Asymptotic quantum cloning is state estimation

The impossibility of perfect cloning and state estimation are two fundamental results in quantum mechanics. It has been conjectured that quantum cloning becomes equivalent to state estimation in the asymptotic regime where the number of clones tends to infinity. We prove this conjecture using two known results of quantum information theory: the monogamy of quantum correlations and the properties of entanglement breaking channels.     

Universal Quantum Cloning Machines for Two Identical Mixed Qubits

We present a series of universal quantum cloning machines for two identical mixed qubits. Every machine is optimal in the sense that it achieves the optimal bound of the single copy shrinking factor. Unlike in the case of pure state cloning, the single copy shrinking factor does not uniquely determine the cloning map in the case of mixed state cloning.     

A remark on the optimal cloning of an N-level quantum system

We study quantum cloning machines (QCM) that act on an unknown N-level quantum state and make M copies. We give a formula for the maximum of the fidelity of cloning and exhibit the unitary transformations that realize this optimal fidelity. We also extend the results to treat the case of M copies from () identical N-level quantum systems. Received 21 September 1999     

The upper bound function of nonadiabatic dynamics in parametric driving quantum systems

The adiabatic control is a powerful technique for many practical applications in quantum state engineering, light-driven chemical reactions and geometrical quantum computations. This paper reveals a speed limit of nonadiabatic transition in a general time-dependent parametric quantum system that leads to an upper bound function which lays down an optimal criteria for the adiabatic controls. The upper bound function of transition rate between instantaneous eigenstates of a time-dependent system is determined by the power fluctuations of the system relative to the minimum gap between the instantaneous levels. In a parametric Hilbert space, the driving power corresponds to the quantum work done by the parametric force multiplying the parametric velocity along the parametric driving path. The general two-state time-dependent models are investigated as examples to calculate the bound functions in some general driving schemes with one and two driving parameters. The calculations show that the upper bound function provides a tighter real-time estimation of nonadiabatic transition and is closely dependent on the driving frequencies and the energy gap of the system. The deviations of the real phase from Berry phase on different closed paths are induced by the nonadiabatic transitions and can be efficiently controlled by the upper bound functions. When the upper bound is adiabatically controlled, the Berry phases of the electronic spin exhibit nonlinear step-like behaviors and it is closely related to topological structures of the complicated parametric paths on Bloch sphere.     

Deterministic Assisted Clone of an Arbitrary Two- and Three-qubit States via Multi-qubit Brown State

We present two schemes for deterministic assisted clone(DAC) of an unknown two- and three-qubit entangled states with assistance via muti-qubit Brown state. In the schemes, the sender wish to teleport an unknown original entangled state which from the state preparer, and then create a perfect copy of the unknown state at her place. The DAC schemes include two stages. The first stage requires teleportation with Bell-state measurements via a five-qubit Brown state(or seven-qubit Brown state) as the quantum channel. In the second stage, to help the sender realize the quantum cloning, the state preparer performs projective measurements on their own particles which from the sender, then the sender can acquire a perfect copy of the unknown state by means of some appropriate unitary operations. Furthermore, the total success probability for assisted cloning a perfect copy of the unknown state can reach 1 in our schemes.     

A Generalization of Schur–Weyl Duality with Applications in Quantum Estimation

Schur–Weyl duality is a powerful tool in representation theory which has many applications to quantum information theory. We provide a generalization of this duality and demonstrate some of its applications. In particular, we use it to develop a general framework for the study of a family of quantum estimation problems wherein one is given n copies of an unknown quantum state according to some prior and the goal is to estimate certain parameters of the given state. In particular, we are interested to know whether collective measurements are useful and if so to find an upper bound on the amount of entanglement which is required to achieve the optimal estimation. In the case of pure states, we show that commutativity of the set of observables that define the estimation problem implies the sufficiency of unentangled measurements.     

