W-state

= Definition = In [[Quantum information science - theory|quantum information theory]], '''W-[[states]]''' of $n$ [[qubits]] are defined as : $|W\backslash rangle\; =\; \backslash frac\{1\}\{\backslash sqrt\{n\}\}\backslash left(|100\backslash dots\; 0\backslash rangle\; +\; |010\backslash dots\; 0\backslash rangle\; +\; \backslash dots\; +\; |00\backslash dots\; 1\backslash rangle\backslash right)$ = Properties = One of the main properties of the W-[[states]] is concerned with type of [[Theory of entanglement|entanglement]] encoding this [[states|states]]. == Three qubits == Regarding to three qubits scenario: $|W\backslash rangle\; =\; \backslash frac\{1\}\{\backslash sqrt\{3\}\}\backslash left(|100\backslash rangle\; +\; |010\backslash rangle\; +\; |001\backslash rangle\backslash right)$ the way of entanglement encoding in W-states can be easy illustrated on a picture. [[image:BildchenW.jpg|thumb|right|type of entanglement in W-states]] There is no generic three qubit entanglement in W-states and all [[Entanglement monotone|entanglement monotones]] as well as their [[LOCC operations|normal form]] will be equal to zero. However tracing out one of the parties leaves the remaing two entangled. In this sense three qubit W-states contain maximal amount of sum of two qubit entanglement. Referring to the [[LOCC operations|equivalence classes]] W-states define a complemetary class to the [[GHZ]]-states. == General situation == In general case one can speak about ''W-type'' of encoding of entanglement, which means that one deals with some [[Pure states|pure state]] of $n$ qubits which contains no generic $n$ qubit entanglement but rather $m$ qubit, where $m.\; =\; Physical\; realizations\; =\; W-states\; are\; known\; to\; realize\; first\; excitation\; over\; the\; [http://en.wikipedia.org/wiki/Ground\_state\; ground\; state]\; of\; free\; spinless\; [http://en.wikipedia.org/wiki/Fermion\; fermions]\; confined\; to\; one\; dimensional\; chain,\; which\; are\; described\; by\; the\; following\; Hamiltioan\; :$ H^F=-\backslash sum\_iJ\_\{i,i+1\}c^\{\backslash dagger\}\_i\; c\_\{i+1\}$.\; Due\; to\; the\; progress\; made\; in\; physics\; of\; cold\; atoms\; this\; kind\; of\; systems\; can\; be\; pretty\; easily\; produced\; experimentally,\; using\; for\; instance\; trapping\; techniques\; for\; atoms\; and\; putting\; those\; into\; one\; dimensional\; [[Optical\; Lattices|optical\; lattice]].\; [[Category:Handbook\; of\; Quantum\; Information]]$