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arXiv:2006.01517

Can error in quantum deletion machines be beneficial for deletion?

Vijayaraj, Sujan, S. Balakrishnan

Published Jun 2, 2020• 0 citations
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Abstract

In this paper, a generalized input state dependent deletion machine called probabilistic quantum deletion machine is proposed. Considering the Pati-Braunstein deletion machine as a benchmark, the machine is characterized by its deletion probability and the probability of error in deletion. It is observed that there are parameters for which increase in error in deletion can increase the fidelity of deletion. It is also shown that the Pati-Braunstein deletion machine is easily derivable for a certain value of deletion probability. Further the deletion machine can offer better fidelity of deletion than the Pati-Braunstein deletion machine for any input state with the right parameters.

DOI
10.48550/arxiv.2006.01517

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In this paper, a generalized input state dependent deletion machine called probabilistic quantum deletion machine is proposed. Considering the Pati-Braunstein deletion machine as a benchmark, the machine is characterized by its deletion probability and the probability of error in deletion. It is observed that there are parameters for which increase in error in deletion can increase the fidelity of deletion. It is also shown that the Pati-Braunstein deletion machine is easily derivable for a certain value of deletion probability. Further the deletion machine can offer better fidelity of deletion than the Pati-Braunstein deletion machine for any input state with the right parameters.
In this paper, the probabilistic quantum deletion machine constructed from the NB-deletion machine, controlled by the deletion probability p and the error probability q. It is observed that, under specific conditions, controlled errors can enhance the deletion process: when p is minimal and q is maximal, both deletion and retention fidelities reach their optimal values. Compared to the original NB-machine, this probabilistic machine performs better in both deleting and preserving states. Although the output states do not violate Bell’s inequalities, they still achieve teleportation fidelities above the classical limit. The entanglement of machine’s output state appears only when p > 0, and the mixedness increases with p. Altogether, these results indicate that controlled error can enhance certain non-local features of a probabilistic deletion machine.
In this work we prescribe a more generalized quantum-deleting machine (input state dependent). The fidelity of deletion is dependent on some machine parameters such that on alteration of machine parameters we get back to standard deleting machines. We also carried out a various comparative study of various kinds of quantum deleting machines. We also plotted graphs, making a comparative study of fidelity of deletion of the deletion machines, obtained as particular cases on changing the machine parameters of our machine.
In this work, we design a deleting machine and show that, for some given condition on machine parameters, it gives a slightly better result than the Pati–Braunstein (PB) deleting machine (2000 Nature 404 164, 2001 Preprint quant-ph/0007121). Also it is shown that for some particular values of the machine parameters it acts like the PB deleting machine. We also study the combined effect of a cloning and deleting machine, where first the cloning is done by some standard cloning machines such as Wootters–Zurek (1982 Nature 299 802) and Buzek–Hillery (1996 Phys. Rev. A 54 1844) cloning machines and then the copy mode is deleted by the PB deleting machine or our prescribed deleting machine. We then examine the distortion of the input state and the fidelity of deletion.
We further verify the impossibility of deleting an arbitrary unknown quantum state, and also show it is impossible to delete two nonorthogonal quantum states as a consequence of unitarity of quantum mechanics. A quantum approximate (deterministic) deleting machine and a probabilistic (exact) deleting machine are constructed. The estimation for the global fidelity characterizing the efficiency of the quantum approximate deleting is given. We then demonstrate that unknown nonorthogonal states chosen from a set with their multiple copies can evolve into a linear superposition of multiple deletions and failure branches by a unitary process if and only if the states are linearly independent. It is notable that the proof for necessity is somewhat different from Pati's [Phys. Rev. Lett. 83, 2849 (1999)]. Another deleting machine for the input states that are unnecessarily linearly independent is also presented. The bounds on the success probabilities of these deleting machines are derived. So we expound some preliminary analogies between quantum cloning and deleting.
We construct a probabilistic cloning and deleting machine which, taking several copies of an input quantum state, can output a linear superposition of multiple cloning and deleting states. Since the machine can perform cloning and deleting in a single unitary evolution, the probabilistic cloning and other cloning machines proposed in the previous literature can be thought of as special cases of our machine. A sufficient and necessary condition for successful cloning and deleting is presented, and it requires that the copies of an arbitrarily presumed number of the input states are linearly independent. This simply generalizes some results for cloning. We also derive an upper bound for the success probability of the cloning and deleting machine.