# Probabilistic quantum cloning of N quantum states

@article{Liu2019ProbabilisticQC, title={Probabilistic quantum cloning of N quantum states}, author={Haixin Liu and Heng Fan}, journal={arXiv: Quantum Physics}, year={2019} }

Probabilistically creating n perfect clones from m copies for one of N priori known quantum states with minimum failure probability is a long-standing problem. We provide a rigorous proof for the geometric approach to this probabilistic quantum cloning problem when N = 2. Then, we give the general geometric form of the sufficient and necessary condition of probabilistic cloning for N known quantum states. By this general geometric approach, we realize the optimal probabilistic quantum cloning…

## References

SHOWING 1-10 OF 30 REFERENCES

### Quantum cloning

- Physics
- 2005

The impossibility of perfectly copying (or cloning) an arbitrary quantum state is one of the basic rules governing the physics of quantum systems. The processes that perform the optimal approximate…

### Quantum copying: Beyond the no-cloning theorem.

- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1996

It is shown that there exists a ‘‘universal quantum-copying machine’’ ~i.e., transformation! which approximately copies quantum-mechanical states such that the quality of its output does not depend on the input.

### Experimental demonstration of probabilistic quantum cloning.

- Physics, Computer SciencePhysical review letters
- 2011

This work designs an efficient quantum network with a limited amount of resources and performs the first experimental demonstration of probabilistic quantum cloning in a NMR quantum computer.

### Probabilistically Perfect Cloning of Two Pure States: A Geometric Approach

- MathematicsPhysical review letters
- 2016

We solve the long-standing problem of making n perfect clones from m copies of one of two known pure states with minimum failure probability in the general case where the known states have arbitrary…

### Optimal Quantum Cloning Machines

- Computer Science
- 1997

Quantum Cloning Machines (QCM) are universal devices to translate quantum information into classical information and it is proved that the fidelity (quality) of these copies is optimal.

### Experimental Quantum Cloning of Single Photons

- PhysicsScience
- 2002

In this experiment, a single input photon stimulates the emission of additional photons from a source on the basis of parametric down-conversion, which leads to the production of quantum clones with near-optimal fidelity.

### Universal Algorithm for Optimal Estimation of Quantum States from Finite Ensembles via Realizable Ge

- Computer Science
- 1998

A universal algorithm for the optimal quantum state estimation of an arbitrary finite dimensional system that specifies a physically realizable positive operator valued measurement on a finite number of identically prepared systems is presented.

### Quantum cloning machines for equatorial qubits

- Physics
- 2001

Quantum cloning machines for equatorial qubits are studied. For the case of a one to two phase-covariant quantum cloning machine, we present the networks consisting of quantum gates to realize the…

### Phase-covariant quantum cloning of qudits

- Physics
- 2003

We study the phase-covariant quantum cloning machine for qudits, i.e., the input states in a d-level quantum system have complex coefficients with arbitrary phase but constant module. A cloning…