A Simple Algorithm for Complete Factorization of an N-Partite Pure Quantum State

Abstract The uncertainty area δ (p, q): - [∫ W(p, q)2 dp dq] - 1 is proposed in place of δ p • δ q, and it is shown that each pure quantum state is a minimum uncertainty state in this sense: δ (p, q) = 2 π ħ. For mixed states, on the other hand, δ(p, q) > 2π ħ. In a phase space of 2F(=6N) dimensions, S: = k B • log[δF (p,q)/(2 π ħ)F] whit δF (p,q):= [∫ W(p, q)2 dF p dF q]-1 is considered as an alternative to von Neumann`s entropy S̃:= kB • trc [ρ̂ log (ρ̂-1)].

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Comment on ‘‘Obtainment of thermal noise from a pure quantum state’’

Physical Review A ◽

10.1103/physreva.38.1657 ◽

1988 ◽

Vol 38 (3) ◽

pp. 1657-1658 ◽

Cited By ~ 24

Author(s):

S. M. Barnett ◽

P. L. Knight

Keyword(s):

Quantum State ◽

Thermal Noise ◽

Pure Quantum State

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Canonical Thermal Pure Quantum State

Springer Theses - Formulation of Statistical Mechanics Based on Thermal Pure Quantum States ◽

10.1007/978-981-10-1506-9_3 ◽

2017 ◽

pp. 15-30

Author(s):

Sho Sugiura

Keyword(s):

Quantum State ◽

Pure Quantum State

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Thresholds for reduction-related entanglement criteria in quantum information theory

Quantum Information and Computation ◽

10.26421/qic15.13-14-5 ◽

2015 ◽

Vol 15 (13&14) ◽

pp. 1165-1184

Author(s):

Maria A. Jivulescu ◽

Nicolae Lupa ◽

Ion Nechita

Keyword(s):

Information Theory ◽

Quantum Information ◽

Quantum State ◽

Random Matrix ◽

Matrix Theory ◽

Quantum Information Theory ◽

Quantum States ◽

Absolute Reduction ◽

Open Questions ◽

Pure Quantum State

We consider random bipartite quantum states obtained by tracing out one subsystem from a random, uniformly distributed, tripartite pure quantum state. We compute thresholds for the dimension of the system being traced out, so that the resulting bipartite quantum state satisfies the reduction criterion in different asymptotic regimes. We consider as well the basis-independent version of the reduction criterion (the absolute reduction criterion), computing thresholds for the corresponding eigenvalue sets. We do the same for other sets relevant in the study of absolute separability, using techniques from random matrix theory. Finally, we gather and compare the known values for the thresholds corresponding to different entanglement criteria, and conclude with a list of open questions.

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Classical entanglement structure in the wavefunction of inflationary fluctuations

International Journal of Modern Physics D ◽

10.1142/s0218271817430064 ◽

2017 ◽

Vol 26 (12) ◽

pp. 1743006 ◽

Cited By ~ 2

Author(s):

Elliot Nelson ◽

C. Jess Riedel

Keyword(s):

Entropy Production ◽

Production Rate ◽

Early Universe ◽

Quantum State ◽

Entropy Production Rate ◽

Vacuum Fluctuations ◽

Spacetime Geometry ◽

Pure Quantum State ◽

Entanglement Structure ◽

Metric Fluctuations

We argue that preferred classical variables emerge from the entanglement structure of a pure quantum state in the form of redundant records: information shared between many subsystems. Focusing on the early universe, we ask how classical metric perturbations emerge from vacuum fluctuations in an inflationary background. We show that the squeezing of the quantum state for super-horizon modes, along with minimal gravitational interactions, leads to decoherence and to an exponential number of records of metric fluctuations on very large scales, [Formula: see text], where [Formula: see text] is the amplitude of metric fluctuations. This determines a preferred decomposition of the inflationary wavefunction into orthogonal “branches” corresponding to classical metric perturbations, which defines an inflationary entropy production rate and accounts for the emergence of stochastic, inhomogeneous spacetime geometry.

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