Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1211.0231 · Physical Review A

Strategies for enhancing quantum entanglement by local photon subtraction

Tim J. Bartley, Philip J. D. Crowley, Animesh Datta, Joshua Nunn, Lijian Zhang, Ian A. Walmsley

Published Feb 13, 2013• 67 citations
arXivHTMLPDF

Abstract

Subtracting photons from a two-mode squeezed state is a well-known method to increase entanglement. We analyze different strategies of local photon subtraction from a two-mode squeezed state in terms of entanglement gain and success probability. We develop a general framework that incorporates imperfections and losses in all stages of the process: before, during, and after subtraction. By combining all three effects into a single efficiency parameter, we provide analytical and numerical results for subtraction strategies using photon-number-resolving and threshold detectors. We compare the entanglement gain afforded by symmetric and asymmetric subtraction scenarios across the two modes. For a given amount of loss, we identify an optimized set of parameters, such as initial squeezing and subtraction beam splitter transmissivity, that maximize the entanglement gain rate. We identify regimes for which asymmetric subtraction of different Fock states on the two modes outperforms symmetric strategies. In the lossless limit, subtracting a single photon from one mode always produces the highest entanglement gain rate. In the lossy case, the optimal strategy depends strongly on the losses on each mode individually, such that there is no general optimal strategy. Rather, taking losses on each mode as the only input parameters, we can identify the optimal subtraction strategy and required beam splitter transmissivities and initial squeezing parameter. Finally, we discuss the implications of our results for the distillation of continuous-variable quantum entanglement.

DOI
10.1103/physreva.87.022313

Related papers

Directly comparing entanglement-enhancing non-Gaussian operations

Tim J. Bartley, Ian A. Walmsley

Single-photon-level non-Gaussian operations—photon addition, photon subtraction, and their coherent superposition—are powerful tools with which to increase entanglement in continuous-variable optical states. Although such operations are typically not deterministic, there may be other advantages such as noiseless manipulation. Therefore, to fully account for the efficacy of a particular non-Gaussian operation in a practical scenario, we develop figures of merit which trade off the advantages of such protocols against their success probability. Specifically, we define 'entanglement enhancement rate' as the increase in entanglement per trial of a generic non-Gaussian operation on a two-mode squeezed vacuum (TMSV) state. We consider states generated by photon-subtraction, photon-addition and a coherent superposition of subtraction and addition. We compare each strategy when applied to one or both modes of a TMSV state, and also in the presence of channel losses prior to the operation. In many cases, additional properties are analytically calculable, including excess noise arising from the operation and the fidelity of the resulting states to particular Gaussian and non-Gaussian states. Finally, by incorporating loss, we derive optimal interaction parameters for each non-Gaussian operation which maximize the effectiveness of the particular protocol under investigation.

New Journal of Physics•Feb 13, 2015•54 citations

Enhancing quantum entanglement by photon addition and subtraction

Carlos Navarrete–Benlloch, Raúl García−Patrón, Jeffrey H. Shapiro +1 more

The non-Gaussian operations effected by adding or subtracting a photon on entangled optical beams emerging from a parametric down-conversion process have been suggested to enhance entanglement. Heralded photon addition or subtraction is, as a matter of fact, at the heart of continuous-variable entanglement distillation. The use of such processes has recently been experimentally demonstrated in the context of the generation of optical coherent-state superpositions or the verification of canonical commutation relations. Here, we carry out a systematic study of the effect of local photon additions and subtractions on a two-mode squeezed vacuum state, showing that the entanglement generally increases with the number of such operations. This is analytically proven when additions or subtractions are restricted to one mode only, while we observe that the highest entanglement is achieved when these operations are equally shared between the two modes. We also note that adding photons typically provides a stronger entanglement enhancement than subtracting photons, while photon subtraction performs better in terms of energy efficiency. Furthermore, we analyze the interplay between entanglement and non-Gaussianity, showing that it is more subtle than previously expected.

