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Register a new userPractical measurement of joint weak values and their connection to the annihilation operator
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Weak measurements are a new tool for characterizing post-selected quantum systems during their evolution. Weak measurement was originally formulated in terms of von Neumann interactions which are practically available for only the simplest single-particle observables. In the present work, we extend and greatly simplify a recent, experimentally feasible, reformulation of weak measurement for multiparticle observables [Resch and Steinberg (2004, Phys. Rev. Lett., 92, 130402)]. We also show that the resulting ``joint weak values take on a particularly elegant form when expressed in terms of annihilation operators.
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Weak value measurements have recently given rise to a large interest for both the possibility of measurement amplification and the chance of further quantum mechanics foundations investigation. In particular, a question emerged about weak values being proof of the incompatibility between Quantum Mechanics and Non-Contextual Hidden Variables Theories (NCHVT). A test to provide a conclusive answer to this question was given in [M. Pusey, Phys. Rev. Lett. 113, 200401 (2014)], where a theorem was derived showing the NCHVT incompatibility with the observation of anomalous weak values under specific conditions. In this paper we realize this proposal, clearly pointing out the strict connection between weak values and the contextual nature of Quantum Mechanics.
We demonstrate that Aharonov-Albert-Vaidman (AAV) weak values have a direct relationship with the response function of a system, and have a much wider range of applicability in both the classical and quantum domains than previously thought. Using this idea, we have built an optical system, based on a birefringent photonic crystal, with an infinite number of weak values. In this system, the propagation speed of a polarized light pulse displays both superluminal and slow light behavior with a sharp transition between the two regimes. We show that this systems response possesses two-dimensional, vortex-antivortex phase singularities. Important consequences for optical signal processing are discussed.
The time-symmetric formalism endows the weak measurement and its outcome, the weak value, many unique features. In particular, it allows a direct tomography of quantum states without resort to complicated reconstruction algorithms and provides an operational meaning to wave functions and density matrices. To date the direct tomography only takes the forward direction of the weak measurement. Here we propose the direct tomography of a measurement apparatus by combining the backward direction of weak measurement and retrodictive description of quantum measurement. As an experimental demonstration, the scheme is applied to the characterization of both projective measurements and general positive operator-valued measures with a photonic setup. Our work provides new insight on the symmetry between quantum states and measurements, as well as an efficient method to characterize a measurement apparatus.
Weak measurement is a new technique which allows one to describe the evolution of postselected quantum systems. It appears to be useful for resolving a variety of thorny quantum paradoxes, particularly when used to study properties of pairs of particles. Unfortunately, such nonlocal or joint observables often prove difficult to measure weakly in practice (for instance, in optics -- a common testing ground for this technique -- strong photon-photon interactions would be needed). Here we derive a general, experimentally feasible, method for extracting these values from correlations between single-particle observables.
Incompatible observables underlie pillars of quantum physics such as contextuality and entanglement. The Heisenberg uncertainty principle is a fundamental limitation on the measurement of the product of incompatible observables, a `joint measurement. However, recently a method using weak measurement has experimentally demonstrated joint measurement. This method [Lundeen, J. S., and Bamber, C. Phys. Rev. Lett. 108, 070402, 2012] delivers the standard expectation value of the product of observables, even if they are incompatible. A drawback of this method is that it requires coupling each observable to a distinct degree of freedom (DOF), i.e., a disjoint Hilbert space. Typically, this `read-out system is an unused internal DOF of the measured particle. Unfortunately, one quickly runs out of internal DOFs, which limits the number of observables and types of measurements one can make. To address this limitation, we propose and experimentally demonstrate a technique to perform a joint weak-measurement of two incompatible observables using only one DOF as a read-out system. We apply our scheme to directly measure the density matrix of photons polarization.
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