Joint quantum entropy

<p>The joint quantum entropy generalizes the classical <a href="/facts/Joint_entropy/V4WwuX6P">joint entropy</a> to the context of <a href="/facts/Quantum_information_theory/Bl9QIvHj">quantum information theory</a>.  Intuitively, given two <a href="/facts/Quantum_state/7jbxd7Dx">quantum states</a> 
  
    
      
        ρ
      
    
    {\displaystyle \rho }
  
 and 
  
    
      
        σ
      
    
    {\displaystyle \sigma }
  
, represented as <a href="/facts/Density_operator/A1XdylJa">density operators</a> that are subparts of a quantum system, the joint quantum entropy is a measure of the total uncertainty or <a href="/facts/Entropy/s52IXeFz">entropy</a> of the joint system. It is written 
  
    
      
        S
        (
        ρ
        ,
        σ
        )
      
    
    {\displaystyle S(\rho ,\sigma )}
  
 or 
  
    
      
        H
        (
        ρ
        ,
        σ
        )
      
    
    {\displaystyle H(\rho ,\sigma )}
  
, depending on the notation being used for the <a href="/facts/Von_Neumann_entropy/nzeJKowg">von Neumann entropy</a>.  Like other entropies, the joint quantum entropy is measured in <a href="/facts/Bit/RwfjaYSv">bits</a>, i.e. the logarithm is taken in base 2.
</p><p>In this article, we will use 
  
    
      
        S
        (
        ρ
        ,
        σ
        )
      
    
    {\displaystyle S(\rho ,\sigma )}
  
 for the joint quantum entropy.
</p>

Joint quantum entropy open-in-new

Joint quantum entropy