Quantum state preparation and measurement of photonic and phononic Schr\"odinger cat states have gathered significant interest due to their implications for alternative encoding schemes in quantum computation. These schemes employ coherent state superpositions, leveraging the expanded Hilbert space provided by cavity or mechanical resonators in contrast to two-level systems. Moreover, such cat states also serve as a platform for testing fundamental quantum phenomena in macroscopic systems. In this study, we generate four bipartite phononic cat states using an entanglement swapping scheme achieved through projective Bell-state measurements on two superconducting qubits. Employing two superconducting qubits allows for the creation of bipartite phononic cat states remotely, where the two phononic resonators are separated by a far distance. Subsequently, we conduct a Bell inequality test on the bipartite cat state using the Clauser-Horne-Shimony-Holt formulation. Given that the entangled cat states are generated through entanglement swapping, our approach holds promising applications for the advancement of complex quantum network processors based on continuous-variable systems.
Quantum state preparation and measurement of photonic and phononic Schr"odinger cat states have gathered significant interest due to their implications for alternative encoding schemes in quantum computation. These schemes employ coherent state superpositions, leveraging the expanded Hilbert space provided by cavity or mechanical resonators in contrast to two-level systems. Moreover, such cat states also serve as a platform for testing fundamental quantum phenomena in macroscopic systems. In this study, we generate four bipartite phononic cat states using an entanglement swapping scheme achieved through projective Bell-state measurements on two superconducting qubits. Employing two superconducting qubits allows for the creation of bipartite phononic cat states remotely, where the two phononic resonators are separated by a far distance. Subsequently, we conduct a Bell inequality test on the bipartite cat state using the Clauser-Horne-Shimony-Holt formulation. Given that the entangled cat states are generated through entanglement swapping, our approach holds promising applications for the advancement of complex quantum network processors based on continuous-variable systems.
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.
We propose the use of hybrid entanglement in an entanglement swapping protocol, as means of distributing a Bell state with high fidelity to two parties. The hybrid entanglement used in this work is described as a discrete variable (Fock state) and a continuous variable (cat state super- position) entangled state. We model equal and unequal levels of photonic loss between the two propagating continuous variable modes, before detecting these states via a projective vacuum-one-photon measurement, and the other mode via balanced homodyne detection. We investigate homodyne measurement imperfections, and the associated success probability of the measurement schemes chosen in this protocol. We show that our entanglement swapping scheme is resilient to low levels of photonic losses, as well as low levels of averaged unequal losses between the two propagating modes, and show an improvement in this loss resilience over other hybrid entanglement schemes using coherent state superpositions as the propagating modes. Finally, we conclude that our protocol is suitable for potential quantum networking applications which require two nodes to share entanglement separated over a distance of 5 -- 10 km , when used with a suitable entanglement purification scheme.
The quantum superpositions of coherent states offer an alternative to the conventional qubit-based encodings by harnessing the large Hilbert space available in bosonic modes, including those realised in microwave and optical cavities, magnons, and mechanical resonators. Beyond their advantages for local information processing, establishing long-distance quantum networks for such bosonic states is crucial for scalable quantum communication and distributed quantum computation. In this work, we propose an entanglement-swapping-based protocol to generate a bipartite magnonic cat state shared between spatially separated subsystems. Each subsystem comprises a hybrid architecture consisting of a superconducting transmon qubit coupled to a yttrium iron garnet (YIG) sphere that supports magnon modes. By performing a projective Bell-state measurement on the qubits, the initially established magnon-qubit entanglement is coherently transferred to the remote magnon modes, resulting in a nonlocal magnonic cat state. For experimental characterisation of the gener- ated states, we perform quantum state tomography through reconstruction of the Wigner function using joint displaced parity measurements of the magnon modes. Our scheme provides a feasible route towards realising long-distance magnonic entanglement and contributes to the advancement of hybrid quantum network architectures.
We propose the use of hybrid entanglement in an entanglement swapping protocol, as means of distributing a Bell state with high fidelity to two parties, Alice and Bob. The hybrid entanglement used in this work is described as a discrete variable (Fock state) and a continuous variable (cat state superposition) entangled state. We model equal and unequal levels of photonic loss between the two propagating continuous variable modes, before detecting these states via a projective vacuum-one-photon measurement, and the other mode via balanced homodyne detection. We investigate homodyne measurement imperfections, and the associated success probability of the measurement schemes chosen in this protocol. We show that our entanglement swapping scheme is resilient to low levels of photonic losses, as well as low levels of averaged unequal losses between the two propagating modes, and show an improvement in this loss resilience over other hybrid entanglement schemes using coherent state superpositions as the propagating modes. Finally, we conclude that our protocol is suitable for potential quantum networking applications which require two nodes to share entanglement separated over a distance of 5-10 km when used with a suitable entanglement purification scheme.
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.
Multipartite entangled states are crucial for numerous applications in quantum information science. However, the generation and verification of multipartite entanglement on fully controllable and scalable quantum platforms remains an outstanding challenge. We report the deterministic generation of an 18-qubit Greenberger-Horne-Zeilinger (GHZ) state and multicomponent atomic Schrödinger cat states of up to 20 qubits on a quantum processor, which features 20 superconducting qubits, also referred to as artificial atoms, interconnected by a bus resonator. By engineering a one-axis twisting Hamiltonian, the system of qubits, once initialized, coherently evolves to multicomponent atomic Schrödinger cat states-that is, superpositions of atomic coherent states including the GHZ state-at specific time intervals as expected. Our approach on a solid-state platform should not only stimulate interest in exploring the fundamental physics of quantum many-body systems, but also enable the development of applications in practical quantum metrology and quantum information processing.