
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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 Jess Riedel Sure, but there are thousands of different fields/techniques/specialties that are as likely to contribute as... – Feb 14, 6:36 PM
 Eemaan Thind Understanding of fluid dynamics is critical in testing the efficacy of microcantilever sensors for detection... – Feb 14, 6:15 PM
 Comments on Weingarten's preferred branch (19)
 Jess Riedel (5) Unfortunately, I still don't think this is a great framing of the problem that... – Dec 22, 11:57 AM
 Jess Riedel (4) > The derivation of branching we agree remains an incomplete project... But for sure... – Dec 22, 11:56 AM
 Jess Riedel (3) I would very much like to read your 1973 preprint! Please reconsider uploading it.... – Dec 22, 11:55 AM
 Jess Riedel (2) > There is an ensemble of possible final states. I just reach my hand... – Dec 22, 11:55 AM
 Jess Riedel (1) > Construction of branches from environmentally induced decoherence... is intrinsically approximate and requires the... – Dec 22, 11:50 AM
 Don Weingarten Finally, I think you are right that my proposed account of the preferred basis problem... – Dec 17, 5:18 PM
 Don Weingarten 4) As far as eventual thermalization of everything, I pretty much agree with your list... – Dec 17, 5:06 PM
 Don Weingarten 3) Consistent histories: Ugh. A sore point. I think I am actually by some measure... – Dec 17, 5:02 PM
 Don Weingarten 2) Not sure I understand your point about adding entropy. There is an ensemble of... – Dec 17, 4:59 PM
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