scholarly journals Hydrodynamics of quantum entropies in Ising chains with linear dissipation

2022 ◽  
Author(s):  
Vincenzo Alba ◽  
Federico Carollo
Keyword(s):  
Mutual Information ◽  
Hydrodynamic Limit ◽  
Transverse Field ◽  
Quantum Correlations ◽  
Von Neumann Entropy ◽  
Simple Description ◽  
Von Neumann ◽  
Long Time ◽  
Dynamics Of Correlations ◽  
Quasiparticle Picture

Abstract We study the dynamics of quantum information and of quantum correlations after a quantum quench, in transverse field Ising chains subject to generic linear dissipation. As we show, in the hydrodynamic limit of long times, large system sizes, and weak dissipation, entropy-related quantities —such as the von Neumann entropy, the Rényi entropies, and the associated mutual information— admit a simple description within the so-called quasiparticle picture. Specifically, we analytically derive a hydrodynamic formula, recently conjectured for generic noninteracting systems, which allows us to demonstrate a universal feature of the dynamics of correlations in such dissipative noninteracting system. For any possible dissipation, the mutual information grows up to a time scale that is proportional to the inverse dissipation rate, and then decreases, always vanishing in the long time limit. In passing, we provide analytic formulas describing the time-dependence of arbitrary functions of the fermionic covariance matrix, in the hydrodynamic limit.

scholarly journals Computable Rényi mutual information: Area laws and correlations

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 541
Author(s):  
Samuel O. Scalet ◽  
Álvaro M. Alhambra ◽  
Georgios Styliaris ◽  
J. Ignacio Cirac
Keyword(s):  
Mutual Information ◽  
Correlation Functions ◽  
Quantum Correlations ◽  
Matrix Product ◽  
Many Body ◽  
Von Neumann ◽  
Tensor Network ◽  
Network States ◽  
Tensor Network States ◽  
Area Law

The mutual information is a measure of classical and quantum correlations of great interest in quantum information. It is also relevant in quantum many-body physics, by virtue of satisfying an area law for thermal states and bounding all correlation functions. However, calculating it exactly or approximately is often challenging in practice. Here, we consider alternative definitions based on Rényi divergences. Their main advantage over their von Neumann counterpart is that they can be expressed as a variational problem whose cost function can be efficiently evaluated for families of states like matrix product operators while preserving all desirable properties of a measure of correlations. In particular, we show that they obey a thermal area law in great generality, and that they upper bound all correlation functions. We also investigate their behavior on certain tensor network states and on classical thermal distributions.

scholarly journals A field theory study of entanglement wedge cross section: odd entropy

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Ali Mollabashi ◽  
Kotaro Tamaoka
Keyword(s):  
Cross Section ◽  
Entanglement Entropy ◽  
Quantum Correlations ◽  
Von Neumann Entropy ◽  
Mixed States ◽  
Scale Invariant ◽  
Gaussian States ◽  
Von Neumann ◽  
Free Scalar ◽  
The Difference

Abstract We study odd entanglement entropy (odd entropy in short), a candidate of measure for mixed states holographically dual to the entanglement wedge cross section, in two-dimensional free scalar field theories. Our study is restricted to Gaussian states of scale-invariant theories as well as their finite temperature generalizations, for which we show that odd entropy is a well-defined measure for mixed states. Motivated from holographic results, the difference between odd and von Neumann entropy is also studied. In particular, we show that large amounts of quantum correlations ensure the odd entropy to be larger than von Neumann entropy, which is qualitatively consistent with the holographic CFT. In general cases, we also find that this difference is not even a monotonic function with respect to size of (and distance between) subsystems.

scholarly journals Mutual Information and Bose-Einstein Condensation

2013 ◽  
Vol 20 (02) ◽  
pp. 1350008 ◽  
Author(s):  
C. N. Gagatsos ◽  
A. I. Karanikas ◽  
G. Kordas
Keyword(s):  
Mutual Information ◽  
Canonical Ensemble ◽  
Von Neumann Entropy ◽  
Einstein Condensation ◽  
Von Neumann ◽  
Bose Einstein Condensation ◽  
Thermal Entropy ◽  
Spatial Partition ◽  
Bose Einstein ◽  
Grand Canonical

