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 Convergence Conditions of Mixed States and their von Neumann Entropy in Continuous Quantum Measurements

2014 ◽  
Vol 21 (04) ◽  
pp. 1450010
Author(s):  
Toru Fuda
Keyword(s):  
Quantum Measurements ◽  
Von Neumann Entropy ◽  
Projection Operators ◽  
Mixed States ◽  
Convergence Conditions ◽  
Von Neumann ◽  
Zeno Effect ◽  
The Difference ◽  
Arbitrary Precision ◽  
Continuous Quantum Measurements

By carrying out appropriate continuous quantum measurements with a family of projection operators, a unitary channel can be approximated in an arbitrary precision in the trace norm sense. In particular, the quantum Zeno effect is described as an application. In the case of an infinite dimension, although the von Neumann entropy is not necessarily continuous, the difference of the entropies between the states, as mentioned above, can be made arbitrarily small under some conditions.

scholarly journals A canonical purification for the entanglement wedge cross-section

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Souvik Dutta ◽  
Thomas Faulkner
Keyword(s):  
Cross Section ◽  
Minimal Surfaces ◽  
Entanglement Entropy ◽  
Point Of View ◽  
Von Neumann Entropy ◽  
Type I ◽  
Von Neumann ◽  
I Factor ◽  
Split Property ◽  
Splitting Type

Abstract In AdS/CFT we consider a class of bulk geometric quantities inside the entanglement wedge called reflected minimal surfaces. The areas of these surfaces are dual to the entanglement entropy associated to a canonical purification (the GNS state) that we dub the reflected entropy. From the bulk point of view, we show that half the area of the reflected minimal surface gives a reinterpretation of the notion of the entanglement wedge cross-section. We prove some general properties of the reflected entropy and introduce a novel replica trick in CFTs for studying it. The duality is established using a recently introduced approach to holographic modular flow. We also consider an explicit holographic construction of the canonical purification, introduced by Engelhardt and Wall; the reflected minimal surfaces are simply RT surfaces in this new spacetime. We contrast our results with the entanglement of purification conjecture, and finally comment on the continuum limit where we find a relation to the split property: the reflected entropy computes the von Neumann entropy of a canonical splitting type-I factor introduced by Doplicher and Longo.

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.

scholarly journals Islands in linear dilaton black holes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Georgios K. Karananas ◽  
Alex Kehagias ◽  
John Taskas
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Entanglement Entropy ◽  
Von Neumann Entropy ◽  
Two Dimensional ◽  
Extremal Case ◽  
Von Neumann ◽  
Dimensional Black Hole ◽  
Linear Dilaton ◽  
Linear Dilaton Black Hole

Abstract We derive a novel four-dimensional black hole with planar horizon that asymptotes to the linear dilaton background. The usual growth of its entanglement entropy before Page’s time is established. After that, emergent islands modify to a large extent the entropy, which becomes finite and is saturated by its Bekenstein-Hawking value in accordance with the finiteness of the von Neumann entropy of eternal black holes. We demonstrate that viewed from the string frame, our solution is the two-dimensional Witten black hole with two additional free bosons. We generalize our findings by considering a general class of linear dilaton black hole solutions at a generic point along the σ-model renormalization group (RG) equations. For those, we observe that the entanglement entropy is “running” i.e. it is changing along the RG flow with respect to the two-dimensional worldsheet length scale. At any fixed moment before Page’s time the aforementioned entropy increases towards the infrared (IR) domain, whereas the presence of islands leads the running entropy to decrease towards the IR at later times. Finally, we present a four-dimensional charged black hole that asymptotes to the linear dilaton background as well. We compute the associated entanglement entropy for the extremal case and we find that an island is needed in order for it to follow the Page curve.

Generalized information and entanglement entropy, gravitation and holography

2015 ◽  
Vol 30 (16) ◽  
pp. 1530039 ◽  
Author(s):  
O. Obregón
Keyword(s):  
Entanglement Entropy ◽  
Ideal Gas ◽  
Einstein Equations ◽  
Von Neumann Entropy ◽  
Nonextensive Statistical Mechanics ◽  
Von Neumann ◽  
H Theorem ◽  
Gauge Gravity ◽  
Gravity Duality ◽  
Correction Terms

A nonextensive statistical mechanics entropy that depends only on the probability distribution is proposed in the framework of superstatistics. It is based on a Γ(χ2) distribution that depends on β and also on pl. The corresponding modified von Neumann entropy is constructed; it is shown that it can also be obtained from a generalized Replica trick. We further demonstrate a generalized H-theorem. Considering the entropy as a function of the temperature and volume, it is possible to generalize the equation of state of an ideal gas. Moreover, following the entropic force formulation a generalized Newton's law is obtained, and following the proposal that the Einstein equations can be deduced from the Clausius law, we discuss on the structure that a generalized Einstein's theory would have. Lastly, we address the question whether the generalized entanglement entropy can play a role in the gauge/gravity duality. We pay attention to 2d CFT and their gravity duals. The correction terms to the von Neumann entropy result more relevant than the usual UV ones and also than those due to the area dependent AdS3 entropy which result comparable to the UV ones. Then the correction terms due to the new entropy would modify the Ryu–Takayanagi identification between the CFT entanglement entropy and the AdS entropy in a different manner than the UV ones or than the corrections to the AdS3 area dependent entropy.

scholarly journals On the Exact Variance of Tsallis Entanglement Entropy in a Random Pure State

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 539 ◽  
Author(s):  
Lu Wei
Keyword(s):  
Pure State ◽  
Entanglement Entropy ◽  
Tsallis Entropy ◽  
Von Neumann Entropy ◽  
Quadratic Entropy ◽  
Von Neumann ◽  
Special Cases ◽  
Variance Formula ◽  
Finite Sums ◽  
Random Pure State

The Tsallis entropy is a useful one-parameter generalization to the standard von Neumann entropy in quantum information theory. In this work, we study the variance of the Tsallis entropy of bipartite quantum systems in a random pure state. The main result is an exact variance formula of the Tsallis entropy that involves finite sums of some terminating hypergeometric functions. In the special cases of quadratic entropy and small subsystem dimensions, the main result is further simplified to explicit variance expressions. As a byproduct, we find an independent proof of the recently proven variance formula of the von Neumann entropy based on the derived moment relation to the Tsallis entropy.

