[Paper Review] Quantum enhanced joint measurement of multiple non-commuting observables with SU(1,1) interferometer

Yuhong Liu, Jiamin Li+5 more|arXiv (Cornell University)|Dec 5, 2017

Quantum Information and Cryptography32 references46 citations

TL;DR

This paper proposes a quantum-enhanced joint measurement scheme for multiple non-commuting observables—such as phase and amplitude—using an SU(1,1) interferometer. By leveraging quantum entanglement from optical parametric amplifiers and destructive quantum interference at the dark fringe, the scheme achieves a 20% signal-to-noise ratio (SNR) improvement over the standard quantum limit across all measured observables simultaneously, demonstrating a generalizable approach for joint measurements of arbitrary non-commuting quadrature amplitudes.

ABSTRACT

Heisenberg uncertainty relation in quantum mechanics sets the limit on the measurement precision of non-commuting observables, which prevents us from measuring them accurately at the same time. In some applications, however, the information are embedded in two or more non-commuting observables. On the other hand, quantum entanglement allows us to infer through Einstein-Podolsky-Rosen correlations two conjugate observables with precision better than what is allowed by Heisenberg uncertainty relation. With the help of the newly developed SU(1,1) interferometer, we implement a scheme to measure jointly information encoded in multiple non-commuting observables of an optical field with a signal-to-noise ratio improvement of about 20 % over the standard quantum limit on all measured quantities simultaneously. This scheme can be generalized to the joint measurement of information in arbitrary number of non-commuting observables.

Motivation & Objective

• To overcome the Heisenberg uncertainty principle's limitation on simultaneous measurement of non-commuting observables.
• To enable joint measurement of multiple non-commuting observables—such as phase and amplitude—beyond the standard quantum limit.
• To exploit quantum entanglement via EPR correlations to infer multiple conjugate observables with precision exceeding classical limits.
• To demonstrate the feasibility and scalability of the SU(1,1) interferometer for multi-observable joint measurements in quantum metrology.
• To achieve simultaneous sensitivity enhancement across all measured non-commuting observables without trade-offs in noise performance.

Proposed method

• The scheme employs an SU(1,1) interferometer based on two optical parametric amplifiers (OPAs), replacing beam splitters with nonlinear elements to enable quantum noise cancellation.
• The first OPA (OPA1) generates entangled signal and idler beams, creating EPR-type correlations that enable sub-shot-noise inference of non-commuting observables.
• The second OPA (OPA2) acts as a phase-sensitive amplifier, jointly amplifying the signal and idler outputs to enhance SNR for both quadrature-phase amplitudes.
• Homodyne detection is performed at the signal and idler outputs using locked local oscillators to measure specific quadrature amplitudes (e.g., X̂(φ1), X̂(φ2), X̂(φ3)) with high phase stability.
• Phase locking is achieved via sinusoidal modulation and digital feedback loops (PLLs) on piezoelectric transducers to stabilize the relative phases of local oscillators and the OPA2 pump.
• The system is operated at the dark fringe to maximize destructive quantum interference, minimizing noise across all quadrature angles and enabling simultaneous SNR improvement.

Experimental results

Research questions

• RQ1 Can quantum entanglement be harnessed to simultaneously enhance the measurement sensitivity of multiple non-commuting observables beyond the standard quantum limit?
• RQ2 How does the SU(1,1) interferometer architecture enable noise cancellation and signal amplification across multiple quadrature phases simultaneously?
• RQ3 What is the achievable SNR improvement in joint measurement of phase and amplitude modulations using this scheme compared to classical and conventional quantum approaches?
• RQ4 Can the scheme be generalized to joint measurement of an arbitrary number of non-commuting quadrature-phase amplitudes?
• RQ5 How does the performance of the SU(1,1) interferometer compare to classical beam-splitter and amplifier-based schemes under realistic loss and detection inefficiency conditions?

Key findings

• The SU(1,1) interferometer achieves a 20% improvement in signal-to-noise ratio (SNR) for both phase and amplitude modulations compared to the standard quantum limit, with simultaneous enhancement across all measured observables.
• The SNR for the SU(1,1) scheme scales as (G₁ + g₁)² times the classical SNR, where G₁ and g₁ are the gain and noise parameters of the first OPA, enabling significant sensitivity enhancement.
• The scheme outperforms classical beam-splitter and amplifier-based schemes under fair comparison, as the latter suffer from 3 dB SNR penalty due to vacuum noise at unused ports.
• Phase locking of local oscillators and the OPA2 pump via digital feedback loops enables stable, high-fidelity measurement of multiple quadrature amplitudes at different phase angles.
• The method is generalizable to joint measurement of an arbitrary number of non-commuting observables by splitting the signal output and using additional homodyne detectors.
• Experimental results confirm the theoretical prediction: the SU(1,1) scheme achieves higher SNR than classical schemes for both amplitude (X̂) and phase (Ŷ) modulations, with measurable peaks at 0.8 MHz (AM) and 1.2 MHz (PM) in the frequency domain.