scholarly journals Leading order corrections to the quantum extremal surface prescription

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Chris Akers ◽  
Geoff Penington
Keyword(s):  
Quantum State ◽  
Leading Order ◽  
Extremal Surface ◽  
Shannon Theory ◽  
Generalized Entropy ◽  
Replica Trick ◽  
Quantum Shannon Theory ◽  
Paradoxical Results

Abstract We show that a naïve application of the quantum extremal surface (QES) prescription can lead to paradoxical results and must be corrected at leading order. The corrections arise when there is a second QES (with strictly larger generalized entropy at leading order than the minimal QES), together with a large amount of highly incompressible bulk entropy between the two surfaces. We trace the source of the corrections to a failure of the assumptions used in the replica trick derivation of the QES prescription, and show that a more careful derivation correctly computes the corrections. Using tools from one-shot quantum Shannon theory (smooth min- and max-entropies), we generalize these results to a set of refined conditions that determine whether the QES prescription holds. We find similar refinements to the conditions needed for entanglement wedge reconstruction (EWR), and show how EWR can be reinterpreted as the task of one-shot quantum state merging (using zero-bits rather than classical bits), a task gravity is able to achieve optimally efficiently.

scholarly journals Quantum Shannon theory with superpositions of trajectories

2019 ◽  
Vol 475 (2225) ◽  
pp. 20180903 ◽  
Author(s):  
Giulio Chiribella ◽  
Hlér Kristjánsson
Keyword(s):  
Transmission Lines ◽  
Internal State ◽  
Quantum Systems ◽  
Space Time ◽  
Shannon Theory ◽  
Classical Systems ◽  
Theory Of Information ◽  
Quantum Shannon Theory ◽  
Quantum Counterpart ◽  
Multiple Transmission

Shannon's theory of information was built on the assumption that the information carriers were classical systems. Its quantum counterpart, quantum Shannon theory, explores the new possibilities arising when the information carriers are quantum systems. Traditionally, quantum Shannon theory has focused on scenarios where the internal state of the information carriers is quantum, while their trajectory is classical. Here we propose a second level of quantization where both the information and its propagation in space–time is treated quantum mechanically. The framework is illustrated with a number of examples, showcasing some of the counterintuitive phenomena taking place when information travels simultaneously through multiple transmission lines.

scholarly journals Asymptotic Performance of Port-Based Teleportation

2020 ◽  
Author(s):  
Matthias Christandl ◽  
Felix Leditzky ◽  
Christian Majenz ◽  
Graeme Smith ◽  
Florian Speelman ◽  
...  
Keyword(s):  
Matrix Theory ◽  
Building Blocks ◽  
Convergence Result ◽  
Dirichlet Eigenvalue ◽  
Shannon Theory ◽  
Optimal Protocol ◽  
Local Quantum ◽  
Non Local ◽  
Fixed Input ◽  
Quantum Shannon Theory

AbstractQuantum teleportation is one of the fundamental building blocks of quantum Shannon theory. While ordinary teleportation is simple and efficient, port-based teleportation (PBT) enables applications such as universal programmable quantum processors, instantaneous non-local quantum computation and attacks on position-based quantum cryptography. In this work, we determine the fundamental limit on the performance of PBT: for arbitrary fixed input dimension and a large number N of ports, the error of the optimal protocol is proportional to the inverse square of N. We prove this by deriving an achievability bound, obtained by relating the corresponding optimization problem to the lowest Dirichlet eigenvalue of the Laplacian on the ordered simplex. We also give an improved converse bound of matching order in the number of ports. In addition, we determine the leading-order asymptotics of PBT variants defined in terms of maximally entangled resource states. The proofs of these results rely on connecting recently-derived representation-theoretic formulas to random matrix theory. Along the way, we refine a convergence result for the fluctuations of the Schur–Weyl distribution by Johansson, which might be of independent interest.

scholarly journals Communication Enhancement through Quantum Coherent Control of N Channels in an Indefinite Causal-Order Scenario

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 1012 ◽  
Author(s):  
Lorenzo M. Procopio ◽  
Francisco Delgado ◽  
Marco Enríquez ◽  
Nadia Belabas ◽  
Juan Ariel Levenson
Keyword(s):  
Information Transmission ◽  
Coherent Control ◽  
Quantum Channels ◽  
New Paradigm ◽  
Causal Order ◽  
Shannon Theory ◽  
Information Preservation ◽  
Transmission Of Information ◽  
Individual Capacity ◽  
Quantum Shannon Theory

In quantum Shannon theory, transmission of information is enhanced by quantum features. Up to very recently, the trajectories of transmission remained fully classical. Recently, a new paradigm was proposed by playing quantum tricks on two completely depolarizing quantum channels i.e., using coherent control in space or time of the two quantum channels. We extend here this control to the transmission of information through a network of an arbitrary number N of channels with arbitrary individual capacity i.e., information preservation characteristics in the case of indefinite causal order. We propose a formalism to assess information transmission in the most general case of N channels in an indefinite causal order scenario yielding the output of such transmission. Then, we explicitly derive the quantum switch output and the associated Holevo limit of the information transmission for N = 2 , N = 3 as a function of all involved parameters. We find in the case N = 3 that the transmission of information for three channels is twice that of transmission of the two-channel case when a full superposition of all possible causal orders is used.

