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The phase state of dense matter in the intermediate density range (～1-10 times the nuclear saturation density) is both intriguing and unclear and can have important observable effects in the present gravitational wave era of neutron stars.As matter density increases in compact stars,the sound velocity is expected to approach the conformal limit (cs/c =1/√3) at high densities and should also fulfill the causality limit (cs/c ＜ 1).However,its detailed behavior remains a prominent topic of debate.It was suggested that the sound velocity of dense matter could be an important indicator of a deconfinement phase transition,where a particular shape might be expected for its density dependence.In this work,we explore the general properties of the sound velocity and the adiabatic index of dense matter in hybrid stars as well as in neutron stars and quark stars.Various conditions are employed for the hadron-quark phase transition with varying interface tension.We find that the expected behavior of the sound velocity can also be achieved by the nonperturbative properties of the quark phase,in addition to a deconfinement phase transition.Moreover,it leads to a more compact star with a similar mass.We then propose a new class of quark star equation of states,which can be tested by future high-precision radius measurements of pulsar-like objects.