Related papers: Cloning is as Hard as Learning for Stabilizer Stat…
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 a priori probabilities. The solution…
Understanding the computational complexity of learning efficient classical programs in various learning models has been a fundamental and important question in classical computational learning theory. In this work, we study the…
The celebrated quantum no-cloning theorem states that an arbitrary quantum state cannot be cloned perfectly. This raises questions about cloning of classical states, which have also attracted attention. Here, we present a physical approach…
We analyze in details a scheme for cloning of Gaussian states based on linear optical components and homodyne detection recently demonstrated by U. L. Andersen et al. [PRL 94 240503 (2005)]. The input-output fidelity is evaluated for a…
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…
While exact cloning of an unknown quantum state is prohibited by the linearity of quantum mechanics, approximate cloning is possible and has been used, e.g., to derive limits on the security of quantum communication protocols. In the case…
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…
We derive a tight upper bound for the fidelity of a universal N to M qubit cloner, valid for any M \geq N, where the output of the cloner is required to be supported on the symmetric subspace. Our proof is based on the concatenation of two…
Cloning machines, that is, transformations that achieve the best approximate copying of a quantum state compatible with the no-cloning theorem, have been a fundamental research topic over the last five years. This study is of particular…
We define a quantum learning task called agnostic tomography, where given copies of an arbitrary state $\rho$ and a class of quantum states $\mathcal{C}$, the goal is to output a succinct description of a state that approximates $\rho$ at…
We propose new optimality criterion for the estimation of state-dependent cloning. We call this measure the relative error because the one compares the errors in the copies with contiguous size taking into account the similarity of states…
Perfect cloning of a known set of states with arbitrary prior probabilities is possible if we allow the cloner to sometimes fail completely. In the optimal case the probability of failure is at its minimum allowed by the laws of quantum…
In this work, we introduce a novel state-dependent quantum cloning (copying) process by introducing a new class of ancillary system -- an adaptive ancilla -- modifying the conventional state-dependent quantum copying process. This…
We have found a quantum cloning machine that optimally duplicates the entanglement of a pair of $d$-dimensional quantum systems. It maximizes the entanglement of formation contained in the two copies of any maximally-entangled input state,…
We establish the best possible approximation to a perfect quantum cloning machine which produces two clones out of a single input. We analyze both universal and state-dependent cloners. The maximal fidelity of cloning is shown to be 5/6 for…
We investigate several classes of state-dependent quantum cloners for three-level systems. These cloners optimally duplicate some of the four maximally-conjugate bases with an equal fidelity, thereby extending the phase-covariant qubit…
Recent years have seen significant activity on the problem of using data for the purpose of learning properties of quantum systems or of processing classical or quantum data via quantum computing. As in classical learning, quantum learning…
State-dependent cloning machines that have so far been considered either deterministically copy a set of states approximately, or probablistically copy them exactly. In considering the case of two equiprobable pure states, we derive the…
From Ref. [Phys. Rev. Lett. 80(1998)4999] one knows that the quantum states secretly chosen from a certain set can be probabilistically cloned with positive cloning efficiencies if and only if all the states in the set are linearly…
We show that, there are physical means for cloning two non-orthogonal pure states which are secretly chosen from a certain set $% \$={ | \Psi_0 > , | \Psi_1 > }$. The states are cloned through a unitary evolution together with a…