Quantum Channel Certification with Incoherent Strategies
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910697957359616 |
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| author | Fawzi, Omar Flammarion, Nicolas Garivier, Aurélien Oufkir, Aadil |
| author_facet | Fawzi, Omar Flammarion, Nicolas Garivier, Aurélien Oufkir, Aadil |
| contents | In the problem of quantum channel certification, we have black box access to a quantum process and would like to decide if this process matches some predefined specification or is $\varepsilon$-far from this specification. The objective is to achieve this task while minimizing the number of times the black box is used.
Here, we focus on optimal incoherent strategies for two relevant extreme cases of channel certification. The first one is when the predefined specification is a unitary channel, e.g., a gate in a quantum circuit.
In this case, we show that testing whether the black box is described by a fixed unitary operator in dimension $d$ or $\varepsilon$-far from it in the trace norm requires $Θ(d/\varepsilon^2)$ uses of the black box. The second setting we consider is when the predefined specification is a completely depolarizing channel with input dimension $d_{\text{in}}$ and output dimension $d_{\text{out}}$.
In this case, we prove that, in the non-adaptive setting, $\tildeΘ(d_{\text{in}}^2d_{\text{out}}^{1.5}/\varepsilon^2)$ uses of the channel are necessary and sufficient to verify whether it is equal to the depolarizing channel or $\varepsilon$-far from it in the diamond norm.
Finally, we prove a lower bound of $Ω(d_{\text{in}}^2d_{\text{out}}/\varepsilon^2)$ for this problem in the adaptive setting. Note that the special case $d_{\text{in}} = 1$ corresponds to the well-studied quantum state certification problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_01188 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum Channel Certification with Incoherent Strategies Fawzi, Omar Flammarion, Nicolas Garivier, Aurélien Oufkir, Aadil Quantum Physics Data Structures and Algorithms Information Theory In the problem of quantum channel certification, we have black box access to a quantum process and would like to decide if this process matches some predefined specification or is $\varepsilon$-far from this specification. The objective is to achieve this task while minimizing the number of times the black box is used. Here, we focus on optimal incoherent strategies for two relevant extreme cases of channel certification. The first one is when the predefined specification is a unitary channel, e.g., a gate in a quantum circuit. In this case, we show that testing whether the black box is described by a fixed unitary operator in dimension $d$ or $\varepsilon$-far from it in the trace norm requires $Θ(d/\varepsilon^2)$ uses of the black box. The second setting we consider is when the predefined specification is a completely depolarizing channel with input dimension $d_{\text{in}}$ and output dimension $d_{\text{out}}$. In this case, we prove that, in the non-adaptive setting, $\tildeΘ(d_{\text{in}}^2d_{\text{out}}^{1.5}/\varepsilon^2)$ uses of the channel are necessary and sufficient to verify whether it is equal to the depolarizing channel or $\varepsilon$-far from it in the diamond norm. Finally, we prove a lower bound of $Ω(d_{\text{in}}^2d_{\text{out}}/\varepsilon^2)$ for this problem in the adaptive setting. Note that the special case $d_{\text{in}} = 1$ corresponds to the well-studied quantum state certification problem. |
| title | Quantum Channel Certification with Incoherent Strategies |
| topic | Quantum Physics Data Structures and Algorithms Information Theory |
| url | https://arxiv.org/abs/2303.01188 |