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Quantum Cloning using Protective Measurement

Sudheer Kumar

Published Mar 16, 2015• 0 citations
OpenAlex

Abstract

Here we show that, in principle it is possible to clone (measure) a single arbitrary unknown quantum state of a spin-$\frac{1}{2}$ particle (an electron) with arbitrary precision and with success probability tending to one, using protective measurement. We first transfer the information from spin to spatial degree of freedom (d.o.f) of system electron, then trap it in a double well potential, and finally measure it protectively using a probe electron (which donot get entangled with system electron, but still extracts expectation value of an observable from a single quantum system (system electron)) to obtain information about the unknown spin polarization. Nonorthogonal state discrimination being a subclass of cloning, part of the paper (till finding out $\theta_{m}$, polar angle corresponding to the unknown spin polarization) is sufficient for discrimination.

Related papers

Quantum Cloning using Protective Measurement

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Here we show that, in principle it is possible to clone (measure) a single arbitrary unknown quantum state of a spin-$\frac{1}{2}$ particle (an electron) with arbitrary precision and with success probability tending to one, using protective measurement. We first transfer the information from spin to spatial degree of freedom (d.o.f) of system electron, then trap it in a double well potential, and finally measure it protectively using a probe electron (which donot get entangled with system electron, but still extracts expectation value of an observable from a single quantum system (system electron)) to obtain information about the unknown spin polarization. Nonorthogonal state discrimination being a subclass of cloning, part of the paper (till finding out $θ_{m}$, polar angle corresponding to the unknown spin polarization) is sufficient for discrimination.

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Experimental Optimal Cloning of Four-Dimensional Quantum States of Photons

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Assisted cloning of an arbitrary unknown two-qubit state via a genuine four-qubit entangled state and positive operator-valued measure

Lian Fang Han, Hao Yuan, Yang Ming +1 more

A protocol for cloning an arbitrary unknown two-qubit state and its orthogonal complement state with the assistance of a state preparer is presented. In this paper, a genuine four-particle entangled state which cannot be reduced to the product of two Bell states is used as the quantum channel. Moreover, positive operator-valued measure (POVM) instead of usual projective measurement is employed. In one hand, the usual teleportation is required. And in another hand, the perfect copies and complement copies of an unknown two-particle state can be implemented with a certain probability in the help of the state preparer.

Indian Journal of Pure & Applied Physics•Aug 1, 2014•3 citations
Here we show that, in principle it is possible to clone (measure) a single arbitrary unknown quantum state of a spin-12\frac{1}{2}21​ particle (an electron) with arbitrary precision and with success probability tending to one, using protective measurement. We first transfer the information from spin to spatial degree of freedom (d.o.f) of system electron, then trap it in a double well potential, and finally measure it protectively using a probe electron (which donot get entangled with system electron, but still extracts expectation value of an observable from a single quantum system (system electron)) to obtain information about the unknown spin polarization. Nonorthogonal state discrimination being a subclass of cloning, part of the paper (till finding out θm\theta_{m}θm​, polar angle corresponding to the unknown spin polarization) is sufficient for discrimination.
Here we show that, in principle it is possible to clone (measure) a single arbitrary unknown quantum state of a spin-12\frac{1}{2}21​ particle (an electron) with arbitrary precision and with success probability tending to one, using protective measurement. We first transfer the information from spin to spatial degree of freedom (d.o.f) of system electron, then trap it in a double well potential, and finally measure it protectively using a probe electron (which donot get entangled with system electron, but still extracts expectation value of an observable from a single quantum system (system electron)) to obtain information about the unknown spin polarization. Nonorthogonal state discrimination being a subclass of cloning, part of the paper (till finding out θmθ_{m}θm​, polar angle corresponding to the unknown spin polarization) is sufficient for discrimination.
Making measurements on single quantum systems is considered difficult, almost impossible if the state is a-priori unknown. Protective measurements suggest a possibility to measure single quantum systems and gain some new information in the process. Protective measurement is described, both in the original and generalized form. The degree to which the system and the apparatus remain entangled in a protective measurement, is assessed. A possible experimental test of protective measurements is discussed.
We first propose a novel protocol to realize quantum cloning of an arbitrary unknown shared state with assistance offered by a state preparer. The initial phase of this protocol involves the utilization of quantum teleportation (QT), enabling the transfer of quantum information from an arbitrary number of senders to another arbitrary number of receivers through a maximally entangled GHZ-type state serving as a network channel, without centralizing the information at any specific location. In the second stage of this protocol, the state preparer performs a special single-qubit projective measurement and multiple Z-basis measurements and then communicates a number of classical bits corresponding to measurement results, the perfect copy or orthogonal-complementing copy of an unknown shared state can be produced at senders hands. Then, using a non-maximally entangled GHZ-type state instead of the aforementioned quantum channel, we extend the proposed protocol from three perspectives: projective measurement, positive operator-value measurement (POVM), and a single generalized Bell-state measurement. Our schemes can relay quantum information over a network without requiring fully trusted central or intermediate nodes, and none of participants can fully access the information.
Optimal quantum cloning is the process of making one or more copies of an arbitrary unknown input quantum state with the highest possible fidelity. All reported demonstrations of quantum cloning have so far been limited to copying two-dimensional quantum states, or qubits. We report the experimental realization of the optimal quantum cloning of four-dimensional quantum states, or ququarts, encoded in the polarization and orbital angular momentum degrees of freedom of photons. Our procedure, based on the symmetrization method, is also shown to be generally applicable to quantum states of arbitrarily high dimension-or qudits-and to be scalable to an arbitrary number of copies, in all cases remaining optimal. Furthermore, we report the bosonic coalescence of two single-particle entangled states.
A protocol for cloning an arbitrary unknown two-qubit state and its orthogonal complement state with the assistance of a state preparer is presented. In this paper, a genuine four-particle entangled state which cannot be reduced to the product of two Bell states is used as the quantum channel. Moreover, positive operator-valued measure (POVM) instead of usual projective measurement is employed. In one hand, the usual teleportation is required. And in another hand, the perfect copies and complement copies of an unknown two-particle state can be implemented with a certain probability in the help of the state preparer.