Undergrad Peres-Horodecki criterion for a 3-qubit system

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SUMMARY

The Peres-Horodecki criterion is necessary and sufficient for determining entanglement in 2x2 and 2x3 density matrices but does not hold for 3-qubit systems represented by 8x8 matrices. Users should be cautious when applying this criterion to larger systems, as it may lead to incorrect conclusions about entanglement. The discussion references the original paper available at arxiv.org for further details.

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  • Understanding of quantum mechanics and entanglement concepts
  • Familiarity with density matrices and their representations
  • Knowledge of the Peres-Horodecki criterion and its applications
  • Basic skills in linear algebra, particularly with matrices
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  • Research the limitations of the Peres-Horodecki criterion for higher-dimensional systems
  • Study alternative methods for detecting entanglement in 3-qubit systems
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MMS
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Hello everyone,

Is the Peres-Horodecki criterion correct for any density matrix nxn?
I have a 3 qubit state (an 8x8 matrix) and I want to check whether it's entangled or not and I'm not sure if it's the right approach. Seems a little too cumbersome.

Thanks in advance.
 
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AFAIK the Peres criterion is sufficient for any density matrix, but it's if and only if only for 2 qubit density matrices, that is for your matrix it may fail and still you might have an entangled state
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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