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.
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.
Large weak values have been used to amplify the sensitivity of a linear response signal for detecting changes in a small parameter, which has also enabled a simple method for precise parameter estimation. However, producing a large weak value requires a low postselection probability for an ancilla degree of freedom, which limits the utility of the technique. We propose an improvement to this method that uses entanglement to increase the efficiency. We show that by entangling and postselecting n ancillas, the postselection probability can be increased by a factor of n while keeping the weak value fixed (compared to n uncorrelated attempts with one ancilla), which is the optimal scaling with n that is expected from quantum metrology. Furthermore, we show the surprising result that the quantum Fisher information about the detected parameter can be almost entirely preserved in the postselected state, which allows the sensitive estimation to approximately saturate the relevant quantum Cramér-Rao bound. To illustrate this protocol we provide simple quantum circuits that can be implemented using current experimental realizations of three entangled qubits.
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.
Weak-value amplification has been used to enhance the sensitivity of a linear detector response to small interaction parameters. However, the generation of a large weak value gives rise to reduction in postselection probability, which restricts the feasibility of the weak-value amplification technique. Recently, theoretical works have shown that the use of entanglement can increase the efficiency of the weak-value amplification method. Specifically, it is proven that by entangling n particles of a system, the maximum postselection probability scales quadratically with n [Pang, Dressel, and Brun, Phys. Rev. Lett. 113, 030401 (2014)]. In this work, we demonstrate an experimental realization of entanglement-assisted weak-value amplification in a photonic system, which shows that importing quantum entanglement can indeed improve the efficiency of weak-value amplification.
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 measurements have been under intensive investigation in both experiment and theory. Numerous experiments have indicated that the amplified meter shift is produced by the post-selection, yielding an improved precision compared to conventional methods. However, this amplification effect comes at the cost of a reduced rate of acquiring data, which leads to an increasing uncertainty to determine the level of meter shift. From this point of view, a number of theoretical works have suggested that weak measurements cannot improve the precision, or even damage the metrology information due to the post-selection. In this review, we give a comprehensive analysis of the weak measurements to justify their positive effect on prompting measurement precision. As a further step, we introduce two modified weak measurement protocols to boost the precision beyond the standard quantum limit. Compared to previous works beating the standard quantum limit, these protocols are free of using entangled or squeezed states. The achieved precision outperforms that of the conventional method by two orders of magnitude and attains a practical Heisenberg scaling up to n=106 photons.
Conditional- π phase shift between two photons is essential for entanglement generation and universal quantum logic. For photons, however, direct conditional controls are not possible and must be mediated by nonlinear media. Achieving such operations for photonic polarization qubits has remained difficult due to intrinsically weak photon-photon nonlinearities in atomic systems. Here, we show that a conditional- π phase shift between two weak coherent pulses can be realized via a cavityless closed double- Λ atomic system, where quantum interference between linear and nonlinear atom-photon interactions enables conditional control. By optimizing the interaction parameters, including amplitude and phase compensations, we identify the conditions for conditional- π phase shift between two weak coherent pulses. Experimentally, we observe the conditional- π phase shift with relative output amplitude 0.74 ± 0.06 and phase shift ( 0.95 ± 0.03 ) π between the two-photon amplitudes | H H 〉 and | V V 〉 . A theoretical analysis of Bell-state generation from weak coherent pulses further shows Clauser-Horne-Shimony-Holt inequality violation and nonzero concurrence. Our results clarify both the theoretical requirements and the experimental feasibility of cavityless atom-mediated nonlinearities for photonic quantum logic, establishing a scalable route toward nonlinear quantum photonics.