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arXiv:2509.14625

Improving the efficiency of quantum engineering of SCSs by adding two demultiplexed input photons

Mikhail S. Podoshvedov, Sergey A. Podoshvedov

Published Sep 18, 2025• 0 citations
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Abstract

Conditional addition and subtraction of photons is a powerful tool for quantum engineering of continuous variable (CV) states that forms the fundamental building blocks of advanced photonic technologies. For high fidelity information processing, precise control of quantum engineering of CV states is highly demanded. We propose a scheme for measurement induced quantum engineering of even/odd superposition of coherent states (SCSs) of amplitude>2.5 and with fidelity exceeding>0.99. It includes single-mode squeezed vacuum (SMSV) state and two separate photons. The output parameters of the SCSs are tuned using initial squeezing of the SMSV states and the beam splitter (BS) parameter and depend on number of subtracted photons in two measurement channels. The introduction of two demultiplexed photons is a key element to improving the efficiency of quantum engineering of SCSs. When using two additional photons, both an increase in the fidelity of the output CV state and a gain in probability at least by an order of magnitude compared to the case without auxiliary input photons are observed.

DOI
10.48550/arxiv.2509.14625

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Conditional addition and subtraction of photons is a powerful tool for quantum engineering of continuous variable (CV) states that forms the fundamental building blocks of advanced photonic technologies. For high fidelity information processing, precise control of quantum engineering of CV states is highly demanded. We propose a scheme for measurement induced quantum engineering of even/odd superposition of coherent states (SCSs) of amplitude>2.5 and with fidelity exceeding>0.99. It includes single-mode squeezed vacuum (SMSV) state and two separate photons. The output parameters of the SCSs are tuned using initial squeezing of the SMSV states and the beam splitter (BS) parameter and depend on number of subtracted photons in two measurement channels. The introduction of two demultiplexed photons is a key element to improving the efficiency of quantum engineering of SCSs. When using two additional photons, both an increase in the fidelity of the output CV state and a gain in probability at least by an order of magnitude compared to the case without auxiliary input photons are observed.
Abstract Conditional addition and subtraction of photons is a powerful tool for quantum engineering of continuous variable (CV) states that forms the fundamental building blocks of advanced photonic technologies. For high fidelity information processing, precise control of quantum engineering of CV states is highly demanded. We propose a scheme for measurement induced quantum engineering of even/odd superposition of coherent states (SCSs) of amplitude > 2.5 and with fidelity exceeding > 0.99 . It includes single-mode squeezed vacuum (SMSV) state and two separate photons. The output parameters of the SCSs are tuned using initial squeezing of the SMSV states and the beam splitter parameter and depend on number of subtracted photons in two measurement channels. The introduction of two demultiplexed photons is a key element to improving the efficiency of quantum engineering of SCSs. When using two additional photons, both an increase in the fidelity of the output CV state and a gain in probability at least by an order of magnitude compared to the case without auxiliary input photons are observed.
We propose an efficient way to implement new family of continuous variable (CV) states of definite parity. Measurement induced CV states of definite parity states are realized after subtraction of an arbitrary number of photons from the initial single-mode squeezed vacuum (SMSV) state using a photon number resolving (PNR) detector. Optical design requires irreducible number of optical elements for implementation of the CV states of definite parity. The potential of using the CV states in optical quantum information processing can be high. As an example, we show the possibility of using a family of the CV states of definite parity for quantum engineering of optical even/odd Schrödinger cat states (SCSs). In particular, we report the possibility of implementing the CV states of definite parity that approximate even/odd SCSs of amplitude slightly greater than 4 with fidelity prevailing 0,99 after subtraction of 50,51 photons from original SMSV. The success probability being the third key parameter of the optical design, decreases with an increase in the number of photons, but generally remains at an acceptable level for further use in quantum information processing in the case of a small number of subtracted photons.
