Fig. 4: Squeezed state transfer and entanglement distribution through a thermal microwave channel.

a Effect of the superconducting cable center temperature, T_center, on the temperatures T of the MC tube, the 30 dB attenuators, and the Alice and Bob MC stages. Solid lines represent fits with piecewise linear functions partitioned at T_center = 0.4 K and smoothed in this region with a sigmoid function. The purple dashed line represents the threshold temperature T_κ = 0.22ℏω/k_B, above which thermal noise becomes noticeable. The light blue color denotes the region where the attenuator temperature is below the threshold temperature, T_att ≲ T_κ, such that noise is considered quantum-limited. b Squeezing level S of transferred states as a function of temperature T_center. Each curve corresponds to a fixed JPA pump power and labels S₀ indicate the squeezing levels at the base temperature, T_center = 110 mK. The solid lines represent a theory model for the effect of heating in the cryolink center and the subsequent heating in the Alice and Bob MC stages. The dashed lines represent a theory prediction for the case where only the cryolink center is hot, while the Alice and Bob MC stages remain at their base temperatures. c Purity μ of the transferred squeezed states as a function of T_center. d Entanglement monotone in the form of negativity N, between the local Alice mode and the transferred Bob mode, as a function of T_center. We observe N > 0 for the entire parameter space, implying the presence of quantum entanglement between the microwave modes in Alice and Bob. Dotted lines connecting data points are guides to the eye. When not shown, error bars are smaller than the symbol size.