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Physical Review A

State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting

Longzhu Cen, Zijing Zhang, Jiandong Zhang, Shuo Li, Yifei Sun, Linyu Yan, Yuan Zhe Zhao, Feng Wang

Published Nov 21, 2017• 10 citations
Publisher

Abstract

Circular polarization-entangled photons can be used to obtain an enhancement of the precision in a rotation measurement. In this paper, the method of entanglement transformation is used to produce NOON states in circular polarization from a readily generated linear polarization-entangled photon source. Detection of $N$-fold coincidences serves as the postselection and $N$-fold superoscillating fringes are obtained simultaneously. A parity strategy and conditional probabilistic statistics contribute to a better fringe, saturating the angle sensitivity to the Heisenberg limit. The impact of imperfect state preparation and detection is discussed both separately and jointly. For the separated case, the influence of each system imperfection is pronounced. For the joint case, the feasibility region for surpassing the standard quantum limit is given. Our work pushes the state preparation of circular polarization-entangled photons to the same level as that in the case of linear polarization. It is also confirmed that entanglement can be transformed into different frames for specific applications, serving as a useful scheme for using entangled sources.

DOI
10.1103/physreva.96.053846

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Circular polarization-entangled photons can be used to obtain an enhancement of the precision in a rotation measurement. In this paper, the method of entanglement transformation is used to produce NOON states in circular polarization from a readily generated linear polarization-entangled photon source. Detection of NNN-fold coincidences serves as the postselection and NNN-fold superoscillating fringes are obtained simultaneously. A parity strategy and conditional probabilistic statistics contribute to a better fringe, saturating the angle sensitivity to the Heisenberg limit. The impact of imperfect state preparation and detection is discussed both separately and jointly. For the separated case, the influence of each system imperfection is pronounced. For the joint case, the feasibility region for surpassing the standard quantum limit is given. Our work pushes the state preparation of circular polarization-entangled photons to the same level as that in the case of linear polarization. It is also confirmed that entanglement can be transformed into different frames for specific applications, serving as a useful scheme for using entangled sources.
We present an experimental study of polarization-entangled photon pairs, investigating the dependence of the measurement outcomes on different polarization rotation angles and the slow temporal fluctuations of the generated quantum state. Entangled photon pairs are produced and analyzed using single-photon detectors while systematically varying polarization settings on both sides. Bell tests yield an S parameter of approximately 2.52, confirming strong entanglement. The measured coincidence counts between identical measurement outcomes exhibit the expected sinusoidal dependence on the combined rotation angles, but systematic deviations appear as pronounced peaks and variations in certain configurations. Long-term monitoring over twenty minutes shows correlated fluctuations on both sides in individual detection outcomes of up to 25%, while the total photon flux remains constant, indicating that these deviations originate from slow intrinsic changes in the generated quantum state. These temporal fluctuations can reduce the effective time window over which optimal polarization and phase alignment is maintained, highlighting the importance of implementing real-time compensation or feedback mechanisms in experiments requiring high-fidelity entanglement over extended durations. Our results provide insight into the stability limits of entangled photon sources and underscore the importance of accounting for temporal fluctuations in precision entanglement experiments.
A simple experimental setup consisting of a spontaneous parametric down-conversion source and passive linear optics is proposed for conditional preparation of a maximally entangled polarization state of two photons. Successful preparation is unambiguously heralded by coincident detection of four auxiliary photons. The proposed scheme utilizes the down-conversion term corresponding to the generation of three pairs of photons. We analyze imperfect detection of the auxiliary photons and demonstrate that its deleterious effect on the fidelity of the prepared state can be suppressed at the cost of decreasing the efficiency of the scheme.
Bell inequality experiments have demonstrated that quantum entanglement violates the predictions of local realism. However, all Bell experiments are based on joint measurements of two photons, and their analysis implicitly assumes that "the polarization state of a single photon is ideally linear." This paper proposes an experimental scheme to directly test this assumption: using type-II spontaneous parametric down-conversion (SPDC) to generate polarization-entangled photon pairs, employing fixed-angle measurement of the e-light channel as a coincidence gate to filter entangled photons in the o-light channel, then scanning the o-light analyzer angle with high precision to measure the coincidence count rate as a function of the analyzer angle, testing whether it strictly follows Malus' law I(\theta)=I_0\cos^2(\theta-\theta_0). If systematic deviation is observed in the curve, it would indicate the existence of asymmetric secondary polarization structures in the polarization state of entangled photons, providing an alternative explanatory pathway for Bell inequality violation distinct from nonlocality. This experiment employs a high-precision coincidence measurement scheme to ensure statistical significance and designs multiple control experiments to eliminate systematic errors. The experiment can be implemented in laboratories equipped with standard quantum optics equipment.
Quantum enhancements of precision in metrology can be compromised by system imperfections. These may be mitigated by appropriate optimization of the input state to render it robust, at the expense of making the state difficult to prepare. In this paper, we identify the major sources of imperfection of an optical sensor: input state preparation inefficiency, sensor losses, and detector inefficiency. The second of these has received much attention; we show that it is the least damaging to surpassing the standard quantum limit in a optical interferometric sensor. Further, we show that photonic states that can be prepared in the laboratory using feasible resources allow a measurement strategy using photon-number-resolving detectors that not only attain the Heisenberg limit for phase estimation in the absence of losses, but also deliver close to the maximum possible precision in realistic scenarios including losses and inefficiencies. In particular, we give bounds for the tradeoff between the three sources of imperfection that will allow true quantum-enhanced optical metrology
Commercial sources of polarization entanglement at telecommunication wavelengths are already available on the market, but they lack proper certification or third-party testing. We aim to provide a comprehensive testing framework for photon counting and correlation measurements to characterize the parameters of these sources in a scalable and repeatable manner. The detection setup is included in our considerations, as the non-idealities of the components negatively affect the relevance of the measurement results. We discuss bounds for both true and false coincidences with rigorous probabilistic approach, as their ratio directly impacts the resolution of coincidence measurements and is reflected in Quantum Bit Error Rate (QBER) in the quantum telecommunication system. Quantum State Tomography (QST), polarization visibility measurements, temporal correlations measurements, and computations of other statistics are to be performed and compared at the state-of-the-art level for a three commercially available sources. Given that QST is demanding in terms of number of measurements and post-processing analysis, we discuss the relevance of determining the degree of polarization entanglement considering solely other statistics of direct measurement approach.
In principle, the use of entangled photons provides enhanced precision in optical phase measurements. This precision significantly surpasses the classical shot-noise limit, and thereby has many possible applications in science and technology. In practice, however, entangled multiphoton states have been generated so far using various intrinsically probabilistic and unscalable processes, thereby counteracting the advantages that the entangled photon states might have. The authors overcome these limitations here by using a quantum knitting machine, based on a single semiconductor quantum dot, to generate a polarization-entangled multiphoton state in a deterministic manner. The multiphoton state is then used to demonstrate super-sensitive optical phase measurement. The results pave the way for realizing genuine quantum enhanced optical measurements in the very near future.