dorsal/arxiv
View SchemaOptimal superbroadcasting of mixed qubit states
| Authors | Francesco Buscemi, Giacomo Mauro D'Ariano, Chiara Macchiavello, Paolo Perinotti |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510155 |
| URL | https://arxiv.org/abs/quant-ph/0510155 |
Abstract
"Broadcasting", namely distributing information over many users, suffers in-principle limitations when the information is quantum. This poses a critical issue in quantum information theory, for distributed processing and networked communications. For pure states ideal broadcasting coincides with the so-called "quantum cloning", describing an hypothetical ideal device capable of producing from a finite number N of copies of a state (drawn from a set) a larger number M>N of output copies of the same state. Since such a transformation is not isometric, it cannot be achieved by any physical machine for a quantum state drawn from a non orthogonal set: this is essentially the content of the "no-cloning" theorem. For mixed states the situation is quite different, since from the point of view of each single user a local marginal mixed state is indistinguishable from the partial trace of an entangled state, and there are infinitely many joint output states that correspond to ideal broadcasting. Indeed, for sufficiently large number $N$ of input copies, not only ideal broadcasting of noncommuting mixed states is possible, but one can even purify the state in the process. Such state purification with an increasing number of copies has been named "superbroadcasting". In this paper we will review some recent results on superbroadcasting of qubits, for two different sets of input states, corresponding to universally covariant broadcasting and to phase-covariant broadcasting of equatorial states.
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"abstract": "\"Broadcasting\", namely distributing information over many users, suffers\nin-principle limitations when the information is quantum. This poses a critical\nissue in quantum information theory, for distributed processing and networked\ncommunications. For pure states ideal broadcasting coincides with the so-called\n\"quantum cloning\", describing an hypothetical ideal device capable of producing\nfrom a finite number N of copies of a state (drawn from a set) a larger number\nM\u003eN of output copies of the same state. Since such a transformation is not\nisometric, it cannot be achieved by any physical machine for a quantum state\ndrawn from a non orthogonal set: this is essentially the content of the\n\"no-cloning\" theorem. For mixed states the situation is quite different, since\nfrom the point of view of each single user a local marginal mixed state is\nindistinguishable from the partial trace of an entangled state, and there are\ninfinitely many joint output states that correspond to ideal broadcasting.\nIndeed, for sufficiently large number $N$ of input copies, not only ideal\nbroadcasting of noncommuting mixed states is possible, but one can even purify\nthe state in the process. Such state purification with an increasing number of\ncopies has been named \"superbroadcasting\". In this paper we will review some\nrecent results on superbroadcasting of qubits, for two different sets of input\nstates, corresponding to universally covariant broadcasting and to\nphase-covariant broadcasting of equatorial states.",
"arxiv_id": "quant-ph/0510155",
"authors": [
"Francesco Buscemi",
"Giacomo Mauro D\u0027Ariano",
"Chiara Macchiavello",
"Paolo Perinotti"
],
"categories": [
"quant-ph"
],
"title": "Optimal superbroadcasting of mixed qubit states",
"url": "https://arxiv.org/abs/quant-ph/0510155"
},
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