scholarly journals Purity-Based Continuity Bounds for von Neumann Entropy

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Junaid ur Rehman ◽  
Hyundong Shin
Keyword(s):  
Quantum States ◽  
Von Neumann Entropy ◽  
Trace Distance ◽  
Von Neumann ◽  
Information Theoretic

Abstract We propose continuity bounds for the von Neumann entropy of qubits whose difference in purity is bounded. Considering the purity difference of two qubits to capture the notion of distance between them results into bounds which are demonstrably tighter than the trace distance-based existing continuity bounds of quantum states. Continuity bounds can be utilized in bounding the information-theoretic quantities which are generally difficult to compute.

scholarly journals Limits to Perception by Quantum Monitoring with Finite Efficiency

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1527
Author(s):  
Luis Pedro García-Pintos ◽  
Adolfo del Campo
Keyword(s):  
Quantum Measurements ◽  
Quantum States ◽  
Von Neumann Entropy ◽  
Actual State ◽  
Ising Chain ◽  
Trace Distance ◽  
Gaussian States ◽  
Von Neumann ◽  
Additional Information ◽  
Continuous Quantum Measurements

We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds on the trace distance and the relative entropy between the assigned state and the actual state of the system. These bounds are expressed solely in terms of the purity and von Neumann entropy of the state assigned by the agent, and are shown to characterize how an agent’s perception of the system is altered by access to additional information. We apply our results to Gaussian states and to the dynamics of a system embedded in an environment illustrated on a quantum Ising chain.

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.

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.

scholarly journals Quantum random state generation with predefined entanglement constraint

2014 ◽  
Vol 12 (05) ◽  
pp. 1450030 ◽  
Author(s):  
Anmer Daskin ◽  
Ananth Grama ◽  
Sabre Kais
Keyword(s):  
Error Correction ◽  
Weighted Graph ◽  
Quantum States ◽  
Von Neumann Entropy ◽  
Bipartite Entanglement ◽  
Von Neumann ◽  
Communication Algorithms ◽  
Equivalent Quantum ◽  
State Generation ◽  
Random Quantum States

Entanglement plays an important role in quantum communication, algorithms, and error correction. Schmidt coefficients are correlated to the eigenvalues of the reduced density matrix. These eigenvalues are used in von Neumann entropy to quantify the amount of the bipartite entanglement. In this paper, we map the Schmidt basis and the associated coefficients to quantum circuits to generate random quantum states. We also show that it is possible to adjust the entanglement between subsystems by changing the quantum gates corresponding to the Schmidt coefficients. In this manner, random quantum states with predefined bipartite entanglement amounts can be generated using random Schmidt basis. This provides a technique for generating equivalent quantum states for given weighted graph states, which are very useful in the study of entanglement, quantum computing, and quantum error correction.

scholarly journals Geometry of color perception. Part 2: perceived colors from real quantum states and Hering’s rebit

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
M. Berthier
Keyword(s):  
State Space ◽  
Color Perception ◽  
Quantum States ◽  
Von Neumann Entropy ◽  
Full Detail ◽  
Von Neumann ◽  
Real Dimension ◽  
Quantum Description ◽  
Color Opponency ◽  
Dimension 2

Abstract Inspired by the pioneer work of H.L. Resnikoff, which is described in full detail in the first part of this two-part paper, we give a quantum description of the space $\mathcal{P}$ P of perceived colors. We show that $\mathcal{P}$ P is the effect space of a rebit, a real quantum qubit, whose state space is isometric to Klein’s hyperbolic disk. This chromatic state space of perceived colors can be represented as a Bloch disk of real dimension 2 that coincides with Hering’s disk given by the color opponency mechanism. Attributes of perceived colors, hue and saturation, are defined in terms of Von Neumann entropy.

scholarly journals Entropic Lower Bound for Distinguishability of Quantum States

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Seungho Yang ◽  
Jinhyoung Lee ◽  
Hyunseok Jeong
Keyword(s):  
Lower Bound ◽  
Density Operator ◽  
Success Probability ◽  
Quantum States ◽  
Von Neumann Entropy ◽  
Von Neumann

For a system randomly prepared in a number of quantum states, we present a lower bound for the distinguishability of the quantum states, that is, the success probability of determining the states in the form of entropy. When the states are all pure, acquiring the entropic lower bound requires only the density operator and the number of the possible states. This entropic bound shows a relation between the von Neumann entropy and the distinguishability.

Maps on Quantum States in -algebras Preserving von Neumann Entropy or Schatten -norm of Convex Combinations

2019 ◽  
Vol 62 (1) ◽  
pp. 75-80 ◽  
Author(s):  
Marcell Gaál
Keyword(s):  
Convex Combination ◽  
General Setting ◽  
Positive Semidefinite ◽  
Quantum States ◽  
Von Neumann Entropy ◽  
Density Matrices ◽  
Positive Semidefinite Matrices ◽  
Von Neumann ◽  
Convex Functionals ◽  
Invertible Elements

AbstractVery recently, Karder and Petek completely described maps on density matrices (positive semidefinite matrices with unit trace) preserving certain entropy-like convex functionals of any convex combination. As a result, maps could be characterized that preserve von Neumann entropy or Schatten $p$-norm of any convex combination of quantum states (whose mathematical representatives are the density matrices). In this note we consider these latter two problems on the set of invertible density operators, in a much more general setting, on the set of positive invertible elements with unit trace in a $C^{\ast }$-algebra.

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