
Modewise entanglement of Gaussian states
Alonso Botero and Benni ReznikWe address the decomposition of a multimode pure Gaussian state with respect to a bipartite division of the modes. For any such division the state can always be expressed as a product state involving entangled twomode squeezed states and singlemode local states at each side. The character of entanglement of the state can therefore be understood modewise; that is, a given mode on one side is entangled with only one corresponding mode of the other, and therefore the total bipartite entanglement is the sum of the modewise entanglement. This decomposition is generally not applicable to all mixed Gaussian states. However, the result can be extended to a special family of “isotropic” states, characterized by a phase space covariance matrix with a completely degenerate symplectic spectrum.It is well known that, despite the misleading imagery conjured by the name, entanglement in a multipartite system cannot be understood in terms of pairwise entanglement of the parts. Indeed, there are only pairs of systems, but the number of qualitatively distinct types of entanglement scales exponentially in . A good way to think about this is to recognize that a quantum state of a multipartite system is, in terms of parameters, much more akin to a classical probability distribution than a classical state. When we ask about the information stored in a probability distributions, there are lots and lots of “types” of information, and correlations can be much more complex than just knowing all the pairwise correlations. (“It’s not just that A knows something about B, it’s that A knows something about B conditional on a state of C, and that information can only be unlocked by knowing information from either D or E, depending on the state of F…”).
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 Comments on Weingarten's preferred branch (4)
 Jess Riedel Also, as a separate issue, note that the "branch decomposition ambiguity" you describe in Eq.... – Nov 22, 9:41 PM
 Jess Riedel Hi Don, Thanks very much for your comments, and sorry for the big delay in... – Nov 22, 8:38 PM
 Don Weingarten Hi Jess, 1. I agree that the fuzziness of manyworlds + decoherence is simply repackaged.... – Oct 31, 11:31 PM
 Legendre transform (4)
 Jess Riedel I'm looking at Volume 1 of the 1989 edition and I can't find a picture.... – Oct 12, 1:23 PM
 M. Ouwehand I remember seeing an picture like yours (areas under and to the left of the... – Oct 12, 8:08 AM
 Branches and matrixproduct states (6)
 Jess Riedel This prompted me to take an old email where I listed some models of branching... – Oct 12, 3:16 AM
 interstice Thanks. Do you know of any systems, toy or real, where we can identify a... – Oct 11, 10:06 PM
 Jess Riedel Great question. It is not obvious that we should define branches from the tensor structure... – Oct 10, 8:00 PM
 interstice Right, so to argue that the branches evolve independently, one must first define what branches... – Oct 10, 4:19 PM
 Jess Riedel You're right that the criteria for defining branches I give in the paper doesn't make... – Oct 05, 2:33 PM
 Comments on Weingarten's preferred branch (4)
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