Abstract
We discuss the possibility of protecting the state of a quantum system that goes through noise by measurements and operations before and after the noise process. We extend our previous result on nonexistence of "truly quantum" protocols that protect an unknown qubit state against the depolarizing noise better than "classical" ones [Phys. Rev. A, 95, 022321 (2017)] in two directions. First, we show that the statement is also true in any finite-dimensional Hilbert spaces, which was previously conjectured, the optimal protocol is either the do nothing protocol or the discriminate and reprepare protocol, depending on the strength of the noise. Second, in the case of a qubit, we show that essentially the same conclusion holds for any unital noise. These results describe the fundamental limitations in quantum mechanics from the viewpoint of control theory.
Highlights
Quantum information technology, such as quantum computation, quantum cryptography, etc., is a new framework of information processing where quantum states bear information in place of classical bits
We discuss protection of a quantum state that goes through a noise process by measurements and operations before and after the noise process
Toward identifying the class of noise processes that is optimally suppressed by such a “classical” protocol, we extend our previous result in two directions
Summary
Quantum information technology, such as quantum computation, quantum cryptography, etc., is a new framework of information processing where quantum states (e.g., qubits) bear information in place of classical bits. The present authors, in the qubit case, extended their results to general noise [17]: A unitary operation is the optimal ex-post control protocol to protect a completely unknown pure state against arbitrary noise, i.e., it is never beneficial to extract information in ex-post control. All these results suggest that prior knowledge of the input state in some form is essential for its protection.
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