Abstract
In this somewhat pedagogical paper we revisit complementarity relations in bipartite quantum systems. Focusing on continuous-variable systems, we examine the influential class of EPR-like states through a generalization to Gaussian states and present some new quantitative relations between entanglement and local interference within symmetric and asymmetric double-double-slit scenarios. This approach is then related to ancilla-based quantum measurements, and weak measurements in particular. Finally, we tie up the notions of distinguishability, predictability, coherence and visibility while drawing some specific connections between them.
Highlights
Distinguishability of paths in quantum interference experiments is closely linked with entanglement
One could assume the system is already entangled with another, similar system; the “which-path” information is contained in the correlations between the two systems—i.e., knowing which slit the particle went through in one system supplies information regarding which slit the other particle went through in the other system. This approach was used by Jaeger et al in [1], where the authors proposed a quantitative measure for two-particle interference, denoted by v12, and proved a duality relation between one-particle interference visibility and two-particle interference visibility: v2i + v212 ≤ 1
In this work we derived a complementarity relation analogous to the one presented in [1], for a family of continuous variables (CV) systems described by EPR-like states
Summary
Distinguishability (or predictability) of paths in quantum interference experiments is closely linked with entanglement. One could assume the system is already entangled with another, similar system (in the desired basis); the “which-path” information is contained in the correlations between the two systems—i.e., knowing which slit the particle went through in one system supplies information regarding which slit the other particle went through in the other system This approach was used by Jaeger et al in [1], where the authors proposed a quantitative measure for two-particle interference, denoted by v12 , and proved a duality relation between one-particle interference visibility and two-particle interference visibility: v2i + v212 ≤ 1 (where vi denotes the ith particle’s interference visibility). Our analysis here is more general, considering asymmetric configurations of Gaussian states, which reach the EPR state as a special, limiting case These CV states seem to offer richer relations between local and nonlocal observables than their discrete variables counterparts.
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