Error in DataArray.from_dict(data_array.to_dict()) when using pd.MultiIndex

Error recovering DataArray with from_dict from what was persisted by to_dict when using pandas.MultiIndex.

MCVE Code Sample

import pandas as pd
import xarray as xr
idx = pd.MultiIndex.from_arrays([[1, 2], [3, 4]], names=('one', 'two'))
array = xr.DataArray([0, 1], dims='idx', coords={'idx': idx})
assert array.sel(one=1, two=3) == 0
assert array.sel(one=2, two=4) == 1
array_dict = array.to_dict()
xr.DataArray.from_dict(array_dict)

Expected Output

No error.

Problem Description

ValueError: Could not convert tuple of form (dims, data[, attrs, encoding]): (('idx',), [(1, 3), (2, 4)], {}) to Variable.

Versions

python: 3.7.6
xarray: 0.15.1
pandas: 1.0.3
numpy: 1.18.4
scipy: 1.4.1

Start by running the MCVE against DataArray.to_dict() and DataArray.from_dict() with the pandas.MultiIndex shown. Trace how the serialized coordinate data is passed back into from_dict; done means the round trip completes without ValueError and preserves the indexed values and names.