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arXiv:1909.12826 · Physical Review Letters

Heralded Interaction Control between Quantum Systems

Yiheng Duan, Mahdi Hosseini, Kristin M. Beck, Vladan Vuletić

Published Jun 4, 2020• 5 citations
arXivHTMLPDF

Abstract

Quantum mechanical expectation values for subsets can differ substantially from those for the whole ensemble. This implies that the effect of interactions between two systems can be altered substantially by conditioning. Here, we experimentally demonstrate that, for two light fields ψ_{S} (signal) and ψ_{A} (ancilla) that have only weakly interacted with one another, subsequent measurements on the ancilla can produce substantial conditional amplification, attenuation, or phase shift of ψ_{S}. We observe conditional signal power changes over a large range of 30, and phase shift up to π/2, induced by measurements in ancilla bases that differ only slightly from one another. The method is generically applicable to a variety of systems, and allows one to modify or boost a given interaction by trading in success probability for interaction strength.

DOI
10.1103/physrevlett.124.223602

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Quantum mechanical expectation values for subsets can differ substantially from those for the whole ensemble. This implies that the effect of interactions between two systems can be altered substantially by conditioning. Here, we experimentally demonstrate that, for two light fields ψ_{S} (signal) and ψ_{A} (ancilla) that have only weakly interacted with one another, subsequent measurements on the ancilla can produce substantial conditional amplification, attenuation, or phase shift of ψ_{S}. We observe conditional signal power changes over a large range of 30, and phase shift up to π/2, induced by measurements in ancilla bases that differ only slightly from one another. The method is generically applicable to a variety of systems, and allows one to modify or boost a given interaction by trading in success probability for interaction strength.
Weak value amplification is a popular method in quantum metrology for enhancing the sensitivity at the expense of the signal intensity. Recently, it was suggested that the trade-off between signal intensity and sensitivity can be improved by using an entangled auxiliary system. Here, we experimentally investigate such entanglement-assisted weak measurement of small conditional phase shifts induced by an interaction between ancilla and meter qubits. We utilize entangled photon pairs and implement the required three-qubit quantum logic circuit with linear optics. The circuit comprises a two-qubit controlled phase gate and a three-qubit controlled-controlled phase gate with fully tunable conditional phase shifts. We fully characterize the output states of our circuit by quantum state tomography and perform a comprehensive analysis of the trade-off between the measurement sensitivity and the success probability of the protocol. The observed experimental results are in good qualitative agreement with theoretical predictions, but the overall performance of our setup is limited by various experimental imperfections. We provide a detailed theoretical analysis of the influence of dephasing of the entangled ancilla state, which is one of the main sources of imperfections in the experiment. We also discuss the ultimate scaling with the dimension of the entangled ancilla system.
The viability of quantum communication schemes rely on sending quantum states of light over long distances.However, transmission loss can degrade the signal strength, adding noise.Heralded noiseless amplification of a quantum signal can provide a solution by enabling longer direct transmission distances and by enabling entanglement distillation.The central idea of heralded noiseless amplification-a conditional modification of the probability distribution over photon number of an optical quantum state-is suggestive of a parallel with weak measurement: in a weak measurement, learning partial information about an observable leads to a conditional back-action of a commensurate size.Here we experimentally investigate the application of weak, or variable-strength, measurements to the task of heralded amplification, by using a quantum logic gate to weakly couple a small single-optical-mode quantum state (the signal) to an ancilla photon (the meter).The weak measurement is carried out by choosing the measurement basis of the meter photon and, by conditioning on the meter outcomes, the signal is amplified.We characterise the gain of the amplifier as a function of the measurement strength, and use interferometric methods to show that the operation preserves the coherence of the signal.
Measurements are crucial in quantum mechanics, for fundamental research as well as for applicative fields like quantum metrology, quantum-enhanced measurements and other quantum technologies. In the recent years, weak-interaction-based protocols like Weak Measurements and Protective Measurements have been experimentally realized, showing peculiar features leading to surprising advantages in several different applications. In this work we analyze the validity range for such measurement protocols, that is, how the interaction strength affects the weak value extraction, by measuring different polarization weak values on heralded single photons. We show that, even in the weak interaction regime, the coupling intensity limits the range of weak values achievable, setting a threshold on the signal amplification effect exploited in many weak measurement based experiments.
Deterministic optical quantum logic requires a nonlinear quantum process that alters the phase of a quantum optical state by π through interaction with only one photon. Here, we demonstrate a large conditional cross-phase modulation between a signal field, stored inside an atomic quantum memory, and a control photon that traverses a high-finesse optical cavity containing the atomic memory. This approach avoids fundamental limitations associated with multimode effects for traveling optical photons. We measure a conditional cross-phase shift of [Formula: see text] (and up to [Formula: see text] by postselection on photons that remain in the system longer than average) between the retrieved signal and control photons, and confirm deterministic entanglement between the signal and control modes by extracting a positive concurrence. By upgrading to a state-of-the-art cavity, our system can reach a coherent phase shift of π at low loss, enabling deterministic and universal photonic quantum logic.
Due to the reduced probability of successful post-selection, the weak-value amplification seems to be unavailable for the parameter-estimation. Here, we show theoretically that, some effects due to the weak interactions present only in the properly post-selected sub-ensemble, however are canceled by themselves in the total ensemble. From this point of view, the post-selection induced weak value could be one of the feasible methods for measuring the weak interaction, since the standard measurement does not work. Additionally, we employ the system of trapped ions to simulate the weak measurement and calculate relevant results without the frequently-used weak interaction approximation.