No, you cannot depreciate a home that you own that you do not rent, and you cannot deduct any losses. Since you do not rent it out, it is considered a second residence and you get the same tax benefits as you do for a primary residence. The only expense that you may be able to deduct would be your property taxes as xmasbaby0 indicated in the post above.
For additional information, please review the TurboTax article Buying a Second Home—Tax Tips for Homeowners.
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