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arXiv:2212.08827

Algorithm of quantum engineering of large-amplitude high-fidelity cat states in setup with k beam splitters and with inefficient photon number resolving detection

Mikhail S. Podoshvedov, Sergey A. Podoshvedov, S. P. Kulik

Published Dec 17, 2022• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2212.08827

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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.
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.
Abstract We theoretically propose an efficient way to generate optical analogs of both even and odd Schrӧdinger cat states (SCSs) of large amplitude with high fidelity and reasonable generation rate. The resources consumed are a single-mode squeezed vacuum state (SMSV) and possibly a single photon or nothing. We report the generation of even (odd) SCS with amplitude 4.2 , fidelity higher than 0.99 with success probability a little more than 10 − 7 by subtraction of 30 ( 31 ) photons from SMSV by ideal photon number detection. In order to reduce the requirements for the sensitivity of photon number resolving (PNR) detector, we show the implementation of even/odd SCSs with the same characteristics with two PNR detectors resolving only 15 photons each instead of 30 . In the case of inefficient detector, SCS’s size and its fidelity can be kept close to perfect by using highly transmitting beam splitter, but at the cost of very dramatic reduction of the success probability. In order to have certain harmony between the characteristics (large amplitude, high fidelity and acceptable success probability) in the case of imperfect detection, highly transmitting beam splitters should not be used and number of the subtracted photons must be reduced to 10 11 .
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 report an efficient way to generate both even and odd optical analogs of Schrodinger cat states (SCSs) which are a superposition of two coherent states with opposite amplitudes. The resources consumed are single mode squeezed vacuum (SMSV) state and single photon. SCSs are formed after superimposing the input states with the subsequent detection of the number of photons in the auxiliary mode. We report the generation of even/odd SCSs with amplitude 4.2 with fidelity >0.99 and an acceptable for offline experiments success probability. There is a tendency towards an increase in the size of the SCSs with the fidelity >0.99 more demonstrated with an increase in the number of extracted photons.
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.
Schrödinger cat states are important non-Gaussian resources for quantum information processing and quantum-enhanced metrology. Although photon subtraction from squeezed vacuum states has proven useful for generating such states in the optical domain, scaling to large amplitudes while maintaining high fidelity and heralding probability remains challenging. To address these obstacles, we analyze alternating squeezing and photon-number-subtraction operations. Rather than optimizing for a single heralding outcome, we formulate cat-state generation as a fidelity-constrained multibranch problem, jointly optimizing the total probability of all photon-number outcomes satisfying a prescribed fidelity threshold at one common experimental setting. Already for plain photon subtraction, this provides a more operational measure of the usable generation probability and can favor parameter configurations that differ from single-branch optima. Considering experimental constraints on available squeezing and photon-number-resolving capability, we demonstrate improvements in fidelity and success probability compared with plain photon subtraction, without necessarily increasing the required squeezing resources. Without restrictions on photon-number resolution, we find that the optimal architecture of the alternating scheme reduces to one of two single-subtraction endpoint configurations, depending on the available squeezing resources. When photon-number resolution is additionally limited, genuinely alternating branches can become advantageous. We derive analytical expressions for the conditional states, cat-state fidelities, and heralding probabilities, enabling efficient multibranch optimization and a systematic analysis of resource trade-offs, sensitivity to experimental parameter deviations, and heralding loss. Together, these results identify the architecture best suited to a given resource budget.