  We propose a realistic scheme of generating a traveling odd Schr$\"o$dinger
cat state and a generalized entangled coherent state in circuit quantum
electrodynamics (circuit-QED). A squeezed vacuum state is used as initial
resource of nonclassical states, which can be created through a Josephson
traveling-wave parametric amplifier, and travels through a transmission line.
Because a single-photon subtraction from the squeezed vacuum gives with very
high fidelity an odd Schr$\"o$dinger cat state, we consider a specific
circuit-QED setup consisting of the Josephson amplifier creating the traveling
resource in a line, a beam-splitter coupling two transmission lines, and a
single photon detector located at the end of the other line. When a single
microwave photon is detected by measuring the excited state of a
superconducting qubit in the detector, a heralded cat state is generated with
high fidelity in the opposite line. For example, we show that the high fidelity
of the outcome with the ideal cat state can be achieved with appropriate
squeezing parameters theoretically. As its extended setup, we suggest that
generalized entangled coherent states can be also built probabilistically and
useful for microwave quantum information processing for error-correctable
qudits in circuit-QED.
