"Engineering cat states with a photonic even-parity filter

G. S. Thekkadath, B. A. Bell, I. A. Walmsley, and A. I. Lvovsky

In 1993, Holland and Burnett investigated an intriguing interference phenomenon in the context of quantum-enhanced phase sensing: when two equal photon-number states, |n,n>, are combined on a balanced beam splitter (BS), both output ports of the BS contain only even photon-numbers regardless of n. Here we propose a scheme that utilizes the time-reversal of this interference phenomenon: If a pair of photon-number-resolving detectors at the output ports of a BS both detect n photons, i.e. the detection outcome (n,n), then the input state of the BS is projected onto a state with even photon numbers in both inputs. In this work, we exploit this phenomenon in a scheme designed to engineer quantum states containing only even-photon number terms.

Our scheme works as follows. We combine an arbitrary state |φ> with one of the two modes of a two-mode squeezed vacuum state on a BS. By post-selecting on the outcome (n,n) in the output ports of the BS, the other input mode of the entangled state will be conditionally prepared (i.e. heralded) in a state that contains only even photon-number terms whose amplitude is proportional to those in the state |φ>. For |φ>=|α>, i.e. a coherent state, we can herald a symmetrized version of this state, i.e. |ψ> = |α> + |-α>, which is Schrodinger’s cat state. In this way, in principle, one can herald arbitrarily large cat states with nearly-perfect fidelity regardless of the degree of entanglement of the input resource state. Furthermore, by iteratively applying our scheme, one can engineer more complicated states like |α> + |-α> + |iα> + |-iα>. Such states can be used to encode quantum information in a fault-tolerant “cat code”. To the best of our knowledge, this is the first proposal for preparing a cat code state in the optical domain."