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Bulletin of the South Ural State University series Mathematics Mechanics Physics

PROMISING QUANTUM ENGINEERING OF OPTICAL EVEN/ODD SCHRÖDINGER CAT STATES

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

Published Jan 1, 2022• 1 citation
Publisher

Abstract

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.

DOI
10.14529/mmph220108

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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.
Abstract We introduce a family of new continuous variable (CV) states of definite parity originating from even single-mode squeezed vacuum (SMSV) state by subtracting an arbitrary number of photons from it. A beam splitter (BS) with arbitrary transmittance and reflectance parameters serves as a hub for redirecting input photons in an indistinguishable manner to the output and measuring modes followed by probabilistic measurement, thereby converting the initial SMSV photon distribution into new one after we know the number of registered photons in auхilliary mode. Depending on the parity of the subtracted photons, the family of the generated states is divided into two subfamilies, that is, into even and odd according to the parity of the Fock state subtracted. The family of the CV states is determined solely by one SMSV parameter, which inevitably decreases during their implementation. The algorithm of the quantum engineering can generate macroscopic CV states with a larger average number of photons (say, 4000 and even more) and quantum Fisher information of observable measuring the number of photons many times more (say, from tens of times for small practical values of the squeezing ratio to ≈4 for extremely high squeezing amplitude) than one of the original SMSV. The potential of the new family of the CV states of a certain parity, to which original SMSV, no doubt, belongs, can become decisive for a new push to implementation of optical quantum metrology protocols.
We present a new method to entangle continuous variable (CV) states of certain parity and photonic states for the purpose of generating optical hybrid cluster (HC) states. To do it we introduce two families of the CV states of definite parity which stems from single mode squeezed vacuum (SMSV) state. Potential to apply the CV states of certain parity is high. We report on the generation of the even/odd Schrödinger cat state like (SCS-like) states whose fidelities with even/odd SCS of amplitude of [Formula: see text] are more of [Formula: see text], when 30,31 photons are detected in auxiliary mode of input SMSV state initially mixed with single photon. We show that the quantum efficiency of a photon number resolving (PNR) detector is crucial to maintaining the success rate of even/odd SCSs generator at an acceptable level. The scheme with delocalized photon implements deterministic imperfect entanglement operation between macro and micro states. We show that the beam splitter implements the two-qubits operation [Formula: see text] (CZ) for input CV states of definite parity and photonic states, provided that certain result is detected in measurement mode. An extension of the entangling operation for two entangled delocalized photons (TEDP) allows one to realize three-qubit HC state. Seven-qubit HC state is the result of conjunction of two three-qubit HC states through TEDP state.
Abstract We introduce a new family of continuous variable (CV) states of definite parity originating from the single mode squeezed vacuum (SMSV) state by subtracting an arbitrary number of photons from it. A beam splitter with arbitrary transmittance and reflectance parameters redirects input photons in an indistinguishable manner to the output and measuring modes followed by probabilistic measurement, thereby converting the initial SMSV photon distribution into a new one after we know the number of registered photons. The family of the measurement-induced CV states is solely determined by the SMSV parameter which inevitably decreases when generating the CV states. We show that the quantum state engineering of CV states of definite parity by subtraction of multiphoton state from input SMSV state can significantly enhance their nonclassical properties (more squeezing, larger value of quantum Fisher information) compared to the initial state from which they originate, which, combined with a significant gain in brightness, makes them attractive for ultra-precise measurements. The potential of the new family of CV states of a certain parity, to which original SMSV, no doubt, belongs, can become decisive for a new push to implementation of optical quantum metrology protocols.
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 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 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.