arXiv:1201.4120•Physical Review A•Jul 24, 2012•171 citations

Entanglement improvement via a single-side squeezing-based quantum scissors

Cunjin Liu, Mingxia Zhan, Xiaojian Qiu +3 more

The entanglement improvement is theoretically investigated when applying a single-side quantum scissors (SSQS) with a local squeezing operation and two-asymmetrical beam splitters (BSs) to one mode of an input two-mode squeezed vacuum state (TMSV). It is found that the gain factor can be significantly enhanced with the increasing of local squeezing parameter at the expense of the success probability. The entanglement can also be further improved adjusting the local-squeezing or the transmissivity of BSs in a small initial squeezing region. In addition, our scheme is robust against the photon loss in TMSV. The improved effect becomes more obvious due to the presence of local squeezing. However, the case is not true for a more realistic SSQS. In both cases, the asymmetric BSs play a positive role for the entanglement improvement. These results suggest that the squeezing-based SSQS at single-photon level is beneficial to effectively improve the entanglement, which may have potential applications in quantum communication.

Optics Express•Apr 26, 2022•12 citations

Displacement-enhanced continuous-variable entanglement concentration

Ondřej Černotík, Jaromı́r Fiurášek

We study entanglement concentration of continuous-variable Gaussian states by local photon subtractions enhanced by coherent displacements. Instead of the previously considered symmetric two-mode squeezed vacuum states, we investigate the protocol for input states in the form of split single-mode squeezed vacuum (i.e., states obtained by mixing a single-mode squeezed vacuum with a vacuum state on a beam splitter), which is an experimentally highly relevant configuration. We analyze two scenarios in which the displacement-enhanced photon subtraction is performed either only on one or on both of the modes and show that local displacements can lead to improved performance of the concentration protocol.

arXiv:1212.0974•Physical Review A•Nov 30, 2012•13 citations

Gain of squeezing via photon subtractions

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

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.

arXiv:2502.03234•Feb 5, 2025•0 citations

Distillation of mixed-state continuous-variable entanglement by photon subtraction

Sheng Li Zhang, Peter van Loock

We present a detailed theoretical analysis for the distillation of one copy of a mixed two-mode continuous-variable entangled state using beam splitters and coherent photon-detection techniques, including conventional on-off detectors and photon-number-resolving detectors. The initial Gaussian mixed-entangled states are generated by transmitting a two-mode squeezed state through a lossy bosonic channel, corresponding to the primary source of errors in current approaches to optical quantum communication. We provide explicit formulas to calculate the entanglement in terms of logarithmic negativity before and after distillation, including losses in the channel and the photon detection, and show that one-copy distillation is still possible even for losses near the typical fiber channel attenuation length. A lower bound for the transmission coefficient of the photon-subtraction beam splitter is derived, representing the minimal value that still allows to enhance the entanglement.