We develop a method for generating a more squeezed than single-mode squeezed vacuum (SMSV) state by subtracting 2,4,6 photons from it. In general, the more photons are subtracted, the more gain of the squeezing (more of 3 dB) is observed in the measurement-induced continuous variable (CV) states of definite parity. However, the two-photon subtraction strategy is practically preferred. It can be implemented with higher success probability, wider squeezing gain width ~ 5 dB and least quadrature variance in the corresponding range of initial squeezing. We demonstrate the mitigating effect of a photon-number resolving (PNR) detector with non-unit quantum efficiency on the output characteristics of the measurement-induced CV states, resulting in their slight decrease compared to ideal photon subtraction. Use of a single photon in addition to the SMSV state at beam splitter (BS) input with subsequent registration of odd number of photons (say, 3 photons) allows the implementation of the measurement-induced even CV state which is several times brighter than the initial state and has lower quadrature noise.
We develop a method to generate nonclassical light with a larger quadrature squeezing than one of the single-mode squeezed vacuum (SMSV) states by subtracting 2,4,6 photons from it. In general, the more photons are subtracted, the more gain of the squeezing (more than 3 dB) is observed in the measurement-induced continuous variable (CV) states of definite parity. However, the two-photon subtraction strategy is practically preferred. It can be implemented with higher success probability, wider squeezing gain width ∼5dB, and less quadrature variance. We demonstrate the mitigating effect of a photon-number resolving (PNR) detector with nonunit quantum efficiency on the output characteristics of the measurement-induced CV states, resulting in their slight decrease compared to ideal measurement of photons in the auxiliary mode. Use of a single photon in addition to the SMSV state at beam splitter (BS) input with subsequent registration of an odd number of photons (say, 3 photons) in auxiliary mode allows the implementation of the measurement-induced even CV state, which is several times brighter than the initial state, has lower quadrature noise, and is generated with greater probability.
We present an algorithm of quantum engineering of large-amplitude [Formula: see text] high-fidelity [Formula: see text] even/odd Schrödinger cat states (SCSs) using a single mode squeezed vacuum (SMSV) state as resource. Set of [Formula: see text] beam splitters (BSs) with arbitrary transmittance and reflectance coefficients sequentially following each other acts as a hub that redirects a multiphoton state into the measuring modes simultaneously measured by photon number resolving (PNR) detectors. We show that the multiphoton state splitting guarantees significant increase of the success probability of the SCSs generator compared to its implementation in a single PNR detector version and imposes less requirements on ideal PNR detectors. We prove that the fidelity of the output SCSs and its success probability are in conflict with each other (which can be quantified) in a scheme with ineffective PNR detectors, especially when subtracting large (say, [Formula: see text]) number of photons, i.e., increasing the fidelity to perfect values leads to a sharp decrease in the success probability. In general, the strategy of subtracting up to [Formula: see text] photons from initial SMSV in setup with two BSs is acceptable for achieving sufficiently high values of the fidelity and success probability at the output of the generator of the SCSs of amplitude [Formula: see text] with two inefficient PNR detectors.
We present an algorithm of quantum engineering of large-amplitude>5 high-fidelity>0.99 even/odd Schrodinger cat states (SCSs) using a single mode squeezed vacuum (SMSV) state as resource. Set of k beam splitters (BSs) with arbitrary transmittance and reflectance coefficients sequentially following each other acts as a hub that redirects a multiphoton state into the measuring modes simultaneously measured by photon number resolving (PNR) detectors. We show that the multiphoton state splitting guarantees significant increase of the success probability of the cat state generator compared to its implementation in a single PNR detector version and imposes less requirements on ideal PNR detectors. We prove that the fidelity of the output SCSs and its success probability are in conflict with each other (which can be quantified) in a scheme with ineffective PNR detectors, especially when subtracting large (say, 100) number of photons, i.e., increasing the fidelity to perfect values leads to a sharp decrease in the success probability. In general, the strategy of subtracting up to 20 photons from initial SMSV in setup with two BSs is acceptable for achieving sufficiently high values of the fidelity and success probability at the output of the generator of the SCSs of amplitude <3 with two inefficient PNR detectors.