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Scientific Reports

Entangled states shaping with CV states of definite parity

Dmitry Kuts, Sergey A. Podoshvedov

Published Jan 28, 2022• 6 citations
Publisher

Abstract

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.

DOI
10.1038/s41598-022-05336-2

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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.
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 propose a new approach to generate entangled states, both hybrid and consisting exclusively of continuous variable (CV) states. A single-mode squeezed vacuum is mixed with a delocalized single photon on an arbitrary beam splitter with subsequent registration of measurement outcomes in auxiliary mode. The entangled hybrid states consisting of CV and discrete variable (DV) states are generated whenever any event is measured in auxiliary mode. Negativity is used as a measure of entanglement. Under certain initial conditions, the conditional state becomes as entangled as possible. New types of CV states, either even or odd depending on the parity of the Fock states forming the superpositions, are introduced. If the conditional entangled hybrid state is mixed with a single-mode squeezed vacuum with the subsequent registration of measurement results in DV mode, then the new state becomes CV entangled, i.e., its orthogonal components are already CV states. The entanglement synthesis can be expanded to implement a high-complexity quantum network.
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.
We propose a new approach to the generation of entangled states, both hybrid and consisting exclusively of continuous variable (CV) states. A single mode squeezed vacuum is mixed with a delocalized single photon on arbitrary beam splitter (BS) with subsequent registration of some measurement outcome in auxiliary mode. The entangled states are generated whenever any event is measured in auxiliary mode. Negativity is used as a measure of entanglement. Under certain initial set conditions, the conditioned state becomes as entangled as possible. New types of CV states are introduced. This approach can be expanded to implement a high complexity quantum network.
Abstract We explore a scheme based on adding a nonlocal photon and subtracting some number of photons to entangle an initial single-mode squeezed vacuum (SMSV) state with a photonic state. In a realistic model of interaction of the SMSV state with the photonic state on a beam splitter (BS) with changeable transmissivity and reflectivity the hybrid entanglement is realized for any values of the squeezing of input SMSV state. The maximum hybrid entanglement is achieved at certain values of the squeezing and BS parameter, which can mean implementation of a two-qubit controlled − Z CZ − operation using the BS with appropriate initialization of the input states. The success probability of the gate, taking into account multiphoton outcomes in the measuring mode of the BS, is more than 0.3 . We also propose to use new continuous variable (CV) states of definite parity, which could increase the success probability of generating the maximum hybrid entanglement. We show sufficient robustness of the generated entanglement under photon number resolving detection with practical quantum efficiency.