arXiv:1009.4888•Physical Review A•Dec 14, 2010•86 citations
Subtracting photons from a two-mode squeezed state is a well-known method to increase entanglement. We analyze different strategies of local photon subtraction from a two-mode squeezed state in terms of entanglement gain and success probability. We develop a general framework that incorporates imperfections and losses in all stages of the process: before, during, and after subtraction. By combining all three effects into a single efficiency parameter, we provide analytical and numerical results for subtraction strategies using photon-number-resolving and threshold detectors. We compare the entanglement gain afforded by symmetric and asymmetric subtraction scenarios across the two modes. For a given amount of loss, we identify an optimized set of parameters, such as initial squeezing and subtraction beam splitter transmissivity, that maximize the entanglement gain rate. We identify regimes for which asymmetric subtraction of different Fock states on the two modes outperforms symmetric strategies. In the lossless limit, subtracting a single photon from one mode always produces the highest entanglement gain rate. In the lossy case, the optimal strategy depends strongly on the losses on each mode individually, such that there is no general optimal strategy. Rather, taking losses on each mode as the only input parameters, we can identify the optimal subtraction strategy and required beam splitter transmissivities and initial squeezing parameter. Finally, we discuss the implications of our results for the distillation of continuous-variable quantum entanglement.
Single-photon-level non-Gaussian operations—photon addition, photon subtraction, and their coherent superposition—are powerful tools with which to increase entanglement in continuous-variable optical states. Although such operations are typically not deterministic, there may be other advantages such as noiseless manipulation. Therefore, to fully account for the efficacy of a particular non-Gaussian operation in a practical scenario, we develop figures of merit which trade off the advantages of such protocols against their success probability. Specifically, we define 'entanglement enhancement rate' as the increase in entanglement per trial of a generic non-Gaussian operation on a two-mode squeezed vacuum (TMSV) state. We consider states generated by photon-subtraction, photon-addition and a coherent superposition of subtraction and addition. We compare each strategy when applied to one or both modes of a TMSV state, and also in the presence of channel losses prior to the operation. In many cases, additional properties are analytically calculable, including excess noise arising from the operation and the fidelity of the resulting states to particular Gaussian and non-Gaussian states. Finally, by incorporating loss, we derive optimal interaction parameters for each non-Gaussian operation which maximize the effectiveness of the particular protocol under investigation.
The non-Gaussian operations effected by adding or subtracting a photon on entangled optical beams emerging from a parametric down-conversion process have been suggested to enhance entanglement. Heralded photon addition or subtraction is, as a matter of fact, at the heart of continuous-variable entanglement distillation. The use of such processes has recently been experimentally demonstrated in the context of the generation of optical coherent-state superpositions or the verification of canonical commutation relations. Here, we carry out a systematic study of the effect of local photon additions and subtractions on a two-mode squeezed vacuum state, showing that the entanglement generally increases with the number of such operations. This is analytically proven when additions or subtractions are restricted to one mode only, while we observe that the highest entanglement is achieved when these operations are equally shared between the two modes. We also note that adding photons typically provides a stronger entanglement enhancement than subtracting photons, while photon subtraction performs better in terms of energy efficiency. Furthermore, we analyze the interplay between entanglement and non-Gaussianity, showing that it is more subtle than previously expected.
The entanglement improvement is theoretically investigated when applying a single-side quantum scissors (SSQS) with a local squeezing operation and two-asymmetrical beam splitters (BSs) to one mode of an input two-mode squeezed vacuum state (TMSV). It is found that the gain factor can be significantly enhanced with the increasing of local squeezing parameter at the expense of the success probability. The entanglement can also be further improved adjusting the local-squeezing or the transmissivity of BSs in a small initial squeezing region. In addition, our scheme is robust against the photon loss in TMSV. The improved effect becomes more obvious due to the presence of local squeezing. However, the case is not true for a more realistic SSQS. In both cases, the asymmetric BSs play a positive role for the entanglement improvement. These results suggest that the squeezing-based SSQS at single-photon level is beneficial to effectively improve the entanglement, which may have potential applications in quantum communication.
We study entanglement concentration of continuous-variable Gaussian states by local photon subtractions enhanced by coherent displacements. Instead of the previously considered symmetric two-mode squeezed vacuum states, we investigate the protocol for input states in the form of split single-mode squeezed vacuum (i.e., states obtained by mixing a single-mode squeezed vacuum with a vacuum state on a beam splitter), which is an experimentally highly relevant configuration. We analyze two scenarios in which the displacement-enhanced photon subtraction is performed either only on one or on both of the modes and show that local displacements can lead to improved performance of the concentration protocol.
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 present a detailed theoretical analysis for the distillation of one copy of a mixed two-mode continuous-variable entangled state using beam splitters and coherent photon-detection techniques, including conventional on-off detectors and photon-number-resolving detectors. The initial Gaussian mixed-entangled states are generated by transmitting a two-mode squeezed state through a lossy bosonic channel, corresponding to the primary source of errors in current approaches to optical quantum communication. We provide explicit formulas to calculate the entanglement in terms of logarithmic negativity before and after distillation, including losses in the channel and the photon detection, and show that one-copy distillation is still possible even for losses near the typical fiber channel attenuation length. A lower bound for the transmission coefficient of the photon-subtraction beam splitter is derived, representing the minimal value that still allows to enhance the entanglement.