Ex cop here...
A dog is a great suggestion and one of the best deterrents to burglary.
I also suggest an IP camera with additional cloud storage, with infrared and mobile alerts.
The padlock idea is a good one until they decide to just take the entire cage. You'd be surprised what criminals will do when they see something they want.
This brings up another issue. Bird identification. Microchipping is your best bet on having your bird returned. Many species look identical and when changing environments or getting lost, many birds will not replicate behaviors when in unfamiliar environments.
KEEP YOUR MICROCHIPPING INFORMATION UPDATED! Many microchipped pets can't be returned because the owners either never registered their information with the company or failed to update changes to their address or phone number.
Also take good, clear photos of your bird's band if they have one, as well as their entire body or unique, identifying marks. Make sure you get prints of these photos and store them in a safe place. I also strongly recommend taking photos of all serial numbers for any equipment, firearms, electronics in your home. These should all go in a safety deposit box as well as on a spreadsheet, backed up to a server with 2-factor authentication.
Lastly, there is no such thing as a safe neighborhood. Crime happens everywhere. Statistically, most burglaries happen in the late morning/early afternoon.
Your best defense against burglary is prevention. Using your security measures perfectly, 100% of the time is the best deterrent. Doors with glass or Windows should have a 2-sided keyed deadbolt.
Alarm systems with cellular communication is also a great option, and there are some new systems such as Canary, that are inexpensive and don't require any wiring.
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