Stability theorem of depolarizing channels for the minimal output quantum Rényi entropies
The stability theorem of the depolarizing channel states that if a state is close to achieving the minimal/maximal output value of a certain quantity through the channel, then it must be close to an input state giving the minimal/maximal value. We show that the stability theorem of the depolarizing...
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| Veröffentlicht in: | Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2016-03, Vol.49 (11), p.115304 |
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| container_title | Journal of physics. A, Mathematical and theoretical |
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| creator | Bae, Eunok Gour, Gilad Lee, Soojoon Park, Jeonghoon Sanders, Barry C |
| description | The stability theorem of the depolarizing channel states that if a state is close to achieving the minimal/maximal output value of a certain quantity through the channel, then it must be close to an input state giving the minimal/maximal value. We show that the stability theorem of the depolarizing channel holds for the output quantum p-Rényi entropy for or p = 1, which is an extension of the known case p = 2. As an application, we present a protocol in which Bob determines whether Alice prepares a pure quantum state close to a product state. In the protocol, Alice transmits to Bob multiple copies of a pure state through a depolarizing channel, and Bob estimates its output quantum p-Rényi entropy. By using our stability theorem, we show that Bob can determine whether her preparation is appropriate. |
| doi_str_mv | 10.1088/1751-8113/49/11/115304 |
| format | Article |
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| subjects | Channels Depolarization depolarizing channel Entropy Entropy (Information) Estimates Mathematical analysis quantum Rényi entropy Stability stability theorem Theorems |
| title | Stability theorem of depolarizing channels for the minimal output quantum Rényi entropies |
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