Squeezing Detection Reveals Nonclassicality in Bosonic Systems Without Reference Signals

Researchers are continually seeking methods to verify quantum behaviour in complex photonic systems, and a significant challenge lies in accurately measuring non-classicality without relying on a stable, known reference signal. Suchitra Krishnaswamy, Dhrithi Maria, and Laura Ares, alongside colleagues from Paderborn University’s Institute for Photonic Quantum Systems (PhoQS), now present a novel approach to ‘squeezing detection’ that circumvents this limitation. Their work constructs new criteria for non-classicality, based on partial normal ordering, enabling the investigation of quantum phenomena using arbitrary local oscillator states during balanced homodyne detection, and revealing only the properties of the signal itself. This advancement offers a robust and sensitive framework, particularly valuable for applications where a well-defined coherent reference is inaccessible, and promises to broaden the scope of quantum information technologies.

Reference-free detection of nonclassicality via balanced homodyne measurements is a challenging task

Scientists have demonstrated a new method for detecting nonclassicality in continuous-variable bosonic systems without requiring a known reference signal. The team achieved this by constructing broader classes of criteria for nonclassicality, enabling investigation of quantum phenomena irrespective of the quantumness of selected subsystems.
This innovative approach utilises the concept of partial normal ordering, applied to balanced homodyne detection with potentially nonclassical local oscillator states, revealing only the quantumness of the probed signal. The research establishes a framework that surpasses standard techniques, exhibiting both robustness and enhanced sensitivity.

Experiments show that this methodology allows assessment of photonic system features even when a well-defined coherent laser, typically used as a reference, is unavailable. This breakthrough reveals a widely applicable framework suited for applications in quantum metrology and quantum information, addressing a significant challenge in characterizing quantum states.

Specifically, the study unveils a technique for local-oscillator-agnostic squeezing detection, addressing the limitation of conventional homodyne detection which relies on a coherent state as a phase reference. Researchers formulated squeezing criteria independent of the auxiliary mode, effectively separating the nonclassicality of the signal from potential contributions originating from an unknown local oscillator.

This is achieved through a partial normal ordering approach, ensuring that any negative expectation value definitively indicates nonclassicality in the probed signal. The work opens possibilities for scenarios where generating suitable local oscillators is challenging, such as in environments lacking laser sources.

By constructing a family of two-mode states whose nonclassical nature is independent of the auxiliary mode, the scientists derived a general methodology for formulating witnesses that pinpoint the nonclassicality of the signal mode. Variance-based criteria, serving as a phase-sensitive nonclassicality witness, were obtained as a special case, facilitating application in balanced homodyne detection setups with both classical and nonclassical local oscillators. The team compared their approach with coherent-LO-based measurements, demonstrating improved noise suppression and robustness against experimental imperfections, and discussed optimisation strategies for enhanced quantum metrology applications.

Detecting nonclassicality via subsystem independence and balanced homodyne measurements is a promising approach to quantum characterization

Scientists developed a novel framework for detecting nonclassicality in continuous-variable bosonic systems without requiring a known reference signal. The research team constructed broader criteria for nonclassicality based on the concept of partial normal ordering, enabling investigation of phenomena independent of selected subsystems.

This approach was applied to balanced homodyne detection, utilising arbitrary, potentially nonclassical local oscillator states, while solely revealing information from the probed signal. The study pioneered a methodology to formulate witnesses, where negative expected values signify nonclassicality in the first mode and cannot originate from an auxiliary mode.

Researchers established a family of two-mode states exhibiting nonclassicality independent of the second, auxiliary mode, representing the local oscillator. Variance-based criteria were derived as a phase-sensitive nonclassicality witness, facilitating application in balanced homodyne detection setups with both classical and nonclassical local oscillators.

Experiments employed two distinct bosonic modes, labelled A and B, with the signal in mode A initially considered a coherent state. The state in the auxiliary system B remained unconstrained, allowing for the definition of classical mixed states through a probability measure over complex numbers and the Hilbert space of B.

A state was deemed nonclassical if it did not conform to this classical form, indicating quantumness in either subsystem A or correlations between A and B. To quantify nonclassicality, the team harnessed a generic two-mode operator expansion and defined partial normal ordering, restricting normal ordering to subsystem A.

They demonstrated that the resulting operator yields nonnegative values for classical states, establishing a criterion where a negative expectation value certifies nonclassicality irrespective of the state in B. Specifically, the researchers showed that the partially normal-ordered variance, DA: (∆L)2A: E, serves as a robust indicator of nonclassicality.

