dorsal/arxiv
View SchemaInvertible Quantum Operations and Perfect Encryption of Quantum States
| Authors | Ashwin Nayak, Pranab Sen |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0605041 |
| URL | https://arxiv.org/abs/quant-ph/0605041 |
Abstract
In this note, we characterize the form of an invertible quantum operation, i.e., a completely positive trace preserving linear transformation (a CPTP map) whose inverse is also a CPTP map. The precise form of such maps becomes important in contexts such as self-testing and encryption. We show that these maps correspond to applying a unitary transformation to the state along with an ancilla initialized to a fixed state, which may be mixed. The characterization of invertible quantum operations implies that one-way schemes for encrypting quantum states using a classical key may be slightly more general than the ``private quantum channels'' studied by Ambainis, Mosca, Tapp and de Wolf (FOCS 2000). Nonetheless, we show that their results, most notably a lower bound of 2n bits of key to encrypt n quantum bits, extend in a straightforward manner to the general case.
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"abstract": "In this note, we characterize the form of an invertible quantum operation,\ni.e., a completely positive trace preserving linear transformation (a CPTP map)\nwhose inverse is also a CPTP map. The precise form of such maps becomes\nimportant in contexts such as self-testing and encryption. We show that these\nmaps correspond to applying a unitary transformation to the state along with an\nancilla initialized to a fixed state, which may be mixed.\n The characterization of invertible quantum operations implies that one-way\nschemes for encrypting quantum states using a classical key may be slightly\nmore general than the ``private quantum channels\u0027\u0027 studied by Ambainis, Mosca,\nTapp and de Wolf (FOCS 2000). Nonetheless, we show that their results, most\nnotably a lower bound of 2n bits of key to encrypt n quantum bits, extend in a\nstraightforward manner to the general case.",
"arxiv_id": "quant-ph/0605041",
"authors": [
"Ashwin Nayak",
"Pranab Sen"
],
"categories": [
"quant-ph",
"cs.CR",
"cs.IT",
"math.IT"
],
"title": "Invertible Quantum Operations and Perfect Encryption of Quantum States",
"url": "https://arxiv.org/abs/quant-ph/0605041"
},
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