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arXiv:1609.08936 · Scientific Reports

The power of a control qubit in weak measurements

Raul Coto, Víctor Montenegro, Vitalie Eremeev, Douglas Mundarain, Miguel Orszag

Published Jul 19, 2017• 8 citations
arXivHTMLPDF

Abstract

In the late 80 s, a curious effect suggested by Aharanov et al. was found to lead to an anomalous amplification based on quantum measurements of weakly coupled systems. In this paper, we investigate the quantum control of the weak value amplification of a qubit system coupled to a meter. For the qubit system, the coupling occurs via a second non-interacting qubit, initially quantum correlated with the first one. We show that for weak measurements, the control can be remotely realized via the post-selected state of the second qubit or the degree of squeezing of the meter. In our study of the quantum control of the amplification, we can easily manipulate the degree of quantum correlations between the initially correlated qubits. We find that the degree of entanglement has no effect on the quantum control of the amplification. However, we also found a clear connection between the amplification and quantum discord like measurements as well as classical correlations between the qubits. Finally, we suggest an application of the amplification control on the enhancement of the quantum measurement accuracy, e.g. measuring the relative phase of the post-selected control qubit in a more precise way, as opposed to the non-amplified case.

DOI
10.1038/s41598-017-05370-5

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In the late 80 s, a curious effect suggested by Aharanov et al. was found to lead to an anomalous amplification based on quantum measurements of weakly coupled systems. In this paper, we investigate the quantum control of the weak value amplification of a qubit system coupled to a meter. For the qubit system, the coupling occurs via a second non-interacting qubit, initially quantum correlated with the first one. We show that for weak measurements, the control can be remotely realized via the post-selected state of the second qubit or the degree of squeezing of the meter. In our study of the quantum control of the amplification, we can easily manipulate the degree of quantum correlations between the initially correlated qubits. We find that the degree of entanglement has no effect on the quantum control of the amplification. However, we also found a clear connection between the amplification and quantum discord like measurements as well as classical correlations between the qubits. Finally, we suggest an application of the amplification control on the enhancement of the quantum measurement accuracy, e.g. measuring the relative phase of the post-selected control qubit in a more precise way, as opposed to the non-amplified case.
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.
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.
Abstract Single-photon amplification can be used to overcome the photon loss in long-distance quantum communication. However, the trade-off of success probability and amplification gain should be further improved. We propose a single-photon polarization qubit amplification using weak measurement. The polarization qubit can be amplified by the pre- and post-selection of the single-photon meter state weakly coupling with the input state. The success probability does not decrease asymptotically to 0 with increasing amplification gain in the presented proposal, and is higher than that in entanglement-based schemes, without coincidence detection required. Our proposal is feasible in current technology, and helpful for near-future quantum communication.
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.
Super-quantum discord (SQD) with weak measurement is regarded as a kind of quantum correlation in quantum information processing. We compare and analyze the dynamical evolutions of SQD, quantum discord (QD), and quantum entanglement (QE) between two qubits in the correlated dephasing environmental model. The results indicate that (i) owing to the much smaller influence of weak measurement on the coherence of the system than that of von Neumann projection measurement, SQD with weak measurement is larger than QD, and (ii) dynamical evolution of QD or QE monotonically goes to zero with time, while SQD monotonically tends to a stable value and a freezing phenomenon occurs. The stable value after freezing mainly depends on the measurement strength and the purity of the initial quantum state.
Abstract In our study of super quantum discord between two excitonic qubits inside a coupled semiconductor quantum dots system, our primary focus is to uncover the impact of weak measurement on its quantum characteristics. To achieve this, we analyze how varying the measurement strength x , affects this super quantum correlation in the presence of thermal effects. Additionally, we assess the effect of this variation on the system’s evolution against its associated quantum parameters; external electric fields, exciton–exciton dipole interaction energy and Förster interaction. Our findings indicate that adjusting x to smaller values effectively enhances the super quantum correlation, making weak measurements act as a catalyst. This adjustment ensures its robustness against thermal effects while preserving the non-classical attributes of the system. Furthermore, our study unveils that the effect of weak measurements on this latter surpasses the quantum effects associated with the system. Indeed, manipulating the parameter x allows the weak measurement to function as a versatile tool for modulating quantum characteristics and controlling exciton–exciton interactions within the coupled semiconductor quantum dots system.