Related papers: Mirror modular cloning and fast quantum associativ…
There are various physical scenarios in which one can only implement operations with a certain symmetry. Under such restriction, a system in a symmetry-breaking state can be used as a catalyst, e.g. to prepare another system in a desired…
The relative error of cloning of quantum states with arbitrary prior probabilities is considered. It is assumed that the ancilla may contain some a priori information about the input state to be cloned. The lower bound on the relative error…
We present a quantum algorithm that has rigorous runtime guarantees for several families of binary optimization problems, including Quadratic Unconstrained Binary Optimization (QUBO), Ising spin glasses ($p$-spin model), and $k$-local…
We describe an optical scheme for optimal Gaussian n to m cloning of coherent states. The scheme, which generalizes a recently demonstrated scheme for 1 to 2 cloning, involves only linear optical components and homodyne detection.
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…
We consider cloning transformations of d-dimensional states of the form e^{i\phi_0}|0> + e^{i\phi_1}|1> +...+ e^{i\phi_{d-1}}|d-1> that are covariant with respect to rotations of the phases \phi_i's. The optimal cloning maps are easily…
For quantum computation, we investigate the conjecture that the superposition of macroscopically distinct states is necessary for a large quantum speedup. Although this conjecture was supported for a circuit-based quantum computer…
It is shown that any quantum operation that perfectly clones the entanglement of all maximally-entangled qubit pairs cannot preserve separability. This ``entanglement no-cloning'' principle naturally suggests that some approximate cloning…
We discuss the usefulness of quantum cloning and present examples of quantum computation tasks for which cloning offers an advantage which cannot be matched by any approach that does not resort to it. In these quantum computations, we need…
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…
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…
We investigate how to determine whether the states of a set of quantum systems are identical or not. This paper treats both error-free comparison, and comparison where errors in the result are allowed. Error-free comparison means that we…
It is well known that Grover's algorithm asymptotically transforms an equal superposition state into an eigenstate (of a given basis). Here, we demonstrate a verification algorithm based on weak measurement which can achieve the same…
After the appearance of the no-cloning theorem, approximate quantum cloning machines (QCMs) have become one of the most well-studied subject in quantum information theory. Among several measures to quantify the performance of a QCM,…
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…
Grover's algorithm is a quantum search algorithm that proceeds by repeated applications of the Grover operator and the Oracle until the state evolves to one of the target states. In the standard version of the algorithm, the Grover operator…
We examine the perfect cloning of non-local, orthogonal states with only local operations and classical communication. We provide a complete characterisation of the states that can be cloned under these restrictions, and their relation to…
A fundamental question in quantum mechanics is, whether it is possible to replicate an arbitrary unknown quantum state. Then famous quantum no-cloning theorem [Nature 299, 802 (1982)] says no to the question. But it leaves open the…
Standard quantum inference converts quantum data into classical outputs. We study an alternative inference setting in which the desired output is quantum, preserving coherence. Such settings include quantum purity amplification (QPA),…
We show that one can deterministically generate out of $N$ copies of an unknown unitary operation up to $N^2$ almost perfect copies. The result holds for all operations generated by a Hamiltonian with an unknown interaction strength. This…