Determination of general quantum states by weak measurement

Werner Stulpe, Matthias Singer

Jeff S. Lundeen, C. Bamber

Recent work by Lundeen et al. [Nature (London) 474, 188 (2011)] directly measured the wave function by weakly measuring a variable followed by a normal (i.e., "strong") measurement of the complementary variable. We generalize this method to mixed states by considering the weak measurement of various products of these observables, thereby providing the density matrix an operational definition in terms of a procedure for its direct measurement. The method only requires measurements in two bases and can be performed in situ, determining the quantum state without destroying it.

Indrajith V.S., R. Muthuganesan, R. Sankaranarayanan

Abstract In this article, we study quantum coherence of bipartite state from the perspective of weak measurement, which generalizes the notion of coherence relative to measurement. This is being illustrated by computing coherence for the well-known Bell diagonal and Werner states. Further, we have expanded the notion of coherence to encompass correlations, exploring its connections with other quantifications of nonlocality. We have determined that this coherence measure can be perceived as a generalized version of the Wigner-Yanese skew information measure and several other nonlocal measures. As a natural extension, we introduce uncertainty relations within the context of weak measurements. Additionally, we propose a novel form of variance by considering the weak value of an observable within a comprehensive framework.

Dan Cristian Marinescu, Gabriela M. Marinescu

Erkka Haapasalo, PEKKA J. LAHTI, Jussi Schultz

We generalize the concept of the weak value of a quantum observable to cover arbitrary real positive operator measures. We show that the definition is operationally meaningful in the sense that it can be understood within the quantum theory of sequential measurements. In particular, we show that the weak value can be obtained from a single measurement scheme. We then present a detailed analysis of the recent experiment [J. S. Lundeen et al., Nature (London) 474, 188 (2011)] concerning the reconstruction of the state of a photon using weak measurements. We compare their method with the reconstruction method through informationally complete phase space measurements. In particular, we show that unlike with phase space measurements, the reconstruction of a completely unknown state is not always possible using the method of weak measurements.

Allen Lobo, Carlos Alberto de Lima Ribeiro