Photon-Added Cat and Kitten States Achieve Enhanced Phase-Space Sensitivity

Scientists are continually striving to push the boundaries of quantum precision, and a new study details a method for enhancing the sensitivity of quantum states used in advanced technologies. Arman and Prasanta K. Panigrahi, both from the Department of Physical Sciences at the Indian Institute of Science Education and Research Kolkata, alongside et al., demonstrate how manipulating the phase-space of quantum states , specifically cat and kitten states , with non-Gaussian operations can significantly increase the area containing sub-Planck-scale structures. This research is significant because it reveals that by adding photons to these states, alongside techniques like squeezing and displacement, researchers can broaden the phase-space and improve the performance of quantum error correction and precision measurements, potentially leading to more robust and effective quantum devices.

Photon-added states enhance quantum phase sensitivity

Scientists have demonstrated a metrological advantage in phase-space sensitivity by employing photon-added cat and kitten states compared to their original, unenhanced counterparts. This breakthrough stems from the increased amplitude achieved through photon addition, effectively broadening the phase-space representation of these quantum states, although at the cost of increased energy expenditure. The research team constructed squeezed states and two superposed states, the squeezed Schrödinger cat state and a symmetrically squeezed state, utilising readily available non-classical resources such as weak squeezing and displacement. These states, along with their photon-added variants, were then rigorously compared with parity-matched cat and kitten states using quantum Fisher information and fidelity as key metrics.
The study unveils that quantum Fisher information isocontours reveal specific regimes where kitten states exhibit both high fidelity and large amplitude, facilitating their preparation through a combination of Gaussian operations and photon addition. Crucially, similar advantageous regimes were identified for cat states further enhanced by squeezing and photon addition, confirming improved metrological performance across these state types. Experiments show that increasing the amplitude of these states expands their phase-space area, consequently reducing the size of interferometric fringes, a critical factor in bolstering the effectiveness of quantum error correction within cat codes. Researchers achieved this by meticulously analysing the impact of non-Gaussian operations on the phase-space characteristics of these states.

The work establishes that photon addition, while increasing the average photon number and non-Gaussianity, effectively expands the phase-space support, leading to enhanced sensitivity in quantum measurements. This is particularly significant for applications requiring sub-Planck-scale precision, where the ability to resolve minute displacements and phase rotations is paramount. The team’s findings demonstrate that carefully engineered photon addition can unlock superior performance in quantum sensing and information processing, paving the way for more robust and accurate quantum technologies. Moreover, the research opens avenues for improved quantum error correction, as the reduced size of interferometric fringes directly translates to a greater resilience against noise and decoherence. This is a vital step towards building practical quantum computers and communication networks, where maintaining the integrity of quantum information is a major challenge. The study’s success in leveraging accessible non-classical resources, weak squeezing and displacement, highlights a pragmatic approach to achieving significant advancements in quantum state engineering and metrology, promising a future where quantum technologies can deliver on their full potential.

Photon-added states enhance kitten phase sensitivity for improved

Scientists investigated the advantages of photon-added cat and kitten states, revealing improved phase-space sensitivity compared to their original counterparts, despite a corresponding increase in energy cost. The research team constructed squeezed states and two superposed states, the squeezed cat state and a symmetrically squeezed state, to facilitate this comparison. They then compared the photon-added variants of these states with parity-matched cat and kitten states using both Fisher information and fidelity as key metrics. Experiments employed quantum Fisher information (QFI) isocontours to identify regimes where kitten states exhibited both high fidelity and large amplitude, enabling their preparation via Gaussian operations coupled with photon addition.

Similar regimes were subsequently identified for cat states enhanced by squeezing and photon addition, demonstrating improved performance characteristics. The study pioneered a method for analysing the impact of photon addition on the phase-space distribution of both cat and kitten states, utilising the Wigner function Wβ = (2/π) Tr ρ Π D[2β], where Π = eiπn and D[2β] = e2βa†−2β∗a represents the displacement operator. Overlap of these distributions, denoted Oλ = 2 (π−1) ∫ d2β WβWβ+λ, and the central fringe area (CFA) were calculated to quantify sensitivity to small phase-space displacements (λ). Researchers observed that single photon addition visibly broadened the phase-space distribution for both kitten and cat states, as depicted in Figure 1.