Optimal filters for photon cloning with an optical amplifier

We study the performance of a practical quantum cloning scheme consisting of a continuously pumped broadband optical amplifier followed by optimal spectral and temporal filters for spontaneous emission suppression. Our simulation results demonstrate that the fidelity of this system is no better than a random cloning machine when the average input photon number is below one, but asymptotically approaches the quantum limit of an optimal quantum cloning machine as the input photon number increases. We also show that this system has a better fidelity than cloning based on state estimation, though for a large number of clones both cloning methods asymptotically approach the quantum limit.     

Forcible-Measurement Attack on Quantum Secure Direct Communication Protocol with Cluster State

The security of the quantum secure direct communication （QSDC） protocol with cluster state is analysed. It is shown that the secret would be partially leaked out when an eavesdropper performs forcible measurements on the transmitted particles. With the help of the result in minimum error discrimination, an upper bound （i.e. 40%） of this leakage is obtained. Moreover, the particular measurements which makes the leakage reach this bound are given.     

Deterministic Joint Assisted Cloning of Unknown Two-Qubit Entangled States

We present two schemes for perfect cloning unknown two-qubit and general two-qubit entangled states with assistance from two state preparers, respectively. In the schemes, the sender wish to teleport an unknown two-qubit (or general two-qubit) entangled state which from two state preparers to a remote receiver, and then create a perfect copy of the unknown state at her place. The schemes include two stages. The first stage of the schemes requires usual teleportation. In the second stage, to help the sender realize the quantum cloning, two state preparers perform two-qubit projective measurements on their own qubits which from the sender, then the sender can acquire a perfect copy of the unknown state. To complete the assisted cloning schemes, several novel sets of mutually orthogonal basis vectors are introduced. It is shown that, only if two state preparers collaborate with each other, and perform projective measurements under suitable measuring basis on their own qubit respectively, the sender can create a copy of the unknown state by means of some appropriate unitary operations. The advantage of the present schemes is that the total success probability for assisted cloning a perfect copy of the unknown state can reach 1.     

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.     

Quantum Cloning of an Unknown 2-Atom State via Entangled Cluster States

This paper presented a scheme for cloning a 2-atom state in the QED cavity with the help of Victor who is the state’s preparer. The cloning scheme has two steps. In the first step, the scheme requires probabilistic teleportation of a 2-atom state that is unknown in advance, and uses a 4-atom cluster state as quantum channel. In the second step, perfect copies of the 2-atom entangled state may be realized with the assistance of Victor. The finding is that our scheme has two outstanding advantages: it is not sensitive to the cavity decay, and Bell state is easy to identify.     

Towards practical quantum cryptography

Quantum cryptography bases the security of quantum key exchange on the laws of quantum physics and is likely to become the first application employing quantum effects for communication. Here we present performance tests of a new design based on polarization encoding of attenuated, coherent light pulses. Our measurements show that this compact setup can achieve an effective key-bit rate in the kHz range with low alignment requirements and thus offers the tools for fast and user-friendly quantum key exchange. Received: 27 July 1999 / Revised version: 3 September 1999 / Published online: 10 November 1999     

On Estimation of Fully Entangled Fraction

We study the fully entangled fraction （FEF） of arbitrary mixed states. New upper bounds of FEF are derived. These upper bounds make complements on the estimation of the value of FEF. For weakly mixed quantum states, an upper bound is shown to be very tight to the exact value of FEF.     

Quantum information becomes classical when distributed to many users

Any physical transformation that equally distributes quantum information over a large number M of users can be approximated by a classical broadcasting of measurement outcomes. The accuracy of the approximation is at least of the order O(M(-1)). In particular, quantum cloning of pure and mixed states can be approximated via quantum state estimation. As an example, for optimal qubit cloning with 10 output copies, a single user has an error probability p(err) > or = 0.45 in distinguishing classical from quantum output, a value close to the error probability of the random guess.     

