On global effects caused by locally noneffective unitary operations

S. Gharibian, H. Kampermann, D. Bru{\ss}, Quantum Information & Computation 9 (2009) 1013–1029.

Journal Article | Published | English
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Abstract
Given a bipartite quantum state rho with subsystems A and B of arbitrary dimensions, we study the entanglement detecting capabilities of locally noneffective, or cyclic, unitary operations [L. B. Fu, Europhys. Lett., vol. 75, pp. 1-7, 2006]. Local cyclic unitaries have the special property that they leave their target subsystem invariant. We investigate the distance between rho and the global state after local application of such unitaries as a possible indicator of entanglement. To this end, we derive and discuss closed formulae for the maximal such distance achievable for three cases of interest: (pseudo)pure quantum states, Werner states, and two-qubit states. What makes this criterion interesting, as we show here, is that it surprisingly displays behavior similar to recent anomalies observed for non-locality measures in higher dimensions, as well as demonstrates an equivalence to the CHSH inequality for certain classes of two-qubit states. Yet, despite these similarities, the criterion is not itself a non-locality measure. We also consider entanglement detection in bound entangled states.
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Journal Title
Quantum Information & Computation
Volume
9
Issue
11
Page
1013-1029
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Gharibian S, Kampermann H, Bru{\ss} D. On global effects caused by locally noneffective unitary operations. Quantum Information & Computation. 2009;9(11):1013-1029.
Gharibian, S., Kampermann, H., & Bru{\ss}, D. (2009). On global effects caused by locally noneffective unitary operations. Quantum Information & Computation, 9(11), 1013–1029.
@article{Gharibian_Kampermann_Bru{\ss}_2009, title={On global effects caused by locally noneffective unitary operations}, volume={9}, number={11}, journal={Quantum Information & Computation}, author={Gharibian, Sevag and Kampermann, Hermann and Bru{\ss}, Dagmar}, year={2009}, pages={1013–1029} }
Gharibian, Sevag, Hermann Kampermann, and Dagmar Bru{\ss}. “On Global Effects Caused by Locally Noneffective Unitary Operations.” Quantum Information & Computation 9, no. 11 (2009): 1013–29.
S. Gharibian, H. Kampermann, and D. Bru{\ss}, “On global effects caused by locally noneffective unitary operations,” Quantum Information & Computation, vol. 9, no. 11, pp. 1013–1029, 2009.
Gharibian, Sevag, et al. “On Global Effects Caused by Locally Noneffective Unitary Operations.” Quantum Information & Computation, vol. 9, no. 11, 2009, pp. 1013–29.

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