The asymptotic spectrum of LOCC transformations

We study exact, non-deterministic conversion of multipartite pure quantum states into one-another via local operations and classical communication (LOCC) and asymptotic entanglement transformation under such channels. In particular, we consider the maximal number of copies of any given target state that can be extracted exactly from many copies of any given initial state as a function of the exponential decay in success probability, known as the converese error exponent. We give a formula for the optimal rate presented as an infimum over the asymptotic spectrum of LOCC conversion. A full understanding of exact asymptotic extraction rates between pure states in the converse regime thus depends on a full understanding of this spectrum. We present a characterisation of spectral points and use it to describe the spectrum in the bipartite case. This leads to a full description of the spectrum and thus an explicit formula for the asymptotic extraction rate between pure bipartite states, given a converse error exponent. This extends the result on entanglement concentration in [Hayashi et al, 2003], where the target state is fixed as the Bell state. In the limit of vanishing converse error exponent the rate formula provides an upper bound on the exact asymptotic extraction rate between two states, when the probability of success goes to 1. In the bipartite case we prove that this bound holds with equality.Comment: v1: 21 pages v2: 21 pages, Minor corrections v3: 17 pages, Minor corrections, new reference added, parts of Section 5 and the Appendix removed, the omitted material can be found in an extended form in arXiv:1808.0515

Tensor rank is not multiplicative under the tensor product

The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection between restrictions and degenerations. A result of our study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specifically, if a tensor t has border rank strictly smaller than its rank, then the tensor rank of t is not multiplicative under taking a sufficiently hight tensor product power. The "tensor Kronecker product" from algebraic complexity theory is related to our tensor product but different, namely it multiplies two k-tensors to get a k-tensor. Nonmultiplicativity of the tensor Kronecker product has been known since the work of Strassen. It remains an open question whether border rank and asymptotic rank are multiplicative under the tensor product. Interestingly, lower bounds on border rank obtained from generalised flattenings (including Young flattenings) multiply under the tensor product

“Paul and Mary Would Like You to Bake”: Heritage Television, Englishness, and an Idealized Multicultural National Identity

In a time of devolution and fragmentation in the UK, The Great British Bake Off plays into the elements of heritage film and imperial nostalgia and especially all things considered ‘English’. However, the show also attempts to include a more diverse representation of the British people and recreate a national identity that leaves more space for ethnic minorities. Linking theories on national identity and theories on heritage film, this article examines how the GBBO format acts as heritage television which idealizes certain aspects of English history, as well as how the inclusion and celebration of contestants with an ethnic minority background adds to a portrayal of an idealized form of British multiculturalism. These findings lay the basis for a discussion on the connection between food culture and multiculturalism, and how GBBO tries to combine the past ‘glory’ of England with the present (multicultural) reality of Britain

The Ambiguous Portrayal of Nature in Annihilation

This article examines how Alex Garland’s science fiction horror film Annihilation (2018) works as a form of eco-media, and how it has potential to influence its audience in a positive direction. I argue that the portrayal of nature in the film, from the different horror genres at play, to the themes of disease, destruction and renewal, and the stunning but eerie visuals, challenge the conceptions we have of the environment and climate change, and invites the audience to rethink the relationship between nature and humans