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arXiv:quant-ph/9808043 · Fortschritte der Physik

Copying of Entangled States and the Degradation of Correlations

Paweł Masiak, P. L. Knight

Published Oct 1, 2001• 1 citation
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Abstract

We investigate the degree to which entanglement survives when a correlated pair of two-state systems are copied to two or more copies using either local or non-local processes. We show how the copying process degrades the entanglement, due to a residual correlation between the copied output and the copying machine (itself made of qubits).

DOI
10.1002/1521-3978(200110)49:10/11<1001::aid-prop1001>3.0.co;2-b

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Summary form only given. Copying machines in general use two approaches. One of the extreme cases is a classical copying machine, where measurements (destructive or non-destructive) are made on the original state, the results of which are then fed as parameters into some state preparation scheme which attempts to construct a copy of the original. The opposite extreme is a fully quantum copying machine which by some process that is unseen by external observers, creates a fixed number of copies, usually destroying the original in the process. Naturally in a realistic situation, noise will additionally degrade the quality of the copies, and copiers which utilise both of the processes above are obviously also possible. While quantum copying promises the possibility of many applications in the future, few specific examples of uses for a quantum copier have been considered so far. When discussing practical applications, quantum copiers have mainly been put forward as something to be defended against by quantum cryptography schemes. This talk presents a analysis of a possible application of quantum copiers: using them to improve detection efficiencies.

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We investigate the degree to which entanglement survives when a correlated pair of two-state systems are copied to two or more copies using either local or non-local processes. We show how the copying process degrades the entanglement, due to a residual correlation between the copied output and the copying machine (itself made of qubits).
We study the degree to which quantum entanglement survives when a three-qubit entangled state is copied by using local and non-local processes, respectively, and investigate iterating quantum copying for the three-qubit system. There may exist inter-three-qubit entanglement and inter-two-qubit entanglement for the three-qubit system. We show that both local and non-local copying processes degrade quantum entanglement in the three-particle system due to a residual correlation between the copied output and the copying machine. We also show that the inter-two-qubit entanglement is preserved better than the inter-three-qubit entanglement in the local cloning process. We find that non-local cloning is much more efficient than the local copying for broadcasting entanglement, and output state via non-local cloning exhibits the fidelity better than local cloning.
We study the degree to which quantum entanglement survives when a three-qubit entangled state iscopied by using local and non-local processes, respectively, and investigate iterating quantum copyingfor the three-qubitsystem. There may exist inter-three-qubit entanglement and inter-two-qubit entanglement for the three-qubit system.We show that both local and non-local copying processes degrade quantum entanglement in the three-particle systemdue to a residual correlation between the copied output and the copying machine. We also show that the inter-two-qubitentanglement is preserved better than the inter-three-qubit entanglement in the local cloning process. We find thatnon-local cloning is much more efficient than the local copying for broadcasting entanglement, and output state vianon-local cloning exhibits the fidelity better than local cloning.
We study the degree to which quantum entanglement survives when a three-qubit entangled state iscopied by using local and non-local processes, respectively, and investigate iterating quantum copyingfor the three-qubitsystem. There may exist inter-three-qubit entanglement and inter-two-qubit entanglement for the three-qubit system.We show that both local and non-local copying processes degrade quantum entanglement in the three-particle systemdue to a residual correlation between the copied output and the copying machine. We also show that the inter-two-qubitentanglement is preserved better than the inter-three-qubit entanglement in the local cloning process. We find thatnon-local cloning is much more efficient than the local copying for broadcasting entanglement, and output state vianon-local cloning exhibits the fidelity better than local cloning.
Recently Galvão and Hardy have shown that quantum cloning can improve the performance of some quantum computation tasks. However such performance enhancement is possible only if quantum correlations survive the cloning process. We investigate preservation of the quantum correlations in the process of non-local cloning of entangled pairs of two-level systems. We consider different kinds of quantum cloning machines and compare their effectiveness in the cloning of non-maximally entangled pure states. A mean entanglement is introduced in order to obtain a quantitative evaluation of an average efficiency for the different cloning machines. We show that a reduction of the quantum correlations is significant and it strongly depends upon the kind of cloning machine used. Losses of the entanglement are largest in the case of the universal quantum cloning machine. Generally, in all cases considered the losses of the entanglement are so drastic that the method of enhancement for the performance of the quantum computation using quantum cloning seems to be questionable.
Recently Galvão and Hardy have shown that quantum cloning can improve the performance of some quantum computation tasks. However such performance enhancement is possible only if quantum correlations survive the cloning process. We investigate preservation of the quantum correlations in the process of non-local cloning of entangled pairs of two-level systems. We consider different kinds of quantum cloning machines and compare their effectiveness in the cloning of non-maximally entangled pure states. A mean entanglement is introduced in order to obtain a quantitative evaluation of an average efficiency for the different cloning machines. We show that a reduction of the quantum correlations is significant and it strongly depends upon the kind of cloning machine used. Losses of the entanglement are largest in the case of the universal quantum cloning machine. Generally, in all cases considered the losses of the entanglement are so drastic that the method of enhancement for the performance of the quantum computation using quantum cloning seems to be questionable.
Summary form only given. Copying machines in general use two approaches. One of the extreme cases is a classical copying machine, where measurements (destructive or non-destructive) are made on the original state, the results of which are then fed as parameters into some state preparation scheme which attempts to construct a copy of the original. The opposite extreme is a fully quantum copying machine which by some process that is unseen by external observers, creates a fixed number of copies, usually destroying the original in the process. Naturally in a realistic situation, noise will additionally degrade the quality of the copies, and copiers which utilise both of the processes above are obviously also possible. While quantum copying promises the possibility of many applications in the future, few specific examples of uses for a quantum copier have been considered so far. When discussing practical applications, quantum copiers have mainly been put forward as something to be defended against by quantum cryptography schemes. This talk presents a analysis of a possible application of quantum copiers: using them to improve detection efficiencies.