scholarly journals Selected Advances in Quantum Shannon Theory

2016 ◽  
Vol 2016-12 (102) ◽  
pp. 11-15 ◽  
Author(s):  
Nilanjana Datta
Keyword(s):  
Shannon Theory ◽  
Quantum Shannon Theory

scholarly journals Cosmological singularities, entanglement and quantum extremal surfaces

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
A. Manu ◽  
K. Narayan ◽  
Partha Paul
Keyword(s):  
Dimensional Reduction ◽  
Extremal Surface ◽  
Generalized Entropy ◽  
Big Crunch

Abstract We study aspects of entanglement and extremal surfaces in various families of spacetimes exhibiting cosmological, Big-Crunch, singularities, in particular isotropic AdS Kasner. The classical extremal surface dips into the bulk radial and time directions. Explicitly analysing the extremization equations in the semiclassical region far from the singularity, we find the surface bends in the direction away from the singularity. In the 2-dim cosmologies obtained by dimensional reduction of these and other singularities, we have studied quantum extremal surfaces by extremizing the generalized entropy. The resulting extremization shows the quantum extremal surfaces to always be driven to the semiclassical region far from the singularity. We give some comments and speculations on our analysis.

scholarly journals Quantum capacity analysis of multi-level amplitude damping channels

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Stefano Chessa ◽  
Vittorio Giovannetti
Keyword(s):  
Finite Dimension ◽  
Quantum Systems ◽  
Capacity Analysis ◽  
Quantum Channels ◽  
Shannon Theory ◽  
Amplitude Damping ◽  
Quantum Capacity ◽  
Multi Level ◽  
Quantum Shannon Theory ◽  
Special Case

AbstractEvaluating capacities of quantum channels is the first purpose of quantum Shannon theory, but in most cases the task proves to be very hard. Here, we introduce the set of Multi-level Amplitude Damping quantum channels as a generalization of the standard qubit Amplitude Damping Channel to quantum systems of finite dimension d. In the special case of d = 3, by exploiting degradability, data-processing inequalities, and channel isomorphism, we compute the associated quantum and private classical capacities for a rather wide class of maps, extending the set of models whose capacity can be computed known so far. We proceed then to the evaluation of the entanglement assisted quantum and classical capacities.

scholarly journals Entanglement between two gravitating universes

2021 ◽  
Author(s):  
Vijay Balasubramanian ◽  
Arjun Kar ◽  
Tomonori Ugajin
Keyword(s):  
Quantum Information ◽  
Analytic Continuation ◽  
Path Integral ◽  
Pure State ◽  
Entanglement Entropy ◽  
Replica Symmetry ◽  
Extremal Surface ◽  
Generalized Entropy ◽  
Two Universes ◽  
Effective Description

Abstract We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for the n th Rényi entropy includes a wormhole between the n copies of the gravitating universe, leading to a standard “island formula” for entanglement entropy consistent with unitarity of quantum information. When both universes contain gravity, gravitational corrections to this configuration lead to a violation of unitarity. However, the path integral is now dominated by a novel wormhole with 2n boundaries connecting replica copies of both universes. The analytic continuation of this contribution involves a quotient by Ζ n replica symmetry, giving a cylinder connecting the two universes. When entanglement is large, this configuration has an effective description as a “swap wormhole”, a geometry in which the boundaries of the two universes are glued together by a “swaperator”. This description allows precise computation of a generalized entropy-like formula for entanglement entropy. The quantum extremal surface computing the entropy lives on the Lorentzian continuation of the cylinder/swap wormhole, which has a connected Cauchy slice stretching between the universes – a realization of the ER=EPR idea. The new wormhole restores unitarity of quantum information.

scholarly journals Disentangling the thermofield-double state

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Pouria Dadras
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Strong Coupling ◽  
Entanglement Entropy ◽  
Coarse Grained ◽  
One Dimension ◽  
Leading Order ◽  
Point Function ◽  
Replica Trick ◽  
Large N

Abstract In this paper, we consider the evolution of the thermofield-double state under the double-traced operator that connects its both sides. We will compute the entanglement entropy of the resulting state using the replica trick for the large N field theory. To leading order, it can be computed from the two-point function of the theory, where, in CFTs, it is fixed by the symmetries. Due to the exponential decay of the interaction, the entanglement entropy saturates about the thermal time after the interaction is on. Next, we restrict ourselves to one dimension and assume that the theory at strong coupling is effectively described by the Schwarzian action. We then compute the coarse-grained entropy of the resulting state using the four-point function. The equality of the two entropies implies that the double-traced operators in our theory act coherently. In AdS/CFT correspondence where the thermofield-double state corresponds to a two-sided black hole, the action of a double-traced operator corresponds to shrinking or expanding the black hole in the bulk.

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