dorsal/arxiv
View SchemaRemote operations and interactions for systems of arbitrary dimensional Hilbert space: a state-operator approach
| Authors | Benni Reznik, Yakir Aharonov, Berry Groisman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0107143 |
| URL | https://arxiv.org/abs/quant-ph/0107143 |
| DOI | 10.1103/PhysRevA.65.032312 |
| Journal | Phys. Rev. A 65, 032312 (2002). |
Abstract
We present a systematic simple method for constructing deterministic remote operations on single and multiple systems of arbitrary discrete dimensionality. These operations include remote rotations, remote interactions and measurements. The resources needed for an operation on a two-level system are one ebit and a bidirectional communication of two cbits, and for an n-level system, a pair of entangled n-level particles and two classical ``nits''. In the latter case, there are $n-1$ possible distinct operations per one n-level entangled pair. Similar results apply for generating interaction between a pair of remote systems and for remote measurements. We further consider remote operations on $N$ spatially distributed systems, and show that the number of possible distinct operations increases here exponentially, with the available number of entangled pairs that are initial distributed between the systems. Our results follow from the properties of a hybrid state-operator object (``stator''), which describes quantum correlations between states and operations.
{
"annotation_id": "acd228d2-58e1-4d94-8664-f7d4579954b6",
"date_created": "2026-03-02T18:01:46.089000Z",
"date_modified": "2026-03-02T18:01:46.089000Z",
"file_hash": "2728d1dd5a20784a33c1f66a2654d2b050a50b57035c64cb9cc3d7be4e505234",
"private": false,
"record": {
"abstract": "We present a systematic simple method for constructing deterministic remote\noperations on single and multiple systems of arbitrary discrete dimensionality.\nThese operations include remote rotations, remote interactions and\nmeasurements. The resources needed for an operation on a two-level system are\none ebit and a bidirectional communication of two cbits, and for an n-level\nsystem, a pair of entangled n-level particles and two classical ``nits\u0027\u0027. In\nthe latter case, there are $n-1$ possible distinct operations per one n-level\nentangled pair. Similar results apply for generating interaction between a pair\nof remote systems and for remote measurements. We further consider remote\noperations on $N$ spatially distributed systems, and show that the number of\npossible distinct operations increases here exponentially, with the available\nnumber of entangled pairs that are initial distributed between the systems. Our\nresults follow from the properties of a hybrid state-operator object\n(``stator\u0027\u0027), which describes quantum correlations between states and\noperations.",
"arxiv_id": "quant-ph/0107143",
"authors": [
"Benni Reznik",
"Yakir Aharonov",
"Berry Groisman"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.65.032312",
"journal_ref": "Phys. Rev. A 65, 032312 (2002).",
"title": "Remote operations and interactions for systems of arbitrary dimensional Hilbert space: a state-operator approach",
"url": "https://arxiv.org/abs/quant-ph/0107143"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "e7b93091-7a66-41a3-a4cc-b95f90f7bb47",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}