## 5 Discussion and Concluding Remarks  
In this work, we have shown the theoretical requirements for realizing a pseudospin in a system of coupled elastic waveguides and for the creation of states that couple the pseudospin and spatial degrees of freedom across the array of waveguides, which might be manipulated to create Bell states. We have fabricated a system that supports pseudospin using two aluminum rods coupled along their length with epoxy and confirmed with both measurement and modeling that the signature of a cutoff frequency in the elastic band structure is observed, at 20.24 kHz in experiment and 19.91 kHz in the numerical simulation. A system comprised of three aluminum rods coupled with epoxy along their length has been fabricated and shown to support two pseudospins with cutoff frequencies of 14.08 kHz and 24.43 kHz. By choosing a frequency at which the two pseudospins are resonant 33.25 kHz in the experiment, or 33.78 kHz in the simulation, we make combinations of the pseudospin and spatial modes that may or may not be separable. Varying the ratio of two input transducers that are out of phase, allows us to navigate the Bell state Hilbert space and, indeed, create nonseparable superpositions of the spatial modes and pseudospin state. Remarkably, these nonseparable states require complex coefficients to account for the phase differences in the outputs from the three rods. Through a single input, the relative excitation amplitudes of the coupled waveguides, these complex amplitudes are experimentally and numerically tuned, allowing the navigation of a sizeable portion of the nonseparable ('classically entangled') states of elastic wave states in the tensor product Hilbert space of the directional spinor amplitudes and spatial mode subspaces. Nonseparable or 'classically entangled' states of elastic waves offer the advantage of stability over entangled states of true quantum systems. Nonseparable superpositions of elastic waves are robust against decoherence and will not require operating at cryogenic temperatures to maintain the delicate balance of the superpositions. Nonseparable superpositions of elastic waves do not suffer from the phenomenon of wave function collapse upon measurement. A coherent superposition of quantum states collapses into a pure state upon measurement. Multiple statistical measurements are, therefore, necessary to obtain information on the original superposition. Moreover, the demonstration of our \"entangled' states realizes the potential of acoustic waves in capturing phenomena previously associated with optics. Recently, the use of classical light with entangled degrees of freedom have found applications in quantum information [47] and metrology [5,48]. Our works suggests that the same sort of applications can be realized with acoustic systems. In acoustic system, coupling can be easily manipulated by choices of materials and fabrication. Moreover, due to the flexibility of elastic system, the coupling can easily be tailored to be linear, periodic, and nonlinear (with different types or degrees of nonlinearity) [49, 50, 51]. Finally, extending this notion of classical nonseparability or classical \"entanglement\" to the field of phononics, opens the door for acoustic analogues to true quantum system in quantum information processing. The combination of experiment and numerical simulation employed in this manuscript provides the basis for a more extensive and predictive design of systems with elastic pseudospins for future information processing applications. The following are available online at [[http://www.mdpi.com/2076-3417/10/9/3202/s1](http://www.mdpi.com/2076-3417/10/9/3202/s1)]([http://www.mdpi.com/2076-3417/10/9/3202/s1](http://www.mdpi.com/2076-3417/10/9/3202/s1)), Figure S1.