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Will two entangled qubits be affected by gravity? I mean if one is near blackhole's horizon and other is on earth will the effect of relativity be experienced on the measurement? will there be any delay or error in measurement?

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    $\begingroup$ wouldn't this question be more on topic on Physics SE? $\endgroup$ Apr 30 '20 at 7:58
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    $\begingroup$ a recent paper proposing a test to observe the effects of gravity on entangled states is Bose et al. 2017 $\endgroup$
    – glS
    May 4 '20 at 18:52
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Let's start with the Bell state $\frac1{\sqrt2}(|01\rangle+|10\rangle)$. Let's further assume that the entire universe (or at least the parts of relevance) are pervaded by a static magnetic field along the $z$-axis, which I relate to the unitary evolution $\exp(-itH_z)$.

Now let's place one part of the entangled state next to a massive object, such that its own time evolves slower than ours far away.

As you can see in this QUIRK circuit here, the Bell states changes back and forth between $$\frac1{\sqrt2}(|01\rangle+|10\rangle)\leftrightarrow\frac{e^{i\phi}}{\sqrt2}(|01\rangle-|10\rangle), $$ as time goes by with two different speeds. Now you have to come up with a measurement protocol to distinguish these two states by local operations and communications (don't enter the event horizon!)

Whereas you only catch up a global phase which is not measurable...

UPDATE

There is "Space QUEST (QUantum Entanglement Space Test) mission proposal" at the arxiv, to "...Experimentally test decoherence due to gravity". From the abstract:

Some speculative theories suggest that quantum properties, such as entanglement, may exhibit entirely different behavior to purely classical systems.

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