Approximate Quantum Cloning Research Articles

Process-optimized phase-covariant quantum cloning

After the appearance of the no-cloning theorem, approximate quantum cloning machines (QCMs) has become a well-studied subject in quantum information theory. Among several measures to quantify the performance of a QCM, single-qudit fidelity and global fidelity have been most widely used. In this paper we compute the optimal global fidelity for phase-covariant cloning machines via semidefinite programming optimization, thereby completing a remaining gap in the previous results on QCMs. We also consider optimal simulations of the cloning and transpose cloning map, both by a direct optimization and by a composition of component-wise optimal QCMs. For the cloning map the composition method is suboptimal whereas for the transpose cloning map the method is asymptotically optimal.

The compatibility dimension of quantum measurements

We introduce the notion of compatibility dimension for a set of quantum measurements: it is the largest dimension of a Hilbert space on which the given measurements are compatible. In the Schrödinger picture, this notion corresponds to testing compatibility with ensembles of quantum states supported on a subspace, using the incompatibility witnesses of Carmeli, Heinosaari, and Toigo [Phys. Rev. A 98,012126 (2018) and Phys. Rev. Lett. 122, 130402 (2019).]. We provide several bounds for the compatibility dimension using approximate quantum cloning or algebraic techniques inspired by quantum error correction. We analyze in detail the case of two orthonormal bases and, in particular, that of mutually unbiased bases.

Cloning of Quantum Entanglement.

Quantum no-cloning, the impossibility of perfectly cloning an arbitrary unknown quantum state, is one of the most fundamental limitations due to the laws of quantum mechanics, which underpin the physical security of quantum key distribution. Quantum physics does allow, however, approximate cloning with either imperfect state fidelity and/or probabilistic success. Whereas approximate quantum cloning of single-particle states has been tested previously, experimental cloning of quantum entanglement-a highly nonclassical correlation-remained unexplored. Based on a multiphoton linear optics platform, we demonstrate quantum cloning of two-photon entangled states for the first time. Remarkably our results show that one maximally entangled photon pair can be broadcast into two entangled pairs, both with state fidelities above 50%. Our results are a key step towards cloning of complex quantum systems, and are likely to provide new insights into quantum entanglement.

Quantum process randomness

We argue that the optimization of a quantum process based on the customarily used fidelity between the actual and the expected outputs may not be sufficient. We introduce a quantity namely the “quantum process randomness”, which is the standard deviation of the distribution of Born probabilities corresponding to the orthonormal measurement that projects the expected output onto the eigenstates of the actual output, and obtain a trade-off between fidelity and randomness for an arbitrary quantum process. We consider approximate quantum cloning and teleportation processes to illustrate the concept. We find that the optimal approximate universal and state-dependent quantum cloning machines obtained by maximizing the fidelity is the same as that obtained by optimizing the difference between randomness and fidelity.

Compatibility of Quantum Measurements and Inclusion Constants for the Matrix Jewel

In this work, we establish the connection between the study of free spectrahedra and the compatibility of quantum measurements with an arbitrary number of outcomes. This generalizes previous results by the authors for measurements with two outcomes. Free spectrahedra arise from matricial relaxations of linear matrix inequalities. A particular free spectrahedron which we define in this work is the matrix jewel. We find that the compatibility of arbitrary measurements corresponds to the inclusion of the matrix jewel into a free spectrahedron defined by the effect operators of the measurements under study. We subsequently use this connection to bound the set of (asymmetric) inclusion constants for the matrix jewel using results from quantum information theory and symmetrization. The latter translate to new lower bounds on the compatibility of quantum measurements. Among the techniques we employ are approximate quantum cloning and mutually unbiased bases.

Information-theoretic limitations on approximate quantum cloning and broadcasting

We prove new quantitative limitations on any approximate simultaneous cloning or broadcasting of mixed states. The results are based on information-theoretic (entropic) considerations and generalize the well known no-cloning and no-broadcasting theorems. We also observe and exploit the fact that the universal cloning machine on the symmetric subspace of $n$ qudits and symmetrized partial trace channels are dual to each other. This duality manifests itself both in the algebraic sense of adjointness of quantum channels and in the operational sense that a universal cloning machine can be used as an approximate recovery channel for a symmetrized partial trace channel and vice versa. The duality extends to give control on the performance of generalized UQCMs on subspaces more general than the symmetric subspace. This gives a way to quantify the usefulness of a-priori information in the context of cloning. For example, we can control the performance of an antisymmetric analogue of the UQCM in recovering from the loss of $n-k$ fermionic particles.

