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arXiv:quant-ph/0605074 · Physical Review A

Improving the fidelity of deletion

Satyabrata Adhikari, Binayak Samadder Choudhury

Published May 24, 2006• 6 citations
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Abstract

In this work we study the quantum deletion machine with two transformers, and show that the deletion machine with a single transformer performs better than the deletion machine with more than two transformers. We also observe that the fidelity of deletion depends on the blank state used in the deleter, and so for different blank states the fidelity is different. Further, we study the Pati-Braunsein deleter with transformer.

DOI
10.1103/physreva.73.054303

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Quantum deletion: Beyond the no-deletion principle

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Suppose we are given two identical copies of an unknown quantum state and we wish to delete one copy from among the given two copies. The quantum no-deletion principle restricts us from perfectly deleting a copy but it does not prohibit us from deleting a copy approximately. Here we construct two types of a ``universal quantum deletion machine'' which approximately deletes a copy such that the fidelity of deletion does not depend on the input state. The two types of universal quantum deletion machines are (1) a conventional deletion machine described by one unitary operator and (2) a modified deletion machine described by two unitary operators. Here it is shown that the modified deletion machine deletes a qubit with fidelity $3∕4$, which is the maximum limit for deleting an unknown quantum state. In addition to this we also show that the modified deletion machine retains the qubit in the first mode with average fidelity 0.77 (approx.) which is slightly greater than the fidelity of measurement for two given identical states, showing how precisely one can determine its state [S. Massar and S. Popescu, Phys. Rev. Lett. 74, 1259 (1995)]. We also show that the deletion machine itself is input state independent, i.e., the information is not hidden in the deleting machine, and hence we can delete the information completely from the deletion machine.

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•May 22, 2006•0 citations
In this work we study the quantum deletion machine with two transformers, and show that the deletion machine with a single transformer performs better than the deletion machine with more than two transformers. We also observe that the fidelity of deletion depends on the blank state used in the deleter, and so for different blank states the fidelity is different. Further, we study the Pati-Braunsein deleter with transformer.
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.
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.
Suppose we are given two identical copies of an unknown quantum state and we wish to delete one copy from among the given two copies. The quantum no-deletion principle restricts us from perfectly deleting a copy but it does not prohibit us from deleting a copy approximately. Here we construct two types of a ``universal quantum deletion machine'' which approximately deletes a copy such that the fidelity of deletion does not depend on the input state. The two types of universal quantum deletion machines are (1) a conventional deletion machine described by one unitary operator and (2) a modified deletion machine described by two unitary operators. Here it is shown that the modified deletion machine deletes a qubit with fidelity 3∕43∕43∕4, which is the maximum limit for deleting an unknown quantum state. In addition to this we also show that the modified deletion machine retains the qubit in the first mode with average fidelity 0.77 (approx.) which is slightly greater than the fidelity of measurement for two given identical states, showing how precisely one can determine its state [S. Massar and S. Popescu, Phys. Rev. Lett. 74, 1259 (1995)]. We also show that the deletion machine itself is input state independent, i.e., the information is not hidden in the deleting machine, and hence we can delete the information completely from the 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.