In this work we study an ideal bosonic quantum field system at finite temperature, and in a canonical and a grand canonical ensemble. For a simple spatial partition we derive the corresponding mutual information, a quantity that measures the total amount of information of one of the parts about the other. In order to find it, we first derive the von Neumann entropy that corresponds to the spatially separated subsystem (i.e. the geometric entropy) and then we subtract its extensive part which coincides with the thermal entropy of the subsystem. In the framework of the grand canonical description, we examine the influence of the underlying Bose-Einstein condensation on the behaviour of the mutual information, and we find that its derivative with respect to the temperature possesses a finite discontinuity at exactly the critical temperature.

Classical capacity of a noiseless quantum channel assisted by noisy entanglement

2001 ◽  
Vol 1 (3) ◽  
pp. 70-78
Author(s):  
M Horodecki ◽  
P Horodecki ◽  
R l Horodecki ◽  
D Leung ◽  
B Terha
Keyword(s):  
Mutual Information ◽  
General Formula ◽  
Quantum Channel ◽  
Classical Case ◽  
Von Neumann Entropy ◽  
Entangled States ◽  
Von Neumann ◽  
Classical Capacity ◽  
Quantum Mutual Information

We derive the general formula for the capacity of a noiseless quantum channel assisted by an arbitrary amount of noisy entanglement. In this capacity formula, the ratio of the quantum mutual information and the von Neumann entropy of the sender's share of the noisy entanglement plays the role of mutual information in the completely classical case. A consequence of our results is that bound entangled states cannot increase the capacity of a noiseless quantum channel.

Quantum interferometric power and the role of nonclassical correlations in quantum metrology for a special class of two-qubit states

2017 ◽  
Vol 31 (08) ◽  
pp. 1750052 ◽  
Author(s):  
H. El Hadfi ◽  
Y. Ait Taleb ◽  
M. Daoud
Keyword(s):  
Quantum Fisher Information ◽  
Quantum Correlations ◽  
Von Neumann Entropy ◽  
Phase Estimation ◽  
Quantum Metrology ◽  
Von Neumann ◽  
Local Quantum ◽  
Parameter Precision ◽  
Qubit States

We analyze the effects of quantum correlations on the parameter precision in an interferometric configuration. As probe states, we consider a class of two-qubit states for which the analytical expression of the quantum interferometric power, quantifying the quantum correlations, is explicitly derived. Also, we give and analyze the local quantum Fisher information, which evaluates the sensitivity of the probe state to the phase shift, for some relevant local Hamiltonians. The discord-like quantum correlations based on the notion of quantum interferometric power are compared with the original quantum discord based on von Neumann entropy. We also examine the significance of quantum correlations in enhancing the precision of the phase estimation. Our study corroborates the recent series of investigations focusing on the role of quantum correlations other than entanglement on the efficiency of quantum metrology protocols.

scholarly journals Entanglement dynamics in Rule 54: Exact results and quasiparticle picture

2021 ◽  
Vol 11 (6) ◽  
Author(s):  
Katja Klobas ◽  
Bruno Bertini
Keyword(s):  
Linear Growth ◽  
Von Neumann Entropy ◽  
Entanglement Dynamics ◽  
Von Neumann ◽  
Rényi Entropies ◽  
Quantum Quenches ◽  
Initial States ◽  
Local Observables ◽  
Quasiparticle Picture ◽  
Renyi Entropies

We study the entanglement dynamics generated by quantum quenches in the quantum cellular automaton Rule 54. We consider the evolution from a recently introduced class of solvable initial states. States in this class relax (locally) to a one-parameter family of Gibbs states and the thermalisation dynamics of local observables can be characterised exactly by means of an evolution in space. Here we show that the latter approach also gives access to the entanglement dynamics and derive exact formulas describing the asymptotic linear growth of all Rényi entropies in the thermodynamic limit and their eventual saturation for finite subsystems. While in the case of von Neumann entropy we recover exactly the predictions of the quasiparticle picture, we find no physically meaningful quasiparticle description for other Rényi entropies. Our results apply to both homogeneous and inhomogeneous quenches.

