USE tempdb;
IF OBJECT_ID('T', 'U') IS NOT NULL
    DROP TABLE T;
CREATE TABLE T
(
    ID INT NOT NULL IDENTITY,
    Attributes VARCHAR(MAX),
    Date1 AS JSON_VALUE(Attributes,'$.Date'),
	Date2 AS CAST(JSON_VALUE(Attributes,'$.Date') AS DATE),
);
INSERT T(Attributes)
SELECT '{  "Date" : "2017-12-08" }' UNION SELECT '{  "Date" : "2017-12-10" }'
GO
CREATE NONCLUSTERED INDEX IX_Date1 ON T(Date1);
CREATE NONCLUSTERED INDEX IX_Date2 ON T(Date2);
GO

(2 rows affected)
Warning! The maximum key length for a nonclustered index is 1700 bytes. The index 'IX_Date1' has maximum length of 8000 bytes. For some combination of large values, the insert/update operation will fail.
Msg 2729, Level 16, State 1, Line 15
Column 'Date2' in table 'T' cannot be used in an index or statistics or as a partition key because it is non-deterministic.

SELECT * FROM dbo.T AS T
WHERE T.Date1='2017-12-08'

SELECT * FROM dbo.T AS T
WHERE T.Date1='20171208'