scholarly journals Subsystem complexity after a local quantum quench

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Giuseppe Di Giulio ◽  
Erik Tonni
Keyword(s):  
Fisher Information ◽  
Temporal Evolution ◽  
Entanglement Entropy ◽  
Circuit Complexity ◽  
Information Geometry ◽  
Covariance Matrices ◽  
Qualitative Behaviour ◽  
Initial State ◽  
Local Quantum ◽  
Logarithmic Growth

Abstract We study the temporal evolution of the circuit complexity after the local quench where two harmonic chains are suddenly joined, choosing the initial state as the reference state. We discuss numerical results for the complexity for the entire chain and the subsystem complexity for a block of consecutive sites, obtained by exploiting the Fisher information geometry of the covariance matrices. The qualitative behaviour of the temporal evolutions of the subsystem complexity depends on whether the joining point is inside the subsystem. The revivals and a logarithmic growth observed during these temporal evolutions are discussed. When the joining point is outside the subsystem, the temporal evolutions of the subsystem complexity and of the corresponding entanglement entropy are qualitatively similar.

scholarly journals Complexity of mixed Gaussian states from Fisher information geometry

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Giuseppe Di Giulio ◽  
Erik Tonni
Keyword(s):  
Fisher Information ◽  
Circuit Complexity ◽  
Information Geometry ◽  
Covariance Matrices ◽  
Mixed States ◽  
Gaussian States ◽  
Infinite Line ◽  
Reduced Density ◽  
Special Case ◽  
Thermal States

Abstract We study the circuit complexity for mixed bosonic Gaussian states in harmonic lattices in any number of dimensions. By employing the Fisher information geometry for the covariance matrices, we consider the optimal circuit connecting two states with vanishing first moments, whose length is identified with the complexity to create a target state from a reference state through the optimal circuit. Explicit proposals to quantify the spectrum complexity and the basis complexity are discussed. The purification of the mixed states is also analysed. In the special case of harmonic chains on the circle or on the infinite line, we report numerical results for thermal states and reduced density matrices.

scholarly journals Entropic Entanglement: Information Prison Break

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Alexander Y. Yosifov ◽  
Lachezar G. Filipov
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Entanglement Entropy ◽  
Black Hole Thermodynamics ◽  
Spherically Symmetric ◽  
Quantum Field ◽  
Unitary Evolution ◽  
Local Quantum ◽  
Symmetric Black Hole ◽  
Matter Fields

We argue that certain nonviolent local quantum field theory (LQFT) modification considered at the global horizon (r=2M) of a static spherically symmetric black hole can lead to adiabatic leakage of quantum information in the form of Hawking particles. The source of the modification is (i) smooth at r=2M and (ii) rapidly vanishing at r≫2M. Furthermore, we restore the unitary evolution by introducing extra quanta which departs slightly from the generic Hawking emission without changing the experience of an infalling observer (no drama). Also, we suggest that a possible interpretation of the Bekenstein-Hawking bound as entanglement entropy may yield a nonsingular dynamical horizon behavior described by black hole thermodynamics. Hence, by treating gravity as a field theory and considering its coupling to the matter fields in the Minkowski vacuum, we derive the conjectured fluctuations of the background geometry of a black hole.

Fisher information of accelerated two-qubit systems

2018 ◽  
Vol 32 (05) ◽  
pp. 1850050 ◽  
Author(s):  
N. Metwally
Keyword(s):  
Analytical Solution ◽  
Fisher Information ◽  
General State ◽  
Initial State ◽  
Werner State ◽  
Pure States ◽  
X State ◽  
Different Parts ◽  
Degree Of Entanglement

In this paper, Fisher information for an accelerated system initially prepared in the X-state is discussed. An analytical solution, which consists of three parts: classical, the average over all pure states and a mixture of pure states, is derived for the general state and for Werner state. It is shown that the Unruh acceleration has a depleting effect on the Fisher information. This depletion depends on the degree of entanglement of the initial state settings. For the X-state, for some intervals of Unruh acceleration, the Fisher information remains constant, irrespective to the Unruh acceleration. In general, the possibility of estimating the state’s parameters decreases as the acceleration increases. However, the precision of estimation can be maximized for certain values of the Unruh acceleration. We also investigate the contribution of the different parts of the Fisher information on the dynamics of the total Fisher information.

scholarly journals Island for gravitationally prepared state and pseudo entanglement wedge

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Masamichi Miyaji
Keyword(s):  
Transition Matrix ◽  
Degrees Of Freedom ◽  
Entanglement Entropy ◽  
Initial Boundary ◽  
Necessary Condition ◽  
Initial State ◽  
Boundary Area ◽  
Generalized Entropy ◽  
Fine Grained ◽  
Boundary State

