No-Cloning Theorem in Thermofield Dynamics

Prudencio, Thiago

doi:10.1142/s021974991230001x

Cited by 6 publications

(11 citation statements)

References 50 publications

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“…Recently a holographic recipe has been proposed [5,6] to compute complexity for thermofield double states in strongly coupled quantum field theories. (For related work, including a few lecture notes, see [7]- [59].) The proposal of [5,6], which we refer to as Complexity-Action (CA) proposal, makes use of the holographic representation of the thermofield double state in a strongly coupled quantum field theory in terms of the eternal 1 We will consider the case of two-gates, but one can easily generalize the discussion to the k-gates.…”

Section: Introductionmentioning

confidence: 99%

On complexity of holographic flavors

Abad

Kulaxizi

Parnachev

2018

J. High Energ. Phys.

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Quantum complexity of a thermofield double state in a strongly coupled quantum field theory has been argued to be holographically related to the action evaluated on the Wheeler-DeWitt patch. The growth rate of quantum complexity in systems dual to Einstein-Hilbert gravity saturates a bound which follows from the Heisenberg uncertainty principle. We consider corrections to the growth rate in models with flavor degrees of freedom. They are realized by adding a small number of flavor branes to the system. Holographically, such corrections come from the DBI action of the flavor branes evaluated on the Wheeler-DeWitt patch. We relate corrections to the growth of quantum complexity to corrections to the mass of the system, and observe that the bound on the growth rate is never violated.

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Section: Introductionmentioning

confidence: 99%

On complexity of holographic flavors

Abad

Kulaxizi

Parnachev

2018

J. High Energ. Phys.

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“…In this new analysis we will use the procedure of Thermofield Dynamics [20], in particular the thermal Wigner functions for the Bell-Cat states will be considered along with their negativity properties. The Termofield Dynamics formalism was developed by Umezawa and Takahasi [21,22] and it is a suitable way to introduce temperature in quantum states [23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Negativity of the Wigner function and thermal effects of Bell-Cat states

Lula-Rocha¹,

Floquet²,

Trindade³

et al. 2020

Preprint

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We applied the Thermofield Dynamics formalism to analyze how the non-classical properties of the Bell-Cat states are influenced by a gradual change of temperature values, in a thermal equilibrium system. To this purpose we calculate the thermal Wigner functions for these states, whose negative volume is associated with non-classical properties, and we evaluate how these non-classical features vary with temperature. Our results indicate that these properties are almost absent for temperatures of around 2K.

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“…In quantum information protocols, in particular QT, TFD has the possibility of dealing with non-locality and entanglement at finite temperature scenario making use of the algebraic structure of such thermofield states. This route for the investigation of non-locality in thermal environments brings new features relating quantum information protocols in a thermofield scenario and have been explored in some recent proposes associated to maximally entangled states 78,79,80 , no-cloning theorem 81 , quantum gates 82 . Thermofield states are also used for description of eternal anti-de Sitter (AdS) black holes 83,84 with association to quantum complexity 85 and can also be associated to Gaussian states 86 .…”

Section: Introductionmentioning

confidence: 99%

“…We also discuss the TFD formulations involving the Mandel parameter and Gibbs like operators under the action of gate operations. No-cloning theorem for thermofields 81 and the problem of non-broadcasting 88 in temperature dependent situations are investigated, where the connection among different thermofield states at different temperatures and how such a method can be used in the domain of metastable and non-equilibrium states are also discussed.…”

Section: Introductionmentioning

confidence: 99%

Thermofield qubits, generalized expectations and quantum information protocols

Prudencio,

Filho,

Santana

2014

Preprint

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Thermofield dynamics (TFD) approach is a real time quantum field method for dealing with finite temperature quantum states in a purified version of usual density operator formalism at finite temperature. In the domain of quantum information, TFD represents a quite promising direction for dealing with qubits under thermal influence and can also be associated to Gaussian states. Here, we propose a generalized TFD mean expectation for the case of thermofield qubits considering the action of gate operators. We propose quantum teleportation protocols involving thermofield states, considering thermal-to-thermal and thermal-to-non-thermal transfering cases. In particular, we discuss the case in which Alice and Bob are at different temperatures. Action of gate operators on the result of the Mandel parameter for thermofields and on Gibbs-like density operators are also discussed. The nocloning and non-broadcasting theorems in TFD are also considered and cases

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No-Cloning Theorem in Thermofield Dynamics

Cited by 6 publications

References 50 publications

On complexity of holographic flavors

On complexity of holographic flavors

Negativity of the Wigner function and thermal effects of Bell-Cat states

Thermofield qubits, generalized expectations and quantum information protocols

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