Memory-built-in quantum cloning in a hybrid solid-state spin register

As a way to circumvent the quantum no-cloning theorem, approximate quantum cloning protocols have received wide attention with remarkable applications. Copying of quantum states to memory qubits provides an important strategy for eavesdropping in quantum cryptography. We report an experiment that realizes cloning of quantum states from an electron spin to a nuclear spin in a hybrid solid-state spin register with near-optimal fidelity. The nuclear spin provides an ideal memory qubit at room temperature, which stores the cloned quantum states for a millisecond under ambient conditions, exceeding the lifetime of the original quantum state carried by the electron spin by orders of magnitude. The realization of a cloning machine with built-in quantum memory provides a key step for application of quantum cloning in quantum information science.

Realizing various approximate quantum cloning with XY-type exchange interactions of flux qubits

In this paper, we realize all kinds of 1 → 2 approximate quantum cloning, including optimal 1 → 2 symmetric (or asymmetric) universal quantum cloning (UQC) and phase-covariant cloning (PCC), symmetric economical phase-covariant cloning (EPCC) and real state quantum cloning, with the XY-type exchange interactions of the flux qubits which are coupled by dc superconducting quantum interference devices (SQUIDs). It is shown that our schemes can be realized with the current experimental technology.

Quantum cloning machine of a state in a belt of Bloch sphere

We analyze the problem of approximate quantum cloning when the quantum state is between two latitudes on the Bloch's sphere. We present an analytical formula for the optimized 1-to-2 cloning. The formula unifies the universal quantum cloning (UQCM) and the phase covariant quantum cloning.

APPROXIMATE QUANTUM CLONING IN d DIMENSIONAL SPACE

We present a simpler method to deduce three types of approximate 1 → 2 quantum cloning machines in d dimensions, i.e. Wootters–Zurek, the universal, and phase-covariant quantum cloning machines. The explicit different transformations of these cloners are determined by different input states. Our method shows a relatively easy way to understand approximate quantum cloning.

Optimal asymmetric phase-covariant quantum cloning

We propose a relatively simple method to derive the optimal asymmetric approximate quantum cloning. The results obtained agree with the previous contributions. Utilizing the method we also obtain the optimal asymmetric 1 → 3 phase-covariant quantum cloning and 1 → 2 and 1 → 3 economical ones, which work without ancilla, in 2-dimension. Maybe the method can be effective to derive the optimal asymmetric approximate N → M quantum cloning in d-dimension.

Combinations of probabilistic and approximate quantum cloning and deleting

We first construct a probabilistic and approximate quantum cloning machine (PACM) and then clarify the relation between the PACM and other cloning machines. After that, we estimate the global fidelity of the approximate cloning that improves the previous estimation for the deterministic cloning machine; and also derive a bound on the success probability of producing perfect multiple clones. Afterwards, we further establish a more generalized probabilistic and approximate cloning and deleting machine (PACDM) and discuss the connections of the PACDM to some of the existing quantum cloning and deleting machines. Finally the global fidelity and a bound on the success probability of the PACDM are obtained. Summarily, the quantum devices established in this paper improve and also greatly generalize some of the existing machines.

Approximate quantum cloning with nuclear magnetic resonance.

Here we describe a nuclear magnetic resonance (NMR) experiment that uses a three qubit NMR device to implement the one-to-two approximate quantum cloning network of Buzek et al. [Phys. Rev. A 56, 3446 (1997)]. As expected the experimental results indicate that the network clones all input states with similar fidelities, but as a result of decoherence and incoherent evolution arising from B(1) inhomogeneity the total fidelity achieved does not exceed the measurement bound.

Approximate quantum cloning and the impossibility of superluminal information transfer

We show that nonlocality of quantum mechanics cannot lead to superluminal transmission of information, even if most general local operations are allowed, as long as they are linear and trace preserving. In particular, any quantum mechanical approximate cloning transformation does not allow signalling. On the other hand, the no-signalling constraint on its own is not sufficient to prevent a transformation from surpassing the known cloning bounds. We illustrate these concepts on the basis of some examples.