Nonclassical properties of photon-added two-mode squeezed thermal states and their decoherence in the thermal channel

Meng, Xiang‐Guo; Wang, Zhen; Fan, Heng; Wang, Ji‐Suo; Yang, Zhenshan

doi:10.1364/josab.29.001844

Cited by 38 publications

(17 citation statements)

References 65 publications

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“…Generally, for a single-mode quantum state , its Wigner distribution reads W( ) = tr[ Δ( )], [37,38] where Δ( ) is the coherent representation of single-mode Wigner operator. Hence, using the the normal ordering of the density operator c and the integral formula in Equation (C3), the Wigner distribution of the state ( a + ra † ) m |z⟩ can be calculated as (see Appendix C)…”

Section: Negativity Of Wigner Distributionmentioning

confidence: 99%

“…Generally, for a single‐mode quantum state ρ, its Wigner distribution reads

W (α) =

[ρ Δ (α)]

, [ 37,38 ] where

Δ (α)

is the coherent representation of single‐mode Wigner operator. Hence, using the the normal ordering of the density operator

ρ_{c}

and the integral formula in Equation (C3), the Wigner distribution of the state

{(υ a + r a^{†})}^{m} false| z false⟩

can be calculated as (see Appendix C)

w_{c} false(α false) = w_{c}^{m} false(α false) w_{c, 0} false(α false)

where

w_{c, 0} false(α false) = π^{- 1} e^{{- 2 false| α - z false|}^{2}}

is exactly the Wigner distribution of the coherent state

| z ⟩

, and the part

w_{c}^{m} false(α false) = \frac{{(υ r)}^{m}}{2^{m} {scriptD}_{m}} {scriptF}_{m, m} (ϰ, ϰ^{*}; - \frac{2 r}{υ})

comes from the contribution of the coherent superposition

{false(υ a + r a^{†} false)}^{m}

, where we have set

ϰ =

\sqrt{2 / (υ r)} false(υ<...>

…”

Section: Negativity Of Wigner Distributionmentioning

confidence: 99%

See 1 more Smart Citation

Nonclassicality via the Superpositions of Photon Addition and Subtraction and Quantum Decoherence for Thermal Noise

et al. 2020

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Two new photon-modulated states are introduced by operating a more general coherent superposition (a + ra †) m on two classical states (coherent and thermal) and their nonclassicality caused by the operation (a + ra †) m is investigated via examining the squeezing, sub-Poissonian statistics, nonclassical depth, and negativity of Wigner distribution. Their density-operator and Wigner-distribution evolutions in the thermal channel are also explored. It is found that the high-order operation (a + ra †) m has better performance in creating nonclassicality for certain ratios r and more robustness against decoherence of the two photon-modulated states for thermal noise. For convenience, a new three-variable special polynomial and its generating function are introduced via the normal ordering of operators.

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Section: Negativity Of Wigner Distributionmentioning

confidence: 99%

“…Generally, for a single‐mode quantum state ρ, its Wigner distribution reads

W (α) =

[ρ Δ (α)]

, [ 37,38 ] where

Δ (α)

is the coherent representation of single‐mode Wigner operator. Hence, using the the normal ordering of the density operator

ρ_{c}

and the integral formula in Equation (C3), the Wigner distribution of the state

{(υ a + r a^{†})}^{m} false| z false⟩

can be calculated as (see Appendix C)

w_{c} false(α false) = w_{c}^{m} false(α false) w_{c, 0} false(α false)

where

w_{c, 0} false(α false) = π^{- 1} e^{{- 2 false| α - z false|}^{2}}

is exactly the Wigner distribution of the coherent state

| z ⟩

, and the part

w_{c}^{m} false(α false) = \frac{{(υ r)}^{m}}{2^{m} {scriptD}_{m}} {scriptF}_{m, m} (ϰ, ϰ^{*}; - \frac{2 r}{υ})

comes from the contribution of the coherent superposition

{false(υ a + r a^{†} false)}^{m}

, where we have set

ϰ =

\sqrt{2 / (υ r)} false(υ<...>

…”

