"state" in state space analysis?
At a given time this circuit has several solutions.
Of course, once all voltages and currents are stabilised, there is only one solution ( current through L1 and R1 = 0.01A, C2 voltage = 1 volt).
But otherwise, when you apply power to this circuit, the values of the currents and voltages at a given time depends on how the power was applied : When ? Suddenly ? Gradually ? etc...
Fortunately
one can describe the behavior of this circuit without mentioning all possible histories. It suffices to describe the state of the circuit with just enough details to predict its evolution.
It the case of your circuit 2 numerical values are necessary and sufficient to predict the future, for example the current through inductor and the voltage across the capacitor. A lot of other variables can be used.