Entanglement of 0p-, 1s0d- and 1p0f-shell nucleon pairs

2017 ◽  
Vol 26 (05) ◽  
pp. 1750023
Author(s):  
Edward Kwaśniewicz ◽  
Dariusz Kurzyk
Keyword(s):  
Calculated Data ◽  
Decomposition Theorem ◽  
Von Neumann Entropy ◽  
Entangled State ◽  
Partial Density ◽  
Von Neumann ◽  
Quantum Numbers ◽  
Spin Quantum ◽  
Pure States ◽  
Dominant Part

The entanglement of pure states of the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-shell nucleon pairs has been studied. The von Neumann entropy of the partial density matrix has been employed to quantify the entanglement of the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-shell nucleon pairs. The Slater decomposition theorem has been used to verify if any pure state of a nucleon pair is an entangled state. Results of calculations have evidenced that a dominant part of the isospin [Formula: see text] proton–neutron states of the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-shell nucleon pairs, respectively, are strongly entangled. It is shown that the calculated data are a source of valuable information on the spin quantum numbers of the entangled protons from two-proton decay.

Non-Abelian gauge redundancy and entropic ambiguities

2015 ◽  
Vol 12 (06) ◽  
pp. 1560001
Author(s):  
A. P. Balachandran ◽  
A. R. de Queiroz ◽  
S. Vaidya
Keyword(s):  
Gauge Symmetry ◽  
Quantum State ◽  
Stochastic Matrix ◽  
Von Neumann Entropy ◽  
Zero Temperature ◽  
Abelian Gauge ◽  
Von Neumann ◽  
Algebra Of Observables ◽  
H Theorem ◽  
Pure States

The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. Therefore one reaches the remarkable possibility that there may be many entropies for a given state. We show that this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This ambiguity in entropy, which can occur at zero temperature, can often be traced to a gauge symmetry emergent from the non-trivial topological character of the configuration space of the underlying system. We also establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix. After demonstrating this entropy ambiguity for the simple example of the algebra of 2 × 2 matrices, we argue that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. We work out the simplest situation with such non-Abelian symmetry, that of an ethylene molecule.

WEHRL ENTROPY OF A MIXED STATE THREE-LEVEL ATOM INTERACTING WITH A CAVITY FIELD

2010 ◽  
Vol 09 (06) ◽  
pp. 623-630
Author(s):  
S. ABDEL-KHALEK ◽  
Y. HASSOUNI ◽  
M. ABDEL-ATY
Keyword(s):  
Mixed State ◽  
Von Neumann Entropy ◽  
Entangled State ◽  
Cavity Field ◽  
Wehrl Entropy ◽  
Von Neumann ◽  
Level Atom ◽  
Total Correlation ◽  
State Case ◽  
Mutual Entropy

In this paper, the Wehrl entropy approach is discussed and compared with the quantum entanglement using a mixed-state three-level atom interacting with a cavity field. In the pure state case, the behavior of the atomic Wehrl entropy shows the same behavior of the entanglement due to the von-Neumann entropy, while the mixed state case gives the total correlation due to quantum mutual entropy. If the system is in an entangled state, the formalism can be used to quantify the entanglement as well as the total correlations.

THE HSW CHANNEL CAPACITY FOR THE DIAGONAL UNITAL QUDIT CHANNELS

2004 ◽  
Vol 02 (04) ◽  
pp. 489-493
Author(s):  
YU-CHUN WU ◽  
ZHENG-WEI ZHOU ◽  
GUANG-CAN GUO
Keyword(s):  
Channel Capacity ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Pure States

The Holevo–Schumacher–Westermoreland (HSW) channel capacity for the diagonal unital qudit channels is considered. In Phys. Rev.A69, 022302, the HSW channel capacity for the diagonal unital qudit channels Φ is given as χ(Φ)=1- min ρH(Φ(ρ)), where minimization is over the input states of the channel. In this paper, using the concavity of von Neumann entropy, we show that using only pure states we can work out its HSW channel capacity. Hence, our result simplifies the computation.

PURE STATE ENTANGLEMENT BETWEEN SEPARATED REGIONS USING IMPENETRABLE BOSONS

2008 ◽  
Vol 06 (supp01) ◽  
pp. 739-744 ◽  
Author(s):  
JAVIER MOLINA-VILAPLANA ◽  
SOUGATO BOSE ◽  
VLADIMIR E. KOREPIN
Keyword(s):  
Time Evolution ◽  
Pure State ◽  
Ground States ◽  
Coarse Grained ◽  
Von Neumann Entropy ◽  
Entangled State ◽  
Von Neumann ◽  
Number Of Particles

We study a way of establishing a pure entangled state between two segments of a 1D ring using impenetrable bosons. The two bosons are initially simply placed at two positions on the ring which is an unentangled state. After some time evolution, we project the segments to a pure state through coarse grained measurements which ascertain whether there is a particle present in a given segment without revealing any information about its position within the segment. Subject to finding a particle in each segment, we quantify the entanglement established between the segments through the von Neumann entropy of a subsystem. We also investigate whether this entanglement increases with the number of particles and compare the entanglement in dynamical and ground states.

scholarly journals The von Neumann Entropy for Mixed States

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 49 ◽  
Author(s):  
Jorge Anaya-Contreras ◽  
Héctor Moya-Cessa ◽  
Arturo Zúñiga-Segundo
Keyword(s):  
Mixed State ◽  
Infinite System ◽  
Complete System ◽  
Von Neumann Entropy ◽  
Mixed States ◽  
Field Interaction ◽  
Von Neumann ◽  
Level Atom ◽  
Quantized Field ◽  
Pure States

The Araki–Lieb inequality is commonly used to calculate the entropy of subsystems when they are initially in pure states, as this forces the entropy of the two subsystems to be equal after the complete system evolves. Then, it is easy to calculate the entropy of a large subsystem by finding the entropy of the small one. To the best of our knowledge, there does not exist a way of calculating the entropy when one of the subsystems is initially in a mixed state. For the case of a two-level atom interacting with a quantized field, we show that it is possible to use the Araki–Lieb inequality and find the von Neumann entropy for the large (infinite) system. We show this in the two-level atom-field interaction.

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.

THE UNREASONABLE EFFECTIVENESS OF EXPONENTIALLY SUPPRESSED CORRECTIONS IN PRESERVING INFORMATION

2013 ◽  
Vol 22 (12) ◽  
pp. 1342030 ◽  
Author(s):  
KYRIAKOS PAPADODIMAS ◽  
SUVRAT RAJU
Keyword(s):  
Hilbert Space ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Nonperturbative Effects ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Information Theoretic ◽  
Black Hole Evaporation ◽  
Strong Subadditivity ◽  
Unreasonable Effectiveness

We point out that nonperturbative effects in quantum gravity are sufficient to reconcile the process of black hole evaporation with quantum mechanics. In ordinary processes, these corrections are unimportant because they are suppressed by e-S. However, they gain relevance in information-theoretic considerations because their small size is offset by the corresponding largeness of the Hilbert space. In particular, we show how such corrections can cause the von Neumann entropy of the emitted Hawking quanta to decrease after the Page time, without modifying the thermal nature of each emitted quantum. Second, we show that exponentially suppressed commutators between operators inside and outside the black hole are sufficient to resolve paradoxes associated with the strong subadditivity of entropy without any dramatic modifications of the geometry near the horizon.

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