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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2506.01903 |
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| _version_ | 1866908389718622208 |
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| author | Lin, Han-Hsuan de Wolf, Ronald |
| author_facet | Lin, Han-Hsuan de Wolf, Ronald |
| contents | A quantum random access code (QRAC) is a map $x\mapstoρ_x$ that encodes $n$-bit strings $x$ into $m$-qubit quantum states $ρ_x$, in a way that allows us to recover any one bit of $x$ with success probability $\geq p$. The measurement on $ρ_x$ that is used to recover, say, $x_1$ may destroy all the information about the other bits; this is in fact what happens in the well-known QRAC that encodes $n=2$ bits into $m=1$ qubits. Does this generalize to large $n$, i.e., could there exist QRACs that are so "obfuscated" that one cannot get much more than one bit out of them? Here we show that this is not the case: for every QRAC there exists a measurement that (with high probability) recovers the full $n$-bit string $x$ up to small Hamming distance, even for the worst-case $x$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01903 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Getting almost all the bits from a quantum random access code Lin, Han-Hsuan de Wolf, Ronald Quantum Physics Information Retrieval A quantum random access code (QRAC) is a map $x\mapstoρ_x$ that encodes $n$-bit strings $x$ into $m$-qubit quantum states $ρ_x$, in a way that allows us to recover any one bit of $x$ with success probability $\geq p$. The measurement on $ρ_x$ that is used to recover, say, $x_1$ may destroy all the information about the other bits; this is in fact what happens in the well-known QRAC that encodes $n=2$ bits into $m=1$ qubits. Does this generalize to large $n$, i.e., could there exist QRACs that are so "obfuscated" that one cannot get much more than one bit out of them? Here we show that this is not the case: for every QRAC there exists a measurement that (with high probability) recovers the full $n$-bit string $x$ up to small Hamming distance, even for the worst-case $x$. |
| title | Getting almost all the bits from a quantum random access code |
| topic | Quantum Physics Information Retrieval |
| url | https://arxiv.org/abs/2506.01903 |