Sanov theorem revisited

 

Generalised quantum Sanov theorem revisited

Ludovico Lami

Given two families of quantum states  and , called the null and the alternative hypotheses, quantum hypothesis testing is the task of determining whether an unknown quantum state belongs to  or . Mistaking  for  is a type I error, and vice versa for the type II error. In quantum Shannon theory, a fundamental role is played by the Stein exponent, i.e. the asymptotic rate of decay of the type II error probability for a given threshold on the type I error probability. Stein exponents have been thoroughly investigated -- and, sometimes, calculated. However, most currently available solutions apply to settings where the hypotheses simple (i.e. composed of a single state), or else the families  and  need to satisfy stringent constraints that exclude physically important sets of states, such as separable states or stabiliser states. In this work, we establish a general formula for the Stein exponent where both hypotheses are allowed to be composite: the alternative hypothesis  is assumed to be either composite i.i.d. or arbitrarily varying, with components taken from a known base set, while the null hypothesis  is fully general, and required to satisfy only weak compatibility assumptions that are met in most physically relevant cases -- for instance, by the sets of separable or stabiliser states. Our result extends and subsumes the findings of [BBH, CMP 385:55, 2021] (that we also simplify), as well as the 'generalised quantum Sanov theorem' of [LBR, arXiv:2408.07067]. The proof relies on a careful quantum-to-classical reduction via measurements, followed by an application of the results on classical Stein exponents obtained in [Lami, arXiv:today]. We also devise new purely quantum techniques to analyse the resulting asymptotic expressions.

RELATED

https://m.youtube.com/watch?v=cMl-xIDSmXI

 

Talk like a pirate day

 

Asymptotic quantification of entanglement with a single copy

Ludovico Lami, Mario Berta, Bartosz Regula

Despite the central importance of quantum entanglement in quantum technologies, the understanding of the optimal ways to exploit it is still beyond our reach, and even measuring entanglement in an operationally meaningful way is prohibitively difficult. Here we study two fundamental tasks in the processing of entanglement: entanglement testing, which is a quantum state discrimination problem concerned with entanglement detection in the many-copy regime, and entanglement distillation, concerned with purifying entanglement from noisy entangled states. We introduce a way of benchmarking the performance of distillation that focuses on the best achievable error rather than its yield in the asymptotic limit. When the underlying set of operations used for entanglement distillation is the axiomatic class of non-entangling operations, we show that the two figures of merit for entanglement testing and distillation coincide. We solve both problems by proving a generalised quantum Sanov's theorem, enabling the exact evaluation of asymptotic error rates of composite quantum hypothesis testing. We show in particular that the asymptotic figure of merit is given by the reverse relative entropy of entanglement, a single-letter quantity that can be evaluated using only a single copy of a quantum state -- a distinct feature among measures of entanglement that quantify the optimal performance of information-theoretic tasks.

https://www.nature.com/articles/s41567-026-03182-x

 

Fascinating reading

Can you hear the drums, Orlando?

 https://en.wikipedia.org/wiki/Crimea%3A_The_Last_Crusade

Tolstoy and Young Stalin synchronicities!

the pretext needed by the new Tsar Alexander to force it through against the reluctant landowners.

INTERVIEWER: The war left Russia with a resentment and suspicion towards the west. Is that right?

ORLANDO FIGES: It did - and this was a powerful factor in Russian attitudes towards the West which continues to this day. There was a strong sense of betrayal by the West which - for the first time in history - had sided with a Muslim power (the Ottoman Empire) against a Christian one (Russia). I think that this sense of resentment fed into the pan-Slav nationalism of the Russians in the later nineteenth century. It is there today in the Russian sense of Western 'double standards' that makes Russian nationalists like Putin so mistrustful of the West. The Tsar Nicholas I is admired by the Putinite regime - because he stood up to the West in defence of Russia's interests

Seth Lloyd endorsed

 Of course, of course.

Decoding Reality: The Universe as Quantum Information

by Vlatko Vedral (Oxford, £16.99)

With French-theory antennae primed, one thinks of Ferdinand de Saussure on reading this: "[T]he information content of anything does not reside in the object itself, but is a relational property of the object in connection with the rest of the Universe." Vedral himself takes pleasure in speculative connections between his own work in quantum-information theory and other realms – the book opens with a story from Italo Calvino, and takes in Nietzsche and the "negative theology" of the Cappadocian Fathers, as the author puts a computational twist on discussions of DNA, dieting and stock-market investing, as well as explaining entropy and quantum computing or teleportation

Nothing comes from nothing

  Creation ex nihilo comes from Catholic dogma, the idea being that God created the universe out of nothing. V. Vedral says that invoking a supernatural being as an explanation for creation does not explain reality because the supernatural being would have to come into existence itself too somehow presumably from nothing (or else from an infinite regression of supernatural beings), thus of course the reality can come from nothing without a supernatural being. Occam's razor principle favours the simplest explanation. Vedral believes information is the fundamental building block of reality as it occurs at the macro level (economics, human behaviour etc.) as well as the subatomic level. 

https://en.wikipedia.org/wiki/Decoding_Reality

There is also still more evidence for Hercules than Jesus so Xtians gfy

Marxist-communism as a national-socialist project

 Like Arduous March DPRK,  Cambodia year Zero,  Red Fascist Ethiopia,  etc, etc, etc, ad nauseum.

https://anthonyteso.substack.com/p/value-without-a-ruling-class-china?r=2sbdk&utm_campaign=post&utm_medium=web&triedRedirect=true

Its a Red- Brown Nazbols thing.

Cryptoanarchy the cure

 Decoding Reality: The Universe as Quantum Information 

https://en.wikipedia.org/wiki/Decoding_Reality

Previously on Hill st blues

Heinz Pagels is a physicist and science writer known for his book "The Cosmic Code: Quantum Physics as the Language of Nature." In this book, Pagels explains fundamental concepts of quantum mechanics in an accessible manner, making complex ideas understandable to a general audience. The book discusses the history of quantum physics and addresses significant topics such as Bell's theorem and elementary particle physics, drawing on the work of various influential scientists. Pagels was also an Adjunct Professor of Physics at Rockefeller University and served as the Executive Director of the New York Academy of Sciences. 

The impossible we do right away. Cracking quantum crypto takes slightly longer.