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.

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 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.

Entanglement in composite systems due to external influences

2018 ◽  
Vol 33 (21) ◽  
pp. 1850128
Author(s):  
D. M. Gitman ◽  
M. S. Meireles ◽  
A. D. Levin ◽  
A. A. Shishmarev ◽  
R. A. Castro
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Density Operator ◽  
Time Dependent ◽  
Von Neumann Entropy ◽  
Entanglement Measure ◽  
Photon Beams ◽  
Von Neumann ◽  
Electron Positron ◽  
In The Beginning

In this paper, we consider two examples of an entanglement in two-qubit systems and an example of entanglement in quantum field theory (QFT). In the beginning, we study the entanglement of two spin states by a magnetic field. A nonzero entanglement appears for interacting spins. When the coupling between the spins is constant, we study the entanglement by several types of time-dependent magnetic fields. In the case of a constant difference between [Formula: see text] components of magnetic fields acting on each spin, we find several time-dependent coupling functions [Formula: see text] that also allow us to analyze analytically and numerically the entanglement measure. Considering two photons moving in an electron medium, we demonstrate that they can be entangled in a controlled way by applying an external magnetic field. The magnetic field affecting electrons of the medium affects photons and, thus, causes an entanglement of the photon beams. The third example is related to the effect of production of electron–positron pairs from the vacuum by a strong external electric field. Here, we have used a general nonperturbative expression for the density operator of the system under consideration. Applying a reduction procedure to this density operator, we construct mixed states of electron and positron subsystems. Calculating the von Neumann entropy of such states, we obtain the loss of information due to the reduction and, at the same time, the entanglement measure of electron and positron subsystems. This entanglement can be considered as an example of an entanglement in QFT.

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 Hyperpolarization and the physical boundary of Liouville space

2021 ◽  
Vol 2 (1) ◽  
pp. 395-407
Author(s):  
Malcolm H. Levitt ◽  
Christian Bengs
Keyword(s):  
Master Equation ◽  
Density Operator ◽  
Spin Dynamics ◽  
Physical Region ◽  
State Density ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Liouville Space ◽  
Density Operators ◽  
Physical Boundary

Abstract. The quantum state of a spin ensemble is described by a density operator, which corresponds to a point in the Liouville space of orthogonal spin operators. Valid density operators are confined to a particular region of Liouville space, which we call the physical region and which is bounded by multidimensional figures called simplexes. Each vertex of a simplex corresponds to a pure-state density operator. We provide examples for spins I=1/2, I=1, I=3/2 and for coupled pairs of spins-1/2. We use the von Neumann entropy as a criterion for hyperpolarization. It is shown that the inhomogeneous master equation for spin dynamics leads to non-physical results in some cases, a problem that may be avoided by using the Lindbladian master equation.

scholarly journals Upper bounds on mixing rates

2013 ◽  
Vol 13 (11&12) ◽  
pp. 986-994
Author(s):  
Elliott H. Lieb ◽  
Anna Vershynina
Keyword(s):  
Density Operator ◽  
Random Variable ◽  
Upper Bounds ◽  
Von Neumann Entropy ◽  
Mixing Rate ◽  
Unitary Evolution ◽  
Von Neumann ◽  
Mixing Rates ◽  
Non Local ◽  
Expected Density

We prove upper bounds on the rate, called "mixing rate", at which the von Neumann entropy of the expected density operator of a given ensemble of states changes under non-local unitary evolution. For an ensemble consisting of two states, with probabilities of p and 1-p, we prove that the mixing rate is bounded above by 4\sqrt{p(1-p)} for any Hamiltonian of norm 1. For a general ensemble of states with probabilities distributed according to a random variable X and individually evolving according to any set of bounded Hamiltonians, we conjecture that the mixing rate is bounded above by a Shannon entropy of a random variable $X$. For this general case we prove an upper bound that is independent of the dimension of the Hilbert space on which states in the ensemble act.

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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