlocality in a system with a macroscopic superposition.
• The CHSH value reaches 2.52 ± 0.06, significantly exceeding the classical bound of 2, demonstrating strong quantum correlations.
• A clear threshold in cat state amplitude is observed beyond which Bell violation declines due to decoherence, with suppression occurring as |β| increases.
• The joint Wigner representation successfully reconstructs the entangled state using only sixteen correlations, validating its efficiency for entanglement characterization.
• Measurement back-action is observed to project the cavity into distinct superpositions, including phase-shifted cat states upon X and Y basis measurements.
• Systematic error checks across all detector settings confirm no significant deviations, reinforcing the robustness of the Bell test results.