Section: Negativity Of Wigner Distributionmentioning

confidence: 99%

Nonclassicality via the Superpositions of Photon Addition and Subtraction and Quantum Decoherence for Thermal Noise

et al. 2020

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“…Noting that the average value of a more general operator

a^{† m} a^{k} b^{† n} b^{l}

in the state ρ is obtained as (see Appendix A)

\begin{matrix} true \\ right {scriptN}_{m, n; k, l}^{a} & = & left tr false(ρ a^{† m} a^{k} b^{† n} b^{l} false) \\ = & left \sum_{i = 0}^{\min false(m, k false)} \frac{m! k! (l + m - i)! g_{3}^{m + k - 2 i} δ_{n + k, m + l}}{i! (m - i)! (k - i)! {false(- 1 false)}^{k + l} g_{2}^{k - l} g_{1}^{m + l - i}} \end{matrix}

where

δ_{n + k, m + l}

is the Kronecker δ function whose off‐antidiagonal elements are zero. Further, letting

m = k

and

n = l

, and using the newly derived alternative expression of the Jacobi polynomials

P_{m}^{(0, n - m)} false(\cdot false)

, [ 59 ] that is,

P_{m}^{(0, n - m)} false(x false) = \sum_{i = 0}^{m} \frac{m! (n + m - i)!}{n! i! {[false(m - i false)!]}^{2}}

…”

Section: Adding or Subtracting Photons On A Tstsmentioning

confidence: 99%

Continuous‐Variable Entanglement and Wigner‐Function Negativity via Adding or Subtracting Photons

Meng

Wang

et al. 2020

Annalen der Physik

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The performance of adding or subtracting photons on two-mode squeezed thermal states via examining the Einstein-Podolsky-Rosen (EPR) correlation, the Hillery-Zubairy (HZ) correlation, the fidelity of teleportation, and the negativity of Wigner function is theoretically investigated. The normalization factors and the teleportation fidelity are related to Jacobi polynomials, and the (evolved) Wigner functions are simply associated with two-variable Hermite polynomials. Compared with the original squeezed thermal states, the EPR correlation and the teleportation fidelity can be enhanced by photon subtraction and basically weakened by photon addition symmetric operations, but they cannot be enhanced for both photon addition and subtraction asymmetric cases. Also, HZ correlation can provide a better option relative to the EPR correlation in detecting the entanglement, and the fidelity for teleporting a squeezed state with a large squeezing can also be enhanced via photon addition symmetric operations, in contrast to teleporting a coherent state. Additionally, the nonclassicality is discussed in terms of the negativity of the (evolved) Wigner functions, which shows that photon addition and subtraction and the squeezing cannot restrain the deteriorate of nonclassicality, and the evolved Wigner functions become Gaussian (corresponding to vacuum) with long decay times as a result of amplitude decay.

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“…Knowing the normal ordering form of the density operator, we can easily calculate the Wigner function of the twomode squeezed thermal state. For a two-mode quantum state ρ, the Wigner function in the coherent state representation is given by the following equation [28] W (α,…”

Section: Wigner Function Of Tmstsmentioning

confidence: 99%

Quantum metrology with two-mode squeezed thermal state: Parity detection and phase sensitivity

Yuan

et al. 2016

Chinese Phys. B

Self Cite

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Based on the Wigner-function method, we investigate the parity detection and phase sensitivity in a Mach-Zehnder interferometer (MZI) with two-mode squeezed thermal state (TMSTS). Using the classical transformation relation of the MZI, we derive the input-output Wigner functions and then obtain the explicit expressions of parity and phase sensitivity. The results from the numerical calculation show that supersensitivity can be reached only if the input TMSTS have a large number photons.

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Nonclassical properties of photon-added two-mode squeezed thermal states and their decoherence in the thermal channel

Cited by 38 publications

References 65 publications

Nonclassicality via the Superpositions of Photon Addition and Subtraction and Quantum Decoherence for Thermal Noise

Nonclassicality via the Superpositions of Photon Addition and Subtraction and Quantum Decoherence for Thermal Noise

Continuous‐Variable Entanglement and Wigner‐Function Negativity via Adding or Subtracting Photons

Quantum metrology with two-mode squeezed thermal state: Parity detection and phase sensitivity

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