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Invertible Quantum Operations and Perfect Encryption of Quantum States

Ashwin Nayak·Pranab Sen
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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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Ashwin Nayak, Pranab Sen. 2006-05-03. Invertible Quantum Operations and Perfect Encryption of Quantum States. https://arxiv.org/abs/quant-ph/0605041

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