The Replica Method and Entropy for a Mixture of Two-Mode Even and Odd Schrödinger Cat States

Dudinets, Ivan V.; Man’ko, Vladimir I.

doi:10.1007/s10946-015-9497-9

Cited by 5 publications

(2 citation statements)

References 25 publications

(53 reference statements)

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“…This entropy can be calculated using the replica method [11], which relies on the fact that S(ρ) = − ∂ ∂n Tr[ρ n ] n=1 . The structure of the state (20), an addition of terms of the form | ± ζ ±ζ|, is maintained when you calculateρ n , with the coefficients being determined in a recursive way [12]. In this way, we get the eigenvalues of the density operator (20),…”

Section: Time-evolution Of An Admixture Of Pure and Mixed Statesmentioning

confidence: 99%

A note on the time evolution of a density operator interpolating between pure and mixed states

Figueiredo

Malbouisson

2020

Eur. Phys. J. B

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In a recent paper [C.J.S. Ferreira, T.M. Silva, B. Baseia, Eur. Phys. J. B 92, 257 ( 2019)], the authors discuss the time evolution of statistical properties of a density operator that interpolates between pure and mixed states, assuming that the time evolution of the system is carried out by a specific time dependence of the coefficients that weight the admixing of the states. Here, we show that this assumption does not correspond exactly to any physical time evolution of the initial state of the system, being only a specific approximation. We present the exact evolution of the system in contact with a dissipative reservoir at zero temperature and discuss the time evolution of interpolations of pure and mixed states.

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Section: Time-evolution Of An Admixture Of Pure and Mixed Statesmentioning

confidence: 99%

A note on the time evolution of a density operator interpolating between pure and mixed states

Figueiredo

Malbouisson

2020

Eur. Phys. J. B

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“…While the relative entropy is closely connected to the von Neumann entropy, the relative Tsallis entropy is related to the Tsallis entropy. The observation based on the fact that the Tsallis entropy becomes the von Neumann entropy has led to the so-called replica method for calculating the von Neumann entropy [39,40]. The relative Tsallis entropy for the states Φ α (ρ) and Φ β (ρ) reads…”

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confidence: 99%

Characterization of the nonlinear qubit map using the probability parametrization

Dudinets¹,

Man’ko²

2018

EPL

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Quantum capacity of a bosonic dephasing channel

2020

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We study the LOCC-assisted quantum capacity of bosonic dephasing channel with energy constraint on input states. We start our analysis by focusing on the energy-constrained squashed entanglement of the channel, which is an upper bound for the energy-constrained LOCC-assisted quantum capacity. As computing energy-constrained squashed entanglement of the channel is challenging due to a double optimization (over the set of density matrices and over the isometric extensions of a squashing channel), we first derive an upper bound for it, and then we discuss how tight that bound is for energy-constrained LOCC-assisted quantum capacity of bosonic dephasing channel. We prove that the optimal input state is diagonal in the Fock basis. Furthermore, we prove that the optimal squashing channel in the set of weakly-degradable and anti-degradable channels is a weakly-self-complementary channel. Restricting the search for optimal squashing channel to the set of weakly-self-complementary one-mode Gaussian quantum channels, we derive explicit upper and lower bounds for the energy-constrained LOCC-assisted quantum capacity of the bosonic dephasing channel in terms of its quantum capacity with different noise parameters. Thanks to the tightness of these bounds we provide a very good estimation of the LOCC-assisted quantum capacity of bosonic dephasing channel. We also study weakly-self-complementary qubit squashing channels which gives tighter upper bound to the energy-constrained LOCC-assisted quantum capacity of bosonic dephasing channel.

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The Replica Method and Entropy for a Mixture of Two-Mode Even and Odd Schrödinger Cat States

Cited by 5 publications

References 25 publications

A note on the time evolution of a density operator interpolating between pure and mixed states

A note on the time evolution of a density operator interpolating between pure and mixed states

Characterization of the nonlinear qubit map using the probability parametrization

Quantum capacity of a bosonic dephasing channel

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