PT symmetry, namely, a combined parity and time-reversal symmetry can make non-unitary quantum walks exhibit entirely real eigenenergy. However, it is known that the concept of PT symmetry can be generalized and an arbitrary anti-unitary symmetry has a possibility to substitute PT symmetry. The aim of the present work is to seek such non-unitary quantum walks with generalized PT symmetry by focusing on effects of spatially random disorder which breaks PT symmetry. We numerically find

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... quantum walks whose quasi-energy is entirely real despite PT symmetry is broken.