The locus of first zeros (λo) for the overlap Oλo = 1 −|λo|2F ψ Q(θ)/4, approached the phase-space origin upon photon addition, while maintaining the original amplitude (α). This behaviour resulted in a decreasing central fringe size of the Wigner distribution and a corresponding increase in sensitivity to smaller shifts, as compared to states without photon addition. The team harnessed the number operator n = a†a, with a and a† representing the bosonic annihilation and creation operators respectively, to model photon addition and subtraction. Furthermore, the work detailed how photon addition increases the average photon number and non-Gaussian nature of the state, quantified by equations such as ⟨n⟩PA = ⟨∆2n⟩ψ ⟨n⟩ψ + 1 + ⟨n⟩ψ + 1 and ⟨n⟩PS = ⟨∆2n⟩ψ ⟨n⟩ψ + ⟨n⟩ψ −1. This enhancement of amplitude and phase-space area directly reduces the size of interferometric fringes, thereby improving the effectiveness of error correction in cat codes, a crucial advancement for quantum information processing.

Photon-added states boost quantum sensitivity significantly

Scientists achieved a demonstrable advantage in phase-space sensitivity for photon-added cat and kitten states compared to their original forms, despite an associated increase in energy cost. The research team observed that broadening the phase-space through photon addition enhances sensitivity, paving the way for improved quantum technologies. Experiments revealed the successful construction of squeezed states, alongside superposed squeezed cat and symmetrically squeezed states, utilising accessible non-classical resources like weak squeezing and displacement. The team meticulously measured the Quantum Fisher Information (QFI) isocontours, identifying regimes where kitten states (KS) exhibit both high fidelity and large amplitude, enabling their preparation through Gaussian operations combined with photon addition.

Similar regimes were identified for cat states enhanced by squeezing and photon addition, demonstrating improved performance in these crucial quantum states. Data shows that increasing amplitude, and consequently the phase-space area, reduces the size of interferometric fringes, directly enhancing the effectiveness of error correction within cat codes, a vital step towards robust quantum computation. Results demonstrate a clear correlation between photon addition and the alteration of phase-space distributions for both KS and cat states, as visualised through Wigner function analysis. The study recorded a shift in parity and an increase in phase-space support upon single photon addition, clearly illustrated in Figure 1.

Measurements confirm that the locus of first zeros for the overlap function approaches the phase-space origin following photon addition, while maintaining the original amplitude, signifying a decrease in central fringe size and an increase in sensitivity to small phase-space displacements. Further analysis quantified the effect of photon additions on the mean photon number of the states. The team established that photon addition increases the available energy resource and enhances the effective amplitude of the state, expressed by the equation ⟨n⟩PA = ⟨∆2n⟩ψ ⟨n⟩ψ + 1 + ⟨n⟩ψ + 1, while photon subtraction has a less pronounced effect, particularly for sub-Poissonian light. The mean photon number for KS states satisfies ⟨n⟩KS = F(|βKS|), where F is a monotonically increasing function of the coherent amplitude, highlighting the amplification effect of photon addition. This work provides a detailed illustration of the impact of photon additions on phase space and associated quantitative measures, such as fringe size, for both cat and KS states.

Kitten states optimise sensitivity and fidelity

Scientists have demonstrated an advantage in phase-space sensitivity for photon-added cat and kitten states compared to their original forms, achieved through phase-space broadening resulting from increased amplitude via photon addition, despite a corresponding increase in energy cost. Researchers constructed squeezed states, alongside superposed squeezed cat and symmetrically squeezed states, utilising accessible non-classical resources like weak squeezing and displacement, these were then compared with parity-matched cat and kitten states using Fisher information and fidelity. The quantum Fisher information (QFI) isocontours revealed regimes where kitten states exhibit both high fidelity and large amplitude, facilitating their preparation through Gaussian operations and photon addition. Furthermore, similar regimes were identified for cat states enhanced by squeezing and photon addition, indicating improved performance in these configurations, increased amplitude, and thus a larger phase-space area, reduces the size of interferometric fringes, thereby enhancing the effectiveness of error correction within cat codes.

Analysis of Wigner functions and central fringe areas confirmed that photon addition broadens the phase-space distribution of both cat and kitten states, increasing their sensitivity to small phase-space displacements, this effect is also observed with increasing amplitude, establishing a clear relationship between photon addition and state sensitivity. The study acknowledges that achieving these enhanced states may require specific interaction regimes, such as those involving the Jaynes-Cummings model, Rabi oscillations, and strong dispersive interactions, potentially impacting the success probabilities of non-Gaussian operations. Future research could explore the practical implementation of these states in quantum technologies, focusing on optimising the balance between energy cost and phase-space sensitivity, the findings suggest a pathway towards improving the performance of quantum error correction and enhancing the precision of quantum metrology, although limitations related to the required interaction regimes need to be addressed. This work establishes a clear link between photon addition, phase-space properties, and the potential for improved performance in non-classical quantum states, offering valuable insights for the development of robust and sensitive quantum systems.