In a balanced homodyne detection setup, the study bypassed the conventional requirement for a coherent state local oscillator. Instead, the team measured the photon-number difference after superimposing the signal and arbitrary local oscillator on a 50/50 beam splitter. This measurement was recast into the observable L = a+eiθb √ 2.† a+eiθb √ 2. − a−eiθb √ 2.† a−eiθb √ 2., where a and b are the annihilation operators for the signal and local oscillator modes, respectively. The resulting fluctuations, quantified by DA: (∆L)2A: E = D (∆L)2E −⟨b†b⟩, provide a LO-agnostic squeezing criterion.

Demonstrating nonclassicality via subsystem-independent witnesses in continuous-variable systems is a challenging task

Scientists have developed a new framework for assessing nonclassicality in continuous-variable bosonic systems without requiring a known reference signal. The research constructs broader criteria for nonclassicality, enabling investigation of phenomena irrespective of the selected subsystems, and is based on the notion of partial normal ordering.

This approach was applied to balanced homodyne detection, revealing the probed signal while utilising arbitrary, potentially nonclassical local oscillator states. Experiments demonstrate that the developed witnesses, based on negative expected values, reliably indicate nonclassicality in the first mode and are independent of the auxiliary mode’s state.

Variance-based criteria were obtained as a special case, allowing application in balanced homodyne detection setups with both classical and nonclassical local oscillators. The team compared this approach with standard coherent-LO-based measurements, demonstrating improved noise suppression behaviour and investigating robustness against experimental imperfections.

For a given signal input, optimisation of the local oscillator was performed to maximise noise suppression, targeting applications in quantum metrology. Researchers considered two bosonic modes, A and B, with the signal in mode A initially defined as a coherent state. The classical mixed states of the composite system were then defined using a probability measure over complex numbers and the auxiliary system.

A state is deemed nonclassical if it cannot be expressed in this form, signifying nonclassicality in mode A or correlations between A and B. The study introduces a construction motivated by normally ordered nonclassicality criteria and the partial transposition criterion, altering only one subsystem. A generic two-mode operator expansion was defined, leading to an operator that takes nonnegative values for classical states.

Consequently, a negative expectation value of this operator certifies nonclassicality, regardless of the state in subsystem B. As an example, applying this criterion to an arbitrary self-adjoint observable L yields a partially normal-ordered variance. In a balanced homodyne detection setup, the measurement goal was to witness squeezing in the signal input without assuming a specific state for the local oscillator.

The measured photon-number difference, after superposition on a 50/50 beam splitter, was recast into an observable L. Calculations reveal the fluctuations, allowing assessment of nonclassicality via the inequality 0 ⟨:(∆L)2:⟩, independent of the local oscillator state. Blocking the signal input, researchers measured vacuum, enabling quantification of noise suppression in decibels, defined as N = 10 log10 ⟨(∆L)2⟩ / ⟨(∆L)2⟩vac. A negative value of N indicates nonclassicality, signifying suppression below vacuum shot noise.

LO-independent certification of nonclassicality via field moment criteria offers a robust approach to device independence

Scientists have developed a new framework for detecting nonclassicality in continuous-variable bosonic systems without requiring a known reference signal. This research constructs broader classes of criteria for nonclassicality, utilising the concept of partial normal ordering to investigate phenomena across different subsystems.

The approach was successfully applied to balanced homodyne detection, revealing information about the probed signal even when using potentially nonclassical local oscillator states. The findings demonstrate a robust and sensitive method for assessing the quantum properties of photonic systems, particularly in scenarios where a defined coherent laser reference is unavailable.

This LO-agnostic condition, based on first and second-order field moments, allows for the certification of squeezing without needing to characterise the local oscillator. While the current work focuses on two modes, the methodology is readily extensible to multi-mode systems and various homodyning scenarios, including eight-port and weak-field homodyning.

The authors acknowledge that the methodology may be affected by additive excess noise, potentially obscuring certain negativities, but emphasise that this noise cannot create non-classicality, reinforcing the robustness of their approach. Future research will focus on state-reconstruction principles beyond witnessing, with an ongoing experimental implementation of the full LO-agnostic and photodetector-agnostic theory currently underway. This work represents a significant step towards more versatile and reliable quantum state characterisation, with potential applications in quantum information and metrology.