dorsal/arxiv
View SchemaA priori probability that a qubit-qutrit pair is separable
| Authors | Paul B. Slater |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0211150 |
| URL | https://arxiv.org/abs/quant-ph/0211150 |
| DOI | 10.1088/1464-4266/5/6/018 |
| Journal | Journal of Optics B: Quantum and Semiclassical Optics, volume 5, issue 6, pages S651-S656 (2003) |
Abstract
We extend to arbitrarily coupled pairs of qubits (two-state quantum systems) and qutrits (three-state quantum systems) our earlier study (quant-ph/0207181), which was concerned with the simplest instance of entangled quantum systems, pairs of qubits. As in that analysis -- again on the basis of numerical (quasi-Monte Carlo) integration results, but now in a still higher-dimensional space (35-d vs. 15-d) -- we examine a conjecture that the Bures/SD (statistical distinguishability) probability that arbitrarily paired qubits and qutrits are separable (unentangled) has a simple exact value, u/(v Pi^3)= >.00124706, where u = 2^20 3^3 5 7 and v = 19 23 29 31 37 41 43 (the product of consecutive primes). This is considerably less than the conjectured value of the Bures/SD probability, 8/(11 Pi^2) = 0736881, in the qubit-qubit case. Both of these conjectures, in turn, rely upon ones to the effect that the SD volumes of separable states assume certain remarkable forms, involving "primorial" numbers. We also estimate the SD area of the boundary of separable qubit-qutrit states, and provide preliminary calculations of the Bures/SD probability of separability in the general qubit-qubit-qubit and qutrit-qutrit cases.
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"abstract": "We extend to arbitrarily coupled pairs of qubits (two-state quantum systems)\nand qutrits (three-state quantum systems) our earlier study (quant-ph/0207181),\nwhich was concerned with the simplest instance of entangled quantum systems,\npairs of qubits. As in that analysis -- again on the basis of numerical\n(quasi-Monte Carlo) integration results, but now in a still higher-dimensional\nspace (35-d vs. 15-d) -- we examine a conjecture that the Bures/SD (statistical\ndistinguishability) probability that arbitrarily paired qubits and qutrits are\nseparable (unentangled) has a simple exact value, u/(v Pi^3)= \u003e.00124706, where\nu = 2^20 3^3 5 7 and v = 19 23 29 31 37 41 43 (the product of consecutive\nprimes). This is considerably less than the conjectured value of the Bures/SD\nprobability, 8/(11 Pi^2) = 0736881, in the qubit-qubit case. Both of these\nconjectures, in turn, rely upon ones to the effect that the SD volumes of\nseparable states assume certain remarkable forms, involving \"primorial\"\nnumbers. We also estimate the SD area of the boundary of separable qubit-qutrit\nstates, and provide preliminary calculations of the Bures/SD probability of\nseparability in the general qubit-qubit-qubit and qutrit-qutrit cases.",
"arxiv_id": "quant-ph/0211150",
"authors": [
"Paul B. Slater"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1464-4266/5/6/018",
"journal_ref": "Journal of Optics B: Quantum and Semiclassical Optics, volume 5,\n issue 6, pages S651-S656 (2003)",
"title": "A priori probability that a qubit-qutrit pair is separable",
"url": "https://arxiv.org/abs/quant-ph/0211150"
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