dorsal/arxiv
View SchemaAccessible versus Holevo Information for a Binary Random Variable
| Authors | Rahul Jain, Ashwin Nayak |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603278 |
| URL | https://arxiv.org/abs/quant-ph/0603278 |
Abstract
The accessible information acc(E) of an ensemble E is the maximum mutual information between a random variable encoded into quantum states, and the probabilistic outcome of a quantum measurement of the encoding. Accessible information is extremely difficult to characterize analytically; even bounds on it are hard to place. The celebrated Holevo bound states that accessible information cannot exceed chi(E), the quantum mutual information between the random variable and its encoding. However, for general ensembles, the gap between the acc(E) and chi(E) may be arbitrarily large. We consider the special case of a binary random variable, which often serves as a stepping stone towards other results in information theory and communication complexity. We give explicit lower bounds on the the accessible information acc(E) of an ensemble E = {(p, rho_0), (1-p, rho_1)}, with 0 <= p <= 1, as functions of p and chi(E). The bounds are incomparable in the sense that they surpass each other in different parameter regimes. Our bounds arise by measuring the ensemble according to a complete orthogonal measurement that preserves the fidelity of the states rho_0,rho_1. As an intermediate step, therefore, we give new relations between the two quantities acc(E), chi(E) and the fidelity B(rho_0,rho_1).
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"abstract": "The accessible information acc(E) of an ensemble E is the maximum mutual\ninformation between a random variable encoded into quantum states, and the\nprobabilistic outcome of a quantum measurement of the encoding. Accessible\ninformation is extremely difficult to characterize analytically; even bounds on\nit are hard to place. The celebrated Holevo bound states that accessible\ninformation cannot exceed chi(E), the quantum mutual information between the\nrandom variable and its encoding. However, for general ensembles, the gap\nbetween the acc(E) and chi(E) may be arbitrarily large.\n We consider the special case of a binary random variable, which often serves\nas a stepping stone towards other results in information theory and\ncommunication complexity. We give explicit lower bounds on the the accessible\ninformation acc(E) of an ensemble E = {(p, rho_0), (1-p, rho_1)}, with 0 \u003c= p\n\u003c= 1, as functions of p and chi(E). The bounds are incomparable in the sense\nthat they surpass each other in different parameter regimes.\n Our bounds arise by measuring the ensemble according to a complete orthogonal\nmeasurement that preserves the fidelity of the states rho_0,rho_1. As an\nintermediate step, therefore, we give new relations between the two quantities\nacc(E), chi(E) and the fidelity B(rho_0,rho_1).",
"arxiv_id": "quant-ph/0603278",
"authors": [
"Rahul Jain",
"Ashwin Nayak"
],
"categories": [
"quant-ph"
],
"title": "Accessible versus Holevo Information for a Binary Random Variable",
"url": "https://arxiv.org/abs/quant-ph/0603278"
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