Absence of quantum Darwinism as a resource in secure quantum communication and computation

Abstract

The emergence of classical world from underlying quantum mechanics is characterized by not only vanishing quantum correlations but also an unfolding of objectivity also known as quantum Darwinism. We show that the absence of this objectivity has a quantum advantage in cryptography and also provides the crucial missing link in efficient classical simulation of quantum circuits with zero discord. For this purpose, we consider a model of mixed state quantum computation where one is promised concordant states at all stages of the quantum circuit. A concordant quantum state has zero discord with respect to any part and there exists a basis made up of a tensor product of orthonormal local subsystem basis in which the density matrix is diagonal. Efficient classical simulation of concordant computation has surprisingly been an outstanding question in quantum information theory. We argue that a key ingredient of an efficient classical simulation algorithm, a knowledge of the local basis in which the multi-party state is diagonal, is made available by quantum Darwinism. Concordant states in the absence of quantum Darwinism cannot be efficiently simulated by existing methods and give a cryptographic advantage in communication. We show this by giving a protocol for secure quantum communication that exploits this insight. Our work also has implications for the quantum-classical border and we discuss how objectivity emerging out of Darwinism demarcates this border in three ways - empirical based on our observations and experience of objectivity, information theoretic due to the absence of any quantum correlations and lastly computational in the sense discussed above. Lastly, we show that the quantum-classical boundary as drawn by quantum Darwinism as well by what can be simulated efficiently in a mixed state quantum computation aligns with the boundary given by Hardy