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International Conference on Next-Gen Quantum and Advanced Computing: Algorithms, Security, and Beyond (NQComp)

The Role of Error in Enhancing Probabilistic Quantum Deletion

A. Nancy, S. Balakrishnan

Published Mar 5, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1109/nqcomp68334.2026.11497661

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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 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.
Quantum mechanics put restriction on performing some task which we can do classically. One such restriction is that we cannot copy an arbitrary quantum state. This is known as No-cloning theorem. Although quantum mechanics forbid us to construct a perfect cloner, there is no restriction to construct an imperfect cloner. Therefore, we have constructed and studied a special kind of quantum cloning machine named as Hybrid quantum cloning machine which is nothing but a different combination of pre-existing quantum cloning machines. We showed that this hybrid quantum cloning machine sometime gives better quality copy than the pre-existing quantum cloners. Quantum entanglement is a very astonishing property in a multi-partite system and it is a very useful ingredient of quantum information theory. Therefore broadcasting (cloning) of entanglement is a very important subject to study. In this regard we have studied the broadcasting of entanglement using state dependent quantum cloning machine. Further, we have investigated the problem of secretly broadcasting of three-qubit entangled state between two distant partners. Linearity of quantum mechanics put another restriction on deletion of an arbitrary quantum state i.e. an arbitrary quantum state against a copy cannot be perfectly deleted. Like cloning machine one can construct an approximate deletion machine also. Therefore, we have constructed an universal deletion machine in the sense that the fidelity of deletion does not depend on the input state and showed that the fidelity of deletion is 3/4 . Further we showed that the fidelity of deletion depends on the blank state at the output and it can be improved from the value 3/4 for certain blank state. Moreover, we have studied the case where two cloned copies are given at the input of the deletion machine.
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.
We propose a scenario to increase the probability of probabilistic quantum deletion and to enhance the fidelity of approximate quantum deletion for two non-orthogonal states via weak measurement. More interestingly, by pretreating the given non-orthogonal states, the probability of probabilistic quantum deletion and fidelity of approximate quantum deletion can reach 1. Since outcomes of the weak measurement that we required are probabilistic, we perform the subsequent deleting process only when the outcome of weak measurement is “yes”. Remarkably, we find that our scenario has better performance in quantum information process; for example, it costs less quantum resources and time.
Using the reduced density operator of quantum state to study the deletion and clone of quantum information.Testify that there no exists quantum deleting machine which makes the deleted states and the blank states be correlated;also we can not construct a machine to perfectly delete arbitrary mixed quantum states.At last,we consider the problem of cloning and deleting of mixed quantum states in the case of probabilistic form,provide a sufficient and necessary condition in the form of probability with a unification formula.By using the results obtained,the processing of quantum information can be further comprehended and has aspiring significance for quantum computer.