Information-disturbance trade-off in generalized entanglement swapping

Abstract

We study information-disturbance trade-off in generalized entanglement swapping protocols wherein starting from Bell pairs (1, 2) and (3, 4), one performs an arbitrary joint measurement on (2, 3), so that (1, 4) now becomes correlated. We obtain trade-off inequalities between information gain in correlations of (1, 4) and residual information in correlations of (1, 2) and (3, 4) respectively and argue that information contained in correlations (information) is conserved if each inequality is an equality. We show that information is conserved for a maximally entangled measurement but is not conserved for any other complete orthogonal measurement and Bell measurement mixed with white noise. However, rather surprisingly, we find that information is conserved for rank-two Bell diagonal measurements, although such measurements do not conserve entanglement. We also show that a separable measurement on (2, 3) can conserve information, even if, as in our example, the post-measurement states of all three pairs (1, 2), (3, 4), and (1, 4) become separable. This implies correlations from an entangled pair can be transferred to separable pairs in nontrivial ways so that no information is lost in the process.

Creating quantum correlations in generalized entanglement swapping

“…Considering multipartite entanglement swapping protocol [2] assisted with different kinds of POVM for generating different kinds of genuine multipartite quantum correlations is another direction for future studies. Finally, finding out the amount of information loss or gain by different pairs [8,9] in our entanglement swapping setups is of fundamental interest.…”

“…where |Ψ ik for k = 0, 1, 2, 3 form a complete orthonormal basis on C 2 ⊗ C 2 and q ik ≥ 0 for all k = 0, 1, 2, 3. With this, we have [9]…”

“…The above entanglement swapping protocol can be generalized in various ways-by modifying the initial states, or by modifying the measurement performed by Bob, or by extending the number of parties [2,3]. These types of generalized entanglement swapping protocol have been studied in different contexts ranging from quantum networks [4,5], quantum nonlocality [6,7] to information loss or gain [8,9].…”

Creating quantum correlations in generalized entanglement swapping

“…The entanglement swapping protocol can be generalized in various ways-by modifying the initial states, or by modifying the measurement performed by Bob, or by extending the number of parties [3,4]. These types of generalized entanglement swapping protocol have been studied in different contexts ranging from quantum networks [5,6] to quantum nonlocality [7,8] to information loss or gain [9,10]. Hence, the natural question that arises in this context is how to design different types of quantum correlation transfer from (1,2) and (3,4) to (1,4) by generalizing the standard entanglement swapping protocol, i.e., either by modifying the initial states, or by modifying the measurements, or both.…”

Uncertainty of quantum channels via modified generalized variance and modified generalized Wigner-Yanase-Dyson skew information

“…The interaction between a quantum system and the external environment would lead to information loss and disturbance on the quantum states. Until now, many kinds of formulations have been established on the trade-off relations between the information and the disturbance [41][42][43][44][45][46][47][48][49][50]. Schumacher [51] has introduced the entanglement fidelity which provides a measure of how well the entanglement between a quantum system and an auxiliary system is preserved under the quantum channel.…”