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arXiv:2409.09840 · Physical Review A

Sub-shot-noise sensitivity via superpositions of two deformed kitten states

Naeem Akhtar, Xiaosen Yang, Jia‐Xin Peng, Inaam Ul Haq, Yuee Xie, Yuanping Chen

Published Mar 5, 2025• 5 citations
arXivHTMLPDF

Abstract

In the present work we explore nonclassical effects in the phase space of two superposed kitten states induced by photon addition and subtraction operations applied in different sequences. We investigate two scenarios: In the first, photon addition is applied to the state, followed by photon subtraction, while in the second, the order of operations is reversed. We demonstrate that applying multiphoton operations to the state results in notable nearly isotropic sub-Planck structures, with the characteristics of these structures being influenced by the photon addition and subtraction. Increasing the number of added photons compresses the sub-Planck structures in both cases. Photon subtraction, however, has the opposite effect on the sub-Planck structures in the first case and no effect in the second. Furthermore, we observe that the optimal choices of multiphoton operations lead to improved isotropy of sub-Planck structures in our cases. The presence of the sub-Planck structures in our states leads to improved sensitivity to displacements, exceeding the standard quantum limit, as verified across all the depicted scenarios.

DOI
10.1103/physreva.111.032407

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In the present work we explore nonclassical effects in the phase space of two superposed kitten states induced by photon addition and subtraction operations applied in different sequences. We investigate two scenarios: In the first, photon addition is applied to the state, followed by photon subtraction, while in the second, the order of operations is reversed. We demonstrate that applying multiphoton operations to the state results in notable nearly isotropic sub-Planck structures, with the characteristics of these structures being influenced by the photon addition and subtraction. Increasing the number of added photons compresses the sub-Planck structures in both cases. Photon subtraction, however, has the opposite effect on the sub-Planck structures in the first case and no effect in the second. Furthermore, we observe that the optimal choices of multiphoton operations lead to improved isotropy of sub-Planck structures in our cases. The presence of the sub-Planck structures in our states leads to improved sensitivity to displacements, exceeding the standard quantum limit, as verified across all the depicted scenarios.
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We observe a metrological advantage in phase-space sensitivity for photon-added cat and kitten states over their original forms, due to phase-space broadening from increased amplitude via photon addition, albeit with higher energy cost. Using accessible non-classical resources, weak squeezing and displacement, we construct a squeezed state and two superposed states: the squeezed cat state and the symmetrically squeezed state. Their photon-added variants are compared with parity-matched cat and KSs using quantum Fisher information and fidelity. The QFI isocontours reveal regimes where KS exhibit high fidelity and large amplitude, enabling their preparation via Gaussian operations and photon addition. Similar regimes are identified for cat states enhanced by squeezing and photon addition, demonstrating improved metrological performance. Moreover, increased amplitude and thus larger phase-space area reduces the size of interferometric fringes, enhancing the effectiveness of quantum error correction in cat codes.
We investigate multi-headed Schrödinger cat states (MHCS) engineered via multiphoton addition and subtraction sequences, namely addition, subtraction, addition-then-subtraction, and subtraction-then-addition across even, odd, three-headed cat states (3HCS), and four-headed cat states (4HCS). Our analysis reveals that operator noncommutativity plays a decisive role in quantum metrology: addition-then-subtraction consistently yields the highest phase sensitivity among the operations considered, even when alternative orderings exhibit stronger Wigner negativity, highlighting a distinction between phase space and operational nonclassicality. Among all states, 4HCS achieves the best performance due to enhanced interference structures, reaching a significant improvement over the shot-noise limit. We also examine robustness under photon loss and dephasing, confirming their practical advantage for quantum sensing.
The phase space structure and statistics of the photon added cat state are studied in the state’s general form. Photon addition leads to a π phase shift at the origin in the observed phase space interference of the Wigner function, which may serve as an error syndrome detector. The maxima and minima of the sub-Planck tiles in the phase space of the kitten state are interchanged after photon addition, leading to their orthogonality. Interestingly, photon addition to the Yurke–Stoler state characterized by Poissonian statistics leads to a sub-Poissonian distribution, which may find potential use in quantum noise reduction.
Compound beams composed of simple experimental blocks (detected in simultaneous detection windows) that form specific quantum-correlated structures are suggested for simulating the properties of different quantum operations used for creating highly nonclassical and entangled multi-mode states needed in quantum communication, metrology, and information protocols. Qualitative and quantitative comparison of multi-photon addition and subtraction in compound multi-mode thermal as well as sub-Poissonian beams and multi-mode twin beams with their intensities extending over two orders in magnitude is provided. Adding and subtracting up to twenty photocounts, optimal conditions for the generation of experimental nonclassical states are identified. In general, photon addition is identified as advantageous over photon subtraction for the multi-mode thermal and sub-Poissonian beams: It induces (enhances) the nonclassicality in the former (latter) state. Contrary to this, photon subtraction outperforms photon addition in the multi-mode twin beams. Moreover, exploiting temporal photon-pair correlations in compound twin beams when post-selecting, nearly ideal experimental photon(s) addition is demonstrated. The results apply for the beams with mean photon number per mode much less than one.
Abstract We study the temporal dynamics of a photon-added SU(2) coherent state, involving vibrational bound states of an iodine molecule. The nonclassicality of Schrödinger cat-like and compass-like photon-added states of this anharmonic potential is explored through the Mandel Q parameter and the negative region in their phase spaces. The Wigner phase space distribution is thoroughly studied for the photon-added molecular state and displayed for cat- and compass-like states. Generation and control of the sub-Planck interference structures become intriguing with photon addition. We ensure that the photon addition helps to improve the quantum sensitivity for a diatomic molecular system by comparing it between photon-added and photon-subtracted states. The detailed study of quantum sensitivity reveals that one can use a photon-added molecular wave packet as a probe to attain sensitivity to displacement that greatly exceeds the standard quantum limit. We also report that the nature of variation of the quantum sensitivity becomes qualitatively commensurate with that of the Wigner-negativity.