23 Sep 2025 Tue 4 pm

The concept of a "cat-state", qualitatively speaking, refers to a quantum superposition of two classical states of opposite quality, as suggested in the thought experiment of "Schrödinger's cat" - a cat in a superposition of a "dead" and an "alive" state. With the advancement of experimental techniques, this concept has become an observable reality, nowadays primarily in the field of optics. One of the potentially interesting applications of such superpositions is to process quantum signals, i.e. to store and transport quantum information. Motivated by nowadays achievable huge quality factors in nanomechanics and the ease of electrical control of charge qubits, we explore the possibility of the realisation of cat-states and their utilisation in quantum signal processing in a nanoelectromechanical (NEM) setup. The proposed NEM terminal consists of two bulk superconductors that are tunnel-coupled to a Cooper pair box (charge qubit), which can also perform mechanical oscillations between them. By controlling the external bias voltage and gate voltage, through the AC Josephson effect, the resonant tunnelling of Cooper pairs between the leads and the oscillating qubit builds nanomechanical coherent states entangled with the electrical states of the charge qubit. Tailoring specific time-protocols for operating the external parameters, bias and gate voltage, one can switch between entangled and pure cat-states. That is tracked by the corresponding Wigner functions and entanglement entropy, also leaving a specific experimentally observable signature in the electric current. Quantum information is encoded electrically into the (superposition of) charge qubit states and, by the aforementioned protocols, transduced between the mechanical and electrical subsystems in Hilbert space. By coupling several terminals, quantum information can be transported between them, constituting the basic element of a quantum network. The nanomechanical setup, allowing for the two-dimensional motion of a charge qubit, opens the possibility of designing spatial control of a qubit position to connect desired nodes in the quantum network.

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