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Separable states are more disordered globally than locally

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M. A. Nielsen, J. Kempe

Quantum Physics · Submitted 30 Nov 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper we prove the stronger result that for separable states the vector of eigenvalues of the density matrix of system AB is majorized by the vector of eigenvalues of the density matrix of system A alone.

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arXiv IDquant-ph/0011117 (version 1)
Pith IDH5M5HZ27, Pith's permanent record of this paper and its review
CitationJ. Kempe, M. A. Nielsen. "Separable states are more disordered globally than locally." arXiv:quant-ph/0011117 (2000). https://pith.science/paper/H5M5HZ27
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,661 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.93 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.24 · compares with prior results 0.68 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

A remarkable feature of quantum entanglement is that an entangled state of two parties, Alice (A) and Bob (B), may be more disordered locally than globally. That is, S(A) > S(A,B), where S(.) is the von Neumann entropy. It is known that satisfaction of this inequality implies that a state is non-separable. In this paper we prove the stronger result that for separable states the vector of eigenvalues of the density matrix of system AB is majorized by the vector of eigenvalues of the density matrix of system A alone. This gives a strong sense in which a separable state is more disordered globally than locally and a new necessary condition for separability of bipartite states in arbitrary dimensions. We also investigate the extent to which these conditions are sufficient to characterize separability, exhibiting examples that show separability cannot be characterized solely in terms of the local and global spectra of a state. We apply our conditions to give a simple proof that non-separable states exist sufficiently close to the completely mixed state of $n$ qudits.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 A remarkable feature of quantum entanglement is that an entangled state of two parties, Alice (A) and Bob (B), may be more disordered locally than globally. background 1.00 0.08 0.06 hedged possibility 0.94
s1 That is, S(A) > S(A,B), where S(.) is the von Neumann entropy. background 0.92 0.10 0.03 asserted 0.99
s2 It is known that satisfaction of this inequality implies that a state is non-separable. background 1.00 0.05 0.03 asserted 1.00
s3 In this paper we prove the stronger result that for separable states the vector of eigenvalues of the density matrix of system AB is majorized by the vector of eigenvalues of the density matrix of system A alone. result 0.91 0.95 0.90 asserted 1.00
s4 This gives a strong sense in which a separable state is more disordered globally than locally and a new necessary condition for separability of bipartite states in arbitrary dimensions. interpretation 0.67 0.92 0.74 asserted 0.96
s5 We also investigate the extent to which these conditions are sufficient to characterize separability, exhibiting examples that show separability cannot be characterized solely in terms of the local and global spectra of a state. result 0.45 0.96 0.07 asserted 1.00
s6 We apply our conditions to give a simple proof that non-separable states exist sufficiently close to the completely mixed state of $n$ qudits. contribution 0.51 0.94 0.04 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

A remarkable feature of quantum entanglement is that an entangled state of two parties, Alice (A) and Bob (B), may be more disordered locally than globally. That is, S(A) > S(A,B), where S(.) is the von Neumann entropy. It is known that satisfaction of this inequality implies that a state is non-separable. In this paper we prove the stronger result that for separable states the vector of eigenvalues of the density matrix of system AB is majorized by the vector of eigenvalues of the density matrix of system A alone. This gives a strong sense in which a separable state is more disordered globally than locally and a new necessary condition for separability of bipartite states in arbitrary dimensions. We also investigate the extent to which these conditions are sufficient to characterize separability, exhibiting examples that show separability cannot be characterized solely in terms of the local and global spectra of a state. We apply our conditions to give a simple proof that non-separable states exist sufficiently close to the completely mixed state of $n$ qudits.

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