A Framework for Bounding Nonlocality of State Discrimination
We consider the class of protocols that can be implemented by local quantum operations and classical communication (LOCC) between two parties. In particular, we focus on the task of discriminating a known set of quantum states by LOCC. Building on the work in the paper Quantum nonlocality without entanglement (Bennett et al., Phys Rev A 59:1070–1091, 1999), we provide a framework for bounding the amount of nonlocality in a given set of bipartite quantum states in terms of a lower bound on the probability of error in any LOCC discrimination protocol. We apply our framework to an orthonormal product basis known as the domino states and obtain an alternative and simplified proof that quantifies its nonlocality. We generalize this result for similar bases in larger dimensions, as well as the “rotated” domino states, resolving a long-standing open question (Bennett et al., Phys Rev A 59:1070–1091, 1999).
KeywordsEntangle State Error Probability Quantum Discord State Discrimination Bipartite State
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- CLM+12.Chitambar, E., Leung, D., Mančinska, L., Ozols, M., Winter, A.: Everything you always wanted to know about LOCC (but were afraid to ask). http://arxiv.org/abs/1210.4583 [quant-ph], 2012
- CLM+13.Childs, A.M., Leung, D., Mančinska, L., Ozols, M.: Interpolatability distinguishes LOCC from separable von Neumann measurements. http://arxiv.org/abs/1306.5992.pdf [quant-ph], 2013
- Cro12.Croke, S.: There is no non-local information in a single qubit. In: APS Meeting Abstracts, page 30011, Feb 2012Google Scholar
- Hel76.Helstrom, C.W.: Quantum Detection and Estimation theory. Mathematics in science and engineering. Academic Press (1976)Google Scholar
- KTYI07.Koashi, M., Takenaga, F., Yamamoto, T., Imoto, N.: Quantum nonlocality without entanglement in a pair of qubits. http://arxiv.org/abs/0709.3196 [quant-ph], 2007