# Microwave-to-Optical Transduction•Microwave-through-Optical Entanglement•Optical-to-Microwave Control•

Stefan Krastanov | MIT ⟶ UMass Amherst

## Entanglement

They can be entangled! \begin{aligned} A=|\phi_{+}\rangle=\frac{|00\rangle+|11\rangle}{\sqrt{2}}\\ B=|\psi_{-}\rangle=\frac{|01\rangle-|10\rangle}{\sqrt{2}}\\ C=|\psi_{+}\rangle=\frac{|01\rangle+|10\rangle}{\sqrt{2}}\\ D=|\phi_{-}\rangle=\frac{|00\rangle-|11\rangle}{\sqrt{2}} \end{aligned}
They can be entangled! \begin{aligned} A=|\phi_{+}\rangle=\frac{|00\rangle+|11\rangle}{\sqrt{2}}\\ B=|\psi_{-}\rangle=\frac{|01\rangle-|10\rangle}{\sqrt{2}}\\ C=|\psi_{+}\rangle=\frac{|01\rangle+|10\rangle}{\sqrt{2}}\\ D=|\phi_{-}\rangle=\frac{|00\rangle-|11\rangle}{\sqrt{2}} \end{aligned}
1. Krastanov et al.
Art installation on Non-contextual Hidden Variable theories

## Entanglement with Color Centers

### Entanglement Protocols

Inherently low probability of success (DLCZ-like)

Full excitation and path erasure (Barret-Kok)

Single-photon reflection

Atom-photon gates (Duan-Kimble)

### Atom-photon gates (Duan-Kimble)

Rate only classical light no optical excitation
DLCZ $$\eta (1-F)$$
BK $$\eta^2$$
reflection $$\eta^2$$

You also need a color center that does not suffer from spectral diffusion or charge state instabilities.

If you end up with significant optical excitation, you also need a way to turn off the hyperfine coupling to the (nuclear) memory.

## Entangling Transmons or other MW qubits

### Probabilistic Heralding

Why are color-center folks never talking about transduction...
$$\hat{H} = g_0 \hat{a}^\dagger\hat{b}\hat{c} + \text{H.c.}$$
$$\hat{H} = g_0 \sqrt{n_a n_b}\hat{c} + \text{H.c.}$$
$$P = \gamma\hbar\omega_\text{opt}n$$
$$\frac{P}{g} \approx \frac{\gamma\hbar\omega_\text{opt}}{g_0}$$