dorsal/arxiv
View SchemaKnowledge excess duality and violation of Bell inequalities
| Authors | R. Filip, M. Gavenda |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0404145 |
| URL | https://arxiv.org/abs/quant-ph/0404145 |
Abstract
A constraint on two complementary knowledge excesses by maximal violation of Bell inequalities for a single copy of any mixed state of two qubits $S,M$ is analyzed. The complementary knowledge excesses ${\bf \Delta K}(\Pi_{M}\to \Pi_{S})$ and ${\bf \Delta K}(\Pi'_{M}\to \Pi'_{S})$ quantify an enhancement of ability to predict results of the complementary projective measurements $\Pi_{S},\Pi'_{S}$ on the qubit $S$ from the projective measurements $\Pi_{M},\Pi'_{M}$ performed on the qubit $M$. For any state $\rho_{SM}$ and for arbitrary $\Pi_{S},\Pi'_{S}$ and $\Pi_{M},\Pi'_{M}$, the knowledge excesses satisfy the following inequality ${\bf \Delta K}^{2}(\Pi_{M}\to \Pi_{S})+{\bf \Delta K}^{2} (\Pi'_{M}\to \Pi'_{S})\leq (B_{max}/2)^2$, where $B_{max}$ is maximum of violation of Bell inequalities under single-copy local operations (local filtering and unitary transformations). Particularly, for the Bell-diagonal states only an appropriate choice of the measurements $\Pi_{S},\Pi'_{S}$ and $\Pi_{M},\Pi'_{M}$ are sufficient to saturate the inequality.
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"abstract": "A constraint on two complementary knowledge excesses by maximal violation of\nBell inequalities for a single copy of any mixed state of two qubits $S,M$ is\nanalyzed. The complementary knowledge excesses ${\\bf \\Delta K}(\\Pi_{M}\\to\n\\Pi_{S})$ and ${\\bf \\Delta K}(\\Pi\u0027_{M}\\to \\Pi\u0027_{S})$ quantify an enhancement of\nability to predict results of the complementary projective measurements\n$\\Pi_{S},\\Pi\u0027_{S}$ on the qubit $S$ from the projective measurements\n$\\Pi_{M},\\Pi\u0027_{M}$ performed on the qubit $M$. For any state $\\rho_{SM}$ and\nfor arbitrary $\\Pi_{S},\\Pi\u0027_{S}$ and $\\Pi_{M},\\Pi\u0027_{M}$, the knowledge excesses\nsatisfy the following inequality ${\\bf \\Delta K}^{2}(\\Pi_{M}\\to \\Pi_{S})+{\\bf\n\\Delta K}^{2} (\\Pi\u0027_{M}\\to \\Pi\u0027_{S})\\leq (B_{max}/2)^2$, where $B_{max}$ is\nmaximum of violation of Bell inequalities under single-copy local operations\n(local filtering and unitary transformations). Particularly, for the\nBell-diagonal states only an appropriate choice of the measurements\n$\\Pi_{S},\\Pi\u0027_{S}$ and $\\Pi_{M},\\Pi\u0027_{M}$ are sufficient to saturate the\ninequality.",
"arxiv_id": "quant-ph/0404145",
"authors": [
"R. Filip",
"M. Gavenda"
],
"categories": [
"quant-ph"
],
"title": "Knowledge excess duality and violation of Bell inequalities",
"url": "https://arxiv.org/abs/quant-ph/0404145"
},
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