Theory and experiment for resource-efficient joint weak-measurement

Abstract

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 photon polarization states.

arXiv comment17 pages, 5 figures

References in corpus (43)

• Quantum entanglement
• Direct Measurement of the Quantum Wavefunction
• Colloquium: Understanding Quantum Weak Values: Basics and Applications
• Witnessing multipartite entanglement
• Measuring small longitudinal phase shifts: weak measurements or standard interferometry?
• Experimental joint weak measurement on a photon pair as a probe of Hardy's Paradox
• Entanglement Certification $-$ From Theory to Experiment
• Violation of Heisenberg's Measurement-Disturbance Relationship by Weak Measurements
• Direct measurement of general quantum states using weak measurement
• Technical advantages for weak value amplification: When less is more
• Violation of the Leggett-Garg inequality with weak measurements of photons
• Anomalous Weak Values Are Proofs of Contextuality
• Direct observation of Hardy's paradox by joint weak measurement with an entangled photon pair
• Optimizing the Signal to Noise Ratio of a Beam Deflection Measurement with Interferometric Weak Values
• Full characterisation of polarisation states of light via direct measurement
• Experimental Violation of Two-Party Leggett-Garg Inequalities with Semi-weak Measurements
• Quantum Cheshire Cats
• Observation of a quantum Cheshire Cat in a matter wave interferometer experiment
• Direct measurement of the density matrix of a quantum system
• The quasiprobability behind the out-of-time-ordered correlator
• Weak Value Amplification Can Outperform Conventional Measurement in the Presence of Detector Saturation
• Implementation of Quantum and Classical Discrete Fractional Fourier Transforms
• Observing Dirac's classical phase space analog to the quantum state
• Entanglement-assisted weak value amplification
• Sequential weak measurement
• Extracting joint weak values with local, single-particle measurements
• Measuring incompatible observables of a single photon
• Anomalous weak values and contextuality: robustness, tightness, and imaginary parts
• Practical measurement of joint weak values and their connection to the annihilation operator
• Direct measurement of a nonlocal entangled quantum state
• Uncertainty limits for quantum metrology obtained from the statistics of weak measurements
• Arrow of Time for Continuous Quantum Measurement
• Anomalous Weak Values and the Violation of a Multiple-measurement Leggett-Garg Inequality
• Experimental Realization of Sequential Weak Measurements of Arbitrary Non-commuting Pauli Observables
• Avoiding Loopholes with Hybrid Bell-Leggett-Garg Inequalities
• Experimental simultaneous read out of the real and imaginary parts of the weak value
• High Precision Multi-parameter Weak Measurement with Hermite-Gaussian Pointer
• Directly Measuring a Multiparticle Quantum Wave Function via Quantum Teleportation
• Simultaneous weak measurement of non-commuting observables
• Generalized overlap quantum state tomography
• An experimental investigation of measurement-induced disturbance and time symmetry in quantum physics
• Gradient-based stopping rules for maximum-likelihood quantum-state tomography
• Determining complementary properties using weak-measurement: uncertainty, predictability, and disturbance

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