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Optics and Spectroscopy

Applications of quantum cloning

Enrico Pomarico, Bruno Sanguinetti, Pavel Sekatski, Hugo Zbinden, Nicolas Gisin

Published Oct 1, 2011• 1 citation

Abstract

Quantum Cloning Machines (QCMs) allow for the copying of information, within the limits imposed by quantum mechanics. These devices are particularly interesting in the high-gain regime, i.e., when one input qubit generates a state of many output qubits. In this regime, they allow for the study of certain aspects of the quantum to classical transition. The understanding of these aspects is the root of the two recent applications that we will review in this paper: the first one is the Quantum Cloning Radiometer, a device which is able to produce an absolute measure of spectral radiance. This device exploits the fact that in the quantum regime information can be copied with only finite fidelity, whereas when a state becomes macroscopic, this fidelity gradually increases to 1. Measuring the fidelity of the cloning operation then allows to precisely determine the absolute spectral radiance of the input optical source. We will then discuss whether a Quantum Cloning Machine could be used to produce a state visible by the naked human eye, and the possibility of a Bell Experiment with humans playing the role of detectors.

DOI: 10.1134/s0030400x11110221

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Quantum Cloning Machines (QCMs) allow for the copying of information, within the limits imposed by quantum mechanics. These devices are particularly interesting in the high-gain regime, i.e., when one input qubit generates a state of many output qubits. In this regime, they allow for the study of certain aspects of the quantum to classical transition. The understanding of these aspects is the root of the two recent applications that we will review in this paper: the first one is the Quantum Cloning Radiometer, a device which is able to produce an absolute measure of spectral radiance. This device exploits the fact that in the quantum regime information can be copied with only finite fidelity, whereas when a state becomes macroscopic, this fidelity gradually increases to 1. Measuring the fidelity of the cloning operation then allows to precisely determine the absolute spectral radiance of the input optical source. We will then discuss whether a Quantum Cloning Machine could be used to produce a state visible by the naked human eye, and the possibility of a Bell Experiment with humans playing the role of detectors.

We present quantum cloning machines that transform

N

identical qubits into

M>N

identical copies and we prove that the fidelity (quality) of these copies is optimal. The connection between cloning and measurement is discussed in detail. When the number of clones

M

tends towards infinity, the fidelity of each clone tends towards the optimal fidelity that can be obtained by a measurement on the input qubits. More generally, quantum cloning machines are universal devices to translate quantum information into classical information.

Copying information is an elementary operation in classical information processing. However, copying seems rather different in the quantum regime. Since the discovery of the universal quantum cloning machine, much has been found from the fundamental point of view about quantum copying. But a basic question as to the utility of universal quantum cloning remains. We have considered its application in quantum state restoration by using cloning circuit for state estimation. It might be expected that classical information from the state estimation might help restore the quantum state that was disturbed during transmission. We find that the fidelity of the final state is, interestingly, independent of error probabilities inside the channel. However, this also turns out to impose a severe constraint on our original aims.

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.

Although perfect copying of unknown quantum systems is forbidden by the laws of quantum mechanics, approximate cloning is possible. A natural way of realizing quantum cloning of photons is by stimulated emission. In this context, the fundamental quantum limit to the quality of the clones is imposed by the unavoidable presence of spontaneous emission. In our experiment, a single input photon stimulates the emission of additional photons from a source on the basis of parametric down-conversion. This leads to the production of quantum clones with near-optimal fidelity. We also demonstrate universality of the copying procedure by showing that the same fidelity is achieved for arbitrary input states.

Beyond the no-cloning theorem, the universal symmetric quantum cloning machine was first addressed by Bu\ifmmode \check{z}\else \v{z}\fi{}ek and Hillery. Here, we realized the $\stackrel{\ensuremath{\rightarrow}}{1}$2 qubit Bu\ifmmode \check{z}\else \v{z}\fi{}ek-Hillery cloning machine with linear optical devices. This method relies on the representation of several qubits by a single photon. We showed that the fidelities between the two output qubits and the original qubit are both

\frac{5}{6}

(which proved to be the optimal fidelity of $\stackrel{\ensuremath{\rightarrow}}{1}$2 qubit universal cloner) for arbitrary input pure states.