BUG: Multindex difference not working on columns with type Timestamp[ns][pyarrow]

[bmaisonn]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

import pandas as pd

df = pd.DataFrame(
    [
        (1, "1900-01-01", "a"),
        (2, "1900-01-01", "b")
     ],
columns=["id", "date", "val"]
).astype({"id": "int64[pyarrow]", "date": "timestamp[ns][pyarrow]", "val":"string[pyarrow]"})

df = df.set_index(["id", "date"])

idx_val = df.index[0]

idx_val in df.index # will show True

df.index.difference([idx_val]) # The two elements are still present in the dataframe

Issue Description

Note that the code will work if we using datetime64[ns] instead of timestamp[ns][pyarrow] type.

Also the code works fine if we convert the index to a none multi index.

Expected Behavior

We expect the same behavior with timestamp[ns][pyarrow] and other type. The element that we use to apply the difference should be removed from the dataframe

Installed Versions

INSTALLED VERSIONS

commit : 0691c5c
python : 3.10.12
python-bits : 64
OS : Linux
OS-release : 5.15.167.4-microsoft-standard-WSL2
Version : #1 SMP Tue Nov 5 00:21:55 UTC 2024
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : C.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.2.3
numpy : 1.26.4
pytz : 2024.2
dateutil : 2.9.0.post0
pip : 22.0.2
Cython : None
sphinx : 8.1.3
IPython : 8.30.0
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : None
blosc : None
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : None
html5lib : None
hypothesis : None
gcsfs : None
jinja2 : 3.1.4
lxml.etree : None
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
psycopg2 : None
pymysql : None
pyarrow : 18.1.0
pyreadstat : None
pytest : 8.3.4
python-calamine : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlsxwriter : None
zstandard : None
tzdata : 2024.2
qtpy : None
pyqt5 : None

[arthurlw]

Thanks for raising this! Confirmed on main.

MultiIndex.difference doesn't exclude the matching row when the index includes a timestamp[ns][pyarrow] column.

[rhshadrach]

MultiIndex._convert_can_do_stop creates a MultiIndex internally from the provided list which results in a DatetimeIndex. This then doesn't compare against PyArrow. It seems to me we should enable comparisons between the two.