Aspects of Entropy Squeezing and Entanglement for Moving Two-Level Atom in Presence of Finite Trio Coherent State

2016 ◽  
Vol 13 (10) ◽  
pp. 7455-7459
Author(s):  
S. I Ali ◽  
A. M Mosallem ◽  
T Emam
Keyword(s):  
Entanglement Entropy ◽  
Photon Number ◽  
Atomic Motion ◽  
Von Neumann Entropy ◽  
Wehrl Entropy ◽  
Entropy Squeezing ◽  
Von Neumann ◽  
Special Values ◽  
Level Atom ◽  
Motion Parameters

In this paper, we investigate the entanglement of the interaction of three modes of radiation field with moving and unmoving two-level atom. The time evolution of the von Neumann entropy, entropy squeezing and marginal atomic Wehrl entropy is investigated. The marginal atomic Wehrl entropy as squeezing indicator of the entanglement of the system is suggested. The results beacon the important roles played by both the atomic motion parameters in the evolution of entanglement, entropy squeezing and marginal atomic Wehrl entropy. Using special values of the photon number of transition and atomic motion parameter, the entanglement phenomena of sudden death and long living entanglenment can be appeared. The results show that there is atomic motion monotonic harmonization atomic Wehrl entropy (WE). It is illustrated that the amount of the above-mentioned phenomena can be tuned by controlling the evolved parameters appropriately.

scholarly journals THE BALANCE OF QUANTUM CORRELATIONS FOR A CLASS OF FEASIBLE TRIPARTITE CONTINUOUS VARIABLE STATES

2012 ◽  
Vol 27 (01n03) ◽  
pp. 1345024 ◽  
Author(s):  
STEFANO OLIVARES ◽  
MATTEO G. A. PARIS
Keyword(s):  
Conservation Laws ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
Continuous Variable ◽  
Noisy Environment ◽  
Mixed States ◽  
Von Neumann ◽  
Entanglement Of Formation ◽  
Pure States ◽  
Gaussian Quantum Discord

We address the balance of quantum correlations for continuous variable (CV) states. In particular, we consider a class of feasible tripartite CV pure states and explicitly prove two Koashi–Winter-like conservation laws involving Gaussian entanglement of formation (EoF), Gaussian quantum discord and sub-system Von Neumann entropies. We also address the class of tripartite CV mixed states resulting from the propagation in a noisy environment, and discuss how the previous equalities evolve into inequalities.

scholarly journals ENTANGLEMENT ENTROPY: HELICITY VERSUS SPIN

2008 ◽  
Vol 06 (01) ◽  
pp. 181-186 ◽  
Author(s):  
SONG HE ◽  
SHUXIN SHAO ◽  
HONGBAO ZHANG
Keyword(s):  
Density Matrix ◽  
Entanglement Entropy ◽  
Specific Form ◽  
Von Neumann Entropy ◽  
Particle State ◽  
Inertial Reference Frame ◽  
Helicity State ◽  
Von Neumann ◽  
Left Handed ◽  
Massive Spin

For a massive spin 1/2 field, we present the reduced spin and helicity density matrix, respectively, for the same pure one particle state. Their relation has also been developed. Furthermore, we calculate and compare the corresponding entanglement entropy for spin and helicity within the same inertial reference frame. Due to the distinct dependence on momentum degree of freedom between spin and helicity states, the resultant helicity entropy is different from that of spin in general. In particular, we find that both helicity entanglement for a spin eigenstate and spin entanglement for a right handed or left handed helicity state do not vanish, and their Von Neumann entropy has no dependence on the specific form of momentum distribution, as long as it is isotropic.

ENTANGLEMENT IN ONE-AND TWO-DIMENSIONAL ANDERSON MODELS WITH LONG-RANGE CORRELATED-DISORDER

2009 ◽  
Vol 07 (05) ◽  
pp. 959-968
Author(s):  
Z. Z. GUO ◽  
Z. G. XUAN ◽  
Y. S. ZHANG ◽  
XIAOWEI WU
Keyword(s):  
Long Range ◽  
Ground State ◽  
Two Dimensions ◽  
Von Neumann Entropy ◽  
Two Dimensional ◽  
Correlation Effects ◽  
Von Neumann ◽  
Range Correlation ◽  
The Difference ◽  
Anderson Models

The ground state entanglement in one- and two-dimensional Anderson models are studied with consideration of the long-range correlation effects and using the measures of concurrence and von Neumann entropy. We compare the effects of the long-range power-law correlation for the on-site energies on entanglement with the uncorrelated cases. We demonstrate the existence of the band structure of the entanglement. The intraband and interband jumping phenomena of the entanglement are also reported and explained to as the localization-delocalization transition of the system. We also demonstrated the difference between the results of one- and two-dimensions. Our results show that the correlation of the on-site energies increases the entanglement.

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