When is a Statistical Operator Separable? -A Comparison of Different Definitions

2001 ◽  
Vol 56 (12) ◽  
pp. 849-854 ◽  
Author(s):  
Thomas Krüger
Keyword(s):  
Quantum Correlations ◽  
The Other ◽  
Von Neumann Entropy ◽  
Total System ◽  
Von Neumann ◽  
Usual Definition ◽  
Separability Criterion ◽  
Precise Meaning ◽  
Property Type ◽  
Statistical Operator

AbstractQuantum correlations are based on the non-separability of the total system ’s statistical operator. The notion of non-separability, on the other hand, is given with respect to the precise meaning of separability only. So it is a crucial task to define separability in terms of statistical operators. A recently proposed approach offers several advantages with respect to the usual definition. The von Neumann entropy S allows to develop a measure Ia/b of the relative non-separability of an operator pa with respect to another operator pb. This is a system im manent quantity of any property type as, e. g. spin or polarization. We compare the effect of the different approaches on S and Ia/b- Finally, the applicability of a comm on separability criterion will be checked.

scholarly journals Distillation of secret key and entanglement from quantum states

2005 ◽  
Vol 461 (2053) ◽  
pp. 207-235 ◽  
Author(s):  
Igor Devetak ◽  
Andreas Winter
Keyword(s):  
Quantum Correlations ◽  
Quantum States ◽  
Von Neumann Entropy ◽  
Secret Key ◽  
Classical Communication ◽  
Von Neumann ◽  
Information Theoretic ◽  
Einstein Podolsky Rosen ◽  
Classical Quantum ◽  
The Difference

We study and solve the problem of distilling a secret key from quantum states representing correlation between two parties (Alice and Bob) and an eavesdropper (Eve) via one–way public discussion: we prove a coding theorem to achieve the ‘wire–tapper’ bound, the difference of the mutual information Alice–Bob and that of Alice–Eve, for so–called classical–quantum–quantum–correlations, via one–way public communication. This result yields information–theoretic formulae for the distillable secret key, giving ‘ultimate’ key rate bounds if Eve is assumed to possess a purification of Alice and Bob's joint state. Specializing our protocol somewhat and making it coherent leads us to a protocol of entanglement distillation via one–way LOCC (local operations and classical communication) which is asymptotically optimal: in fact we prove the so–called ‘hashing inequality’, which says that the coherent information (i.e. the negative conditional von Neumann entropy) is an achievable Einstein–Podolsky–Rosen rate. This result is known to imply a whole set of distillation and capacity formulae, which we briefly review.

Local quantum uncertainty for a class of two-qubit X states and quantum correlations dynamics under decoherence

2017 ◽  
Vol 15 (01) ◽  
pp. 1750001 ◽  
Author(s):  
L. Jebli ◽  
B. Benzimoune ◽  
M. Daoud
Keyword(s):  
Quantum Discord ◽  
Quantum Correlations ◽  
Von Neumann Entropy ◽  
Trace Distance ◽  
Von Neumann ◽  
Quantum Uncertainty ◽  
Local Quantum Uncertainty ◽  
Local Quantum ◽  
Two Parameters ◽  
Qubit States

A special emphasis is devoted to the concept of local quantum uncertainty as an indicator of quantum correlations. We study quantum discord for a class of two-qubit states parametrized by two parameters. Quantum discord based on local quantum uncertainty, von Neumann entropy and trace distance (Schatten 1-norm) are explicitly derived and compared. The behavior of quantum correlations, quantified via local quantum uncertainty, under decoherence effects is investigated. We show that the discordlike local quantum uncertainty exhibits the possibility of freezing behavior during its evolution.

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