dorsal/arxiv
View Schema`Lazy' quantum ensembles
| Authors | George Parfionov, Roman Zapatrin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603019 |
| URL | https://arxiv.org/abs/quant-ph/0603019 |
| DOI | 10.1088/0305-4470/39/34/019 |
| Journal | J. Phys. A: Math. Gen. 39 10891-10900 (2006) |
Abstract
We compare different strategies aimed to prepare an ensemble with a given density matrix $\rho$. Preparing the ensemble of eigenstates of $\rho$ with appropriate probabilities can be treated as `generous' strategy: it provides maximal accessible information about the state. Another extremity is the so-called `Scrooge' ensemble, which is mostly stingy to share the information. We introduce `lazy' ensembles which require minimal efforts to prepare the density matrix by selecting pure states with respect to completely random choice. We consider two parties, Alice and Bob, playing a kind of game. Bob wishes to guess which pure state is prepared by Alice. His null hypothesis, based on the lack of any information about Alice's intention, is that Alice prepares any pure state with equal probability. Then, the average quantum state measured by Bob turns out to be $\rho$, and he has to make a new hypothesis about Alice's intention solely based on the information that the observed density matrix is $\rho$. The arising `lazy' ensemble is shown to be the alternative hypothesis which minimizes the Type I error.
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"abstract": "We compare different strategies aimed to prepare an ensemble with a given\ndensity matrix $\\rho$. Preparing the ensemble of eigenstates of $\\rho$ with\nappropriate probabilities can be treated as `generous\u0027 strategy: it provides\nmaximal accessible information about the state. Another extremity is the\nso-called `Scrooge\u0027 ensemble, which is mostly stingy to share the information.\nWe introduce `lazy\u0027 ensembles which require minimal efforts to prepare the\ndensity matrix by selecting pure states with respect to completely random\nchoice.\n We consider two parties, Alice and Bob, playing a kind of game. Bob wishes to\nguess which pure state is prepared by Alice. His null hypothesis, based on the\nlack of any information about Alice\u0027s intention, is that Alice prepares any\npure state with equal probability. Then, the average quantum state measured by\nBob turns out to be $\\rho$, and he has to make a new hypothesis about Alice\u0027s\nintention solely based on the information that the observed density matrix is\n$\\rho$. The arising `lazy\u0027 ensemble is shown to be the alternative hypothesis\nwhich minimizes the Type I error.",
"arxiv_id": "quant-ph/0603019",
"authors": [
"George Parfionov",
"Roman Zapatrin"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/39/34/019",
"journal_ref": "J. Phys. A: Math. Gen. 39 10891-10900 (2006)",
"title": "`Lazy\u0027 quantum ensembles",
"url": "https://arxiv.org/abs/quant-ph/0603019"
},
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