1,706,112 research outputs found
A Schmidt number for density matrices
We introduce the notion of a Schmidt number of a bipartite density matrix,
characterizing the minimum Schmidt rank of the pure states that are needed to
construct the density matrix. We prove that Schmidt number is nonincreasing
under local quantum operations and classical communication. We show that
-positive maps witness Schmidt number, in the same way that positive maps
witness entanglement. We show that the family of states which is made from
mixing the completely mixed state and a maximally entangled state have
increasing Schmidt number depending on the amount of maximally entangled state
that is mixed in. We show that Schmidt number {\it does not necessarily
increase} when taking tensor copies of a density matrix ; we give an
example of a density matrix for which the Schmidt numbers of and are both 2.Comment: 5 pages RevTex, 1 typo in Proof Lemma 1 correcte
Schmidt balls around the identity
Robustness measures as introduced by Vidal and Tarrach [PRA, 59, 141-155]
quantify the extent to which entangled states remain entangled under mixing.
Analogously, we introduce here the Schmidt robustness and the random Schmidt
robustness. The latter notion is closely related to the construction of Schmidt
balls around the identity. We analyse the situation for pure states and provide
non-trivial upper and lower bounds. Upper bounds to the random Schmidt-2
robustness allow us to construct a particularly simple distillability
criterion. We present two conjectures, the first one is related to the radius
of inner balls around the identity in the convex set of Schmidt number
n-states. We also conjecture a class of optimal Schmidt witnesses for pure
states.Comment: 7 pages, 1 figur
Character of Locally Inequivalent Classes of States and Entropy of Entanglement
In this letter we have established the physical character of pure bipartite
states with the same amount of entanglement in the same Schmidt rank that
either they are local unitarily connected or they are incomparable. There exist
infinite number of deterministically locally inequivalent classes of pure
bipartite states in the same Schmidt rank (starting from three) having same
amount of entanglement. Further, if there exists incomparable states with same
entanglement in higher Schmidt ranks (greater than three), then they should
differ in at least three Schmidt coefficients.Comment: 4 pages, revtex4, no figure, accepted in Physical Review A (rapid
communications
Unique Quantum Paths by Continuous Diagonalization of the Density Operator
In this short note we show that for a Markovian open quantum system it is
always possible to construct a unique set of perfectly consistent Schmidt
paths, supporting quasi-classicality. Our Schmidt process, elaborated several
years ago, is the limit of the Schmidt chain constructed very
recently by Paz and Zurek.Comment: 8 pages REVTe
Existence of the Schmidt decomposition for tripartite systems
For any bipartite quantum system the Schmidt decomposition allows us to
express the state vector in terms of a single sum instead of double sums. We
show the existence of the Schmidt decomposition for tripartite system under
certain condition. If the partial inner product of a basis (belonging to a
Hilbert space of smaller dimension) with the state of the composite system
gives a disentangled basis, then the Schmidt decomposition for a tripartite
system exists. In this case the reduced density matrix of each of the subsystem
has equal spectrum in the Schmidt basis.Comment: Latex prerpint style, 7 page
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