Unifying Two Notions of Nonlocality in Quantum Theory
- URL: http://arxiv.org/abs/2009.04245v1
- Date: Wed, 9 Sep 2020 12:13:39 GMT
- Title: Unifying Two Notions of Nonlocality in Quantum Theory
- Authors: Shiladitya Mal, Aditi Sen De
- Abstract summary: We prove that a full product basis can create entangled states if and only if the full bases or any subspace of it become irreducible in the process of LOCC discrimination.
For a set having entangled states, we modify the quantity accordingly and show that it can provide an explanation for the phenomena of more nonlocality with less entanglement.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Ensembles containing orthogonal product states are found to be
indistinguishable under local operations and classical communication (LOCC),
thereby showing irreversibility in the preparation and distinguishing
processes, which is commonly known as nonlocality without entanglement. On the
other hand, correlations arising from incompatible measurements on entangled
states lead to Bell-nonlocality. We unify these two concepts from the change in
certain property incurred in the ensemble under a suitable global unitary
transformation. Specifically, we prove that under controlled-NOT (CNOT)
operation, a full product basis can create entangled states if and only if the
full bases or any subspace of it become irreducible in the process of LOCC
discrimination. The proposed criteria quantifies the amount of nonlocality
associated with the sets of product states which are even incomplete. For a set
having entangled states, we modify the quantity accordingly and show that it
can provide an explanation for the phenomena of more nonlocality with less
entanglement.
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