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 [Fu, Europhys. Lett., vol. 75]. 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.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 [Fu, Europhys. Lett., vol. 75]. 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.

arXiv:0809.4469Quantum Information and ComputationNov 1, 200915 citations

Signatures of nonclassicality in mixed-state quantum computation

Animesh Datta, Sevag Gharibian

We investigate signatures of nonclassicality in quantum states, in particular, those involved in the DQC1 model of mixed-state quantum computation [E. Knill and R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998)]. To do so, we consider two known nonclassicality criteria. The first quantifies disturbance of a quantum state under locally noneffective unitary operations (LNUs), which are local unitaries acting invariantly on a subsystem. The second quantifies measurement-induced disturbance (MID) in the eigenbasis of the reduced density matrices. We study the role of both figures of nonclassicality in the exponential speedup of the deterministic quantum computation with one qubit (DQC1) model and compare them vis-\`a-vis the interpretation provided in terms of quantum discord. In particular, we prove that a nonzero quantum discord implies a nonzero shift under LNUs. We also use the MID measure to study the locking of classical correlations [D. P. DiVincenzo et al., Phys. Rev. Lett. 92, 067902 (2004)] using two mutually unbiased bases (MUBs). We find the MID measure to exactly correspond to the number of locked bits of correlation. For three or more MUBs, it predicts the possibility of superior locking effects.We investigate signatures of nonclassicality in quantum states, in particular, those involved in the DQC1 model of mixed-state quantum computation [E. Knill and R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998)]. To do so, we consider two known nonclassicality criteria. The first quantifies disturbance of a quantum state under locally noneffective unitary operations (LNUs), which are local unitaries acting invariantly on a subsystem. The second quantifies measurement-induced disturbance (MID) in the eigenbasis of the reduced density matrices. We study the role of both figures of nonclassicality in the exponential speedup of the deterministic quantum computation with one qubit (DQC1) model and compare them vis-\`a-vis the interpretation provided in terms of quantum discord. In particular, we prove that a nonzero quantum discord implies a nonzero shift under LNUs. We also use the MID measure to study the locking of classical correlations [D. P. DiVincenzo et al., Phys. Rev. Lett. 92, 067902 (2004)] using two mutually unbiased bases (MUBs). We find the MID measure to exactly correspond to the number of locked bits of correlation. For three or more MUBs, it predicts the possibility of superior locking effects.

arXiv:0811.4003Physical Review AApr 17, 2009166 citations

The Odd Quantum

S. B. Treiman

Princeton University Press eBooksJan 9, 20240 citations

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 [Fu, Europhys. Lett., vol. 75]. 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.