Full disclosure, I do not own your model of television, but I do own the Sony HTZ9F and pair it with a Sony XBR-75X900F.
After looking at the specs of your television (https://docs.sony.com/release//specs/KDL52W4100_mksp.pdf), i definitely think you could get the soundbar to work with your setup. i see that your television has a digital optical output and could connect through either HDMI or that output. However, if you're purchasing this soundbar for the Dolby Atmos capable features, you might be disappointed. Your television does not appear to support eARC HDMI which is needed to pass the data to the speakers for the true Atmos experience. If that's the case, I'd recommend a step down to a more cost friendly Sony soundbar. If not, go crazy!
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