Abstract We consider spacetime initiated by a finite-sized initial boundary as a generalization of the Hartle-Hawking no-boundary state. We study entanglement entropy of matter state prepared by such spacetime. We find that the entanglement entropy for large subregion is given either by the initial state entanglement or the entanglement island, preventing the entropy to grow arbitrarily large. Consequently, the entanglement entropy is always bounded from above by the boundary area of the island, leading to an entropy bound in terms of the island. The island I is located in the analytically continued spacetime, either at the bra or the ket part of the spacetime in Schwinger-Keldysh formalism. The entanglement entropy is given by an average of complex pseudo generalized entropy for each entanglement island. We find a necessary condition of the initial state to be consistent with the strong sub-additivity, which requires that any probe degrees of freedom are thermally entangled with the rest of the system. We then find a large parameter region where the spacetime with finite-sized initial boundary, which does not have the factorization puzzle at leading order, dominates over the Hartle-Hawking no-boundary state or the bra-ket wormhole. Due to the absence of a moment of time reflection symmetry, the island in our setup is a generalization of the entanglement wedge, called pseudo entanglement wedge. In pseudo entanglement wedge reconstruction, we consider reconstructing the bulk matter transition matrix on A ∪ I, from a fine-grained state on A. The bulk transition matrix is given by a thermofield double state with a projection by the initial state. We also provide an AdS/BCFT model by considering EOW branes with corners. We also find the exponential hardness of such reconstruction task using a generalization of Python’s lunch conjecture to pseudo generalized entropy.

scholarly journals Bidirectional teleportation using Fisher information

2020 ◽  
Vol 35 (33) ◽  
pp. 2050272
Author(s):  
C. Seida ◽  
A. El Allati ◽  
N. Metwally ◽  
Y. Hassouni
Keyword(s):  
Fisher Information ◽  
Uncertainty Principle ◽  
Quantum Fisher Information ◽  
Single Parameter ◽  
Numerical Calculations ◽  
Initial State ◽  
Better Than

In this contribution, we reformulated the bidirectional teleportation protocol suggested in Ref. 7, by means of Bloch vectors as well as the local operations are represented by using Pauli operators. Analytical and numerical calculations for the teleported state and Fisher information are introduced. It is shown that both quantities depend on the initial state settings of the teleported qubits and their triggers. The Fidelities and the Fisher information of the bidirectionally teleported states are maximized when the qubit and its trigger are polarized in the same direction. The minimum values are predicted if both initial qubits have different polarization or nonzero phase. The maximum values of the Fidelity and the quantum Fisher information are the same, but they are predicted at different polarization angles. We display that the multi-parameter form is much better than the single parameter form, where it satisfies the bounds of classical, entangled systems and the uncertainty principle.

scholarly journals Circuit Complexity from Cosmological Islands

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1301
Author(s):  
Sayantan Choudhury ◽  
Satyaki Chowdhury ◽  
Nitin Gupta ◽  
Anurag Mishara ◽  
Sachin Panneer Selvam ◽  
...  
Keyword(s):  
Black Hole ◽  
Parameter Space ◽  
Entanglement Entropy ◽  
Cosmological Solution ◽  
Circuit Complexity ◽  
Space Time ◽  
De Sitter ◽  
Squeezed State ◽  
Black Hole Information ◽  
Made In

Recently, in various theoretical works, path-breaking progress has been made in recovering the well-known page curve of an evaporating black hole with quantum extremal islands, proposed to solve the long-standing black hole information loss problem related to the unitarity issue. Motivated by this concept, in this paper, we study cosmological circuit complexity in the presence (or absence) of quantum extremal islands in negative (or positive) cosmological constant with radiation in the background of Friedmann-Lemai^tre-Robertson-Walker (FLRW) space-time, i.e., the presence and absence of islands in anti de Sitter and the de Sitter space-time having SO(2, 3) and SO(1, 4) isometries, respectively. Without using any explicit details of any gravity model, we study the behavior of the circuit complexity function with respect to the dynamical cosmological solution for the scale factors for the above mentioned two situations in FLRW space-time using squeezed state formalism. By studying the cosmological circuit complexity, out-of-time ordered correlators, and entanglement entropy of the modes of the squeezed state, in different parameter space, we conclude the non-universality of these measures. Their remarkably different features in the different parameter space suggests their dependence on the parameters of the model under consideration.

Sign in / Sign up

Export Citation Format

Share Document