Experimental demonstration of probabilistic quantum cloning

The method of quantum cloning is divided into two main categories: approximate and probabilistic quantum cloning. The former method is used to approximate an unknown quantum state deterministically, and the latter can be used to faithfully copy the state probabilistically. Thus far, many approximate cloning machines have been experimentally demonstrated, but probabilistic cloning remains an experimental challenge, as it requires more complicated networks and a higher level of precision control. In this work, we design an efficient quantum network with a limited amount of resources and perform the first experimental demonstration of probabilistic quantum cloning in a NMR quantum computer. In our experiment, the optimal cloning efficiency proposed by Duan and Guo [Phys. Rev. Lett. 80, 4999 (1998)] is achieved.     

Probabilistically perfect quantum cloning and unambiguous state discrimination

We consider the N → M probabilistically perfect quantum cloning machine that perfectly produces M faithful copies from N identical input states, where the input states are selected, with prior probabilities η₁and η₂ = 1 − η₁, from a given set of the two linearly independent states |ψ₁〉^⊗ N = (cosθ|0〉 + sinθ|1〉)^⊗ N and |ψ₂〉^⊗ N = (sinθ|0〉 + cosθ|1〉)^⊗ N (θ∈(0,π/2)). We derive the optimal distribution of the success probabilities. When M approaches infinite, the probabilistically perfect quantum cloning can be regarded as a kind of the unambiguous state discrimination, and theoretically provides the upper bound of the unambiguous state discrimination. By using the optimal distribution of the success probabilities of the optimal asymmetric 1 → M probabilistically perfect quantum cloning, we can derive the maximum average success probability of the unambiguous discrimination of two nonorthogonal quantum states |ψ₁〉and|ψ₂〉. As an example, we give the explicit transformation of the optimal symmetric 1 → M probabilistically perfect quantum cloning to copy the two input states |ψ₁〉 and |ψ₂〉.     

Necessary and sufficient conditions on n-qudit state for perfect teleportation of an arbitrary single qudit state

Firstly, we investigate the necessary and sufficient conditions that an entangled channel of n-qubits should satisfy to carry out perfect teleportation of an arbitrary single qubit state and dense coding. It is shown that the sender can transmit two classical bits of information by sending one qubit. Further, the case of high-dimension quantum state is also considered. Utilizing n-qudit state as quantum channel, it is proposed that the necessary and sufficient conditions are in all to teleport an arbitrary single qudit state. The sender can transmit 2log₂d classical bits of information to the receiver conditioned on the constraints.     

Duplicating classical bits with universal quantum cloning machine

It seems there is a large gap between quantum cloning and classical duplication since quantum mechanics forbid perfect copies of unknown quantum states. In this paper, we prove that a classical duplication process can be realized by using a universal quantum cloning machine(QCM). A classical bit is encoded not on a single quantum state, but on a large number of single identical quantum states. Errors are inevitable when copying these identical quantum states due to the quantum no-cloning theorem. When a small part of errors are ignored, i.e., errors as the minority are automatically corrected by the majority, the fidelity of duplicated copies of classical information will approach unity infinitely. In this way, the classical bits can be duplicated precisely with a universal QCM, which presents a natural transition from quantum cloning to classical duplication. The implement of classical duplication by using QCM shines new lights on the universality of quantum mechanics.     

Assisted Cloning and Orthogonal Complementing of an Arbitrary Unknown Two-Qubit State with χ-Type Entangled States

We propose a scheme for cloning an arbitrary unknown two-qubit state and its orthogonal complement state with the assistance from the state preparer. Our scheme includes two stages. The first stage requires a quantum teleportation process, in which an arbitrary unknown two-qubit state can be deterministically teleported from the sender to the receiver with χ-type entangled states as the quantum channel. In the second stage, with the assistance of the state preparer, either a perfect copy or an orthogonal complement state of an arbitrary unknown two-qubit state can be obtained with a certain probability.     

Quantum Cloning of an Unknown Two-Particle Entangled State with Assistance

We propose a protocol where one can realize quantum cloning of an unknown two-particle entangled state and its orthogonal-complement state with assistance offered by a state preparer. The first stage of the protocol requires usual teleportation using a (or two) four-particle entangled state(s) as quantum channel(s). In the second stage of the protocol, with the assistance (through a two-particle projective measurement) of the preparer, the perfect copies and complement copies of an unknown state can be produced.