dorsal/arxiv
View SchemaLocal asymptotic normality for qubit states
| Authors | Madalin Guta, Jonas Kahn |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512075 |
| URL | https://arxiv.org/abs/quant-ph/0512075 |
| DOI | 10.1103/PhysRevA.73.052108 |
| Journal | Phys. Rev. A, 73, 052108 (2006) |
Abstract
We consider n identically prepared qubits and study the asymptotic properties of the joint state \rho^{\otimes n}. We show that for all individual states \rho situated in a local neighborhood of size 1/\sqrt{n} of a fixed state \rho^0, the joint state converges to a displaced thermal equilibrium state of a quantum harmonic oscillator. The precise meaning of the convergence is that there exist physical transformations T_{n} (trace preserving quantum channels) which map the qubits states asymptotically close to their corresponding oscillator state, uniformly over all states in the local neighborhood. A few consequences of the main result are derived. We show that the optimal joint measurement in the Bayesian set-up is also optimal within the pointwise approach. Moreover, this measurement converges to the heterodyne measurement which is the optimal joint measurement of position and momentum for the quantum oscillator. A problem of local state discrimination is solved using local asymptotic normality.
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"abstract": "We consider n identically prepared qubits and study the asymptotic properties\nof the joint state \\rho^{\\otimes n}. We show that for all individual states\n\\rho situated in a local neighborhood of size 1/\\sqrt{n} of a fixed state\n\\rho^0, the joint state converges to a displaced thermal equilibrium state of a\nquantum harmonic oscillator. The precise meaning of the convergence is that\nthere exist physical transformations T_{n} (trace preserving quantum channels)\nwhich map the qubits states asymptotically close to their corresponding\noscillator state, uniformly over all states in the local neighborhood.\n A few consequences of the main result are derived. We show that the optimal\njoint measurement in the Bayesian set-up is also optimal within the pointwise\napproach. Moreover, this measurement converges to the heterodyne measurement\nwhich is the optimal joint measurement of position and momentum for the quantum\noscillator. A problem of local state discrimination is solved using local\nasymptotic normality.",
"arxiv_id": "quant-ph/0512075",
"authors": [
"Madalin Guta",
"Jonas Kahn"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.73.052108",
"journal_ref": "Phys. Rev. A, 73, 052108 (2006)",
"title": "Local asymptotic normality for qubit states",
"url": "https://arxiv.org/abs/quant-ph/0512075"
},
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