Quantum copying: A network

We present a network consisting of quantum gates which produces two imperfect copies of an arbitrary qubit. The quality of the copies does not depend on the input qubit. We also show that for a restricted class of inputs it is possible to use a very similar network to produce three copies instead of two. For qubits in this class, the copy quality is again independent of the input and is the same as the quality of the copies produced by the two-copy network.Comment: 10 pages LaTeX, with 1 figure, submitted to the Physical Review

Bounds for state-dependent quantum cloning

Due to the no-cloning theorem, the unknown quantum state can only be cloned approximately or exactly with some probability. There are two types of cloners: universal and state-dependent cloner. The optimal universal cloner has been found and could be viewed as a special state-dependent quantum cloner which has no information about the states. In this paper, we investigate the state-dependent cloning when the state-set contains more than two states. We get some bounds of the global fidelity for these processes. This method is not dependent on the number of the states contained in the state-set. It is also independent of the numbers of copying.Comment: 13 pages, 1 figure, to appear in Phys. Rev.

Quantum disentanglers

It is not possible to disentangle a qubit in an unknown state $|\psi>$ from a set of (N-1) ancilla qubits prepared in a specific reference state $|0>$. That is, it is not possible to {\em perfectly} perform the transformation $(|\psi,0...,0\r +|0,\psi,...,0\r +...+ |0,0,...\psi\r) \to |0,...,0>\otimes |\psi>$. The question is then how well we can do? We consider a number of different methods of extracting an unknown state from an entangled state formed from that qubit and a set of ancilla qubits in an known state. Measuring the whole system is, as expected, the least effective method. We present various quantum ``devices'' which disentangle the unknown qubit from the set of ancilla qubits. In particular, we present the optimal universal disentangler which disentangles the unknown qubit with the fidelity which does not depend on the state of the qubit, and a probabilistic disentangler which performs the perfect disentangling transformation, but with a probability less than one.Comment: 8 pages, 1 eps figur

Multipartite Classical and Quantum Secrecy Monotones

In order to study multipartite quantum cryptography, we introduce quantities which vanish on product probability distributions, and which can only decrease if the parties carry out local operations or carry out public classical communication. These ``secrecy monotones'' therefore measure how much secret correlations are shared by the parties. In the bipartite case we show that the mutual information is a secrecy monotone. In the multipartite case we describe two different generalisations of the mutual information, both of which are secrecy monotones. The existence of two distinct secrecy monotones allows us to show that in multipartite quantum cryptography the parties must make irreversible choices about which multipartite correlations they want to obtain. Secrecy monotones can be extended to the quantum domain and are then defined on density matrices. We illustrate this generalisation by considering tri-partite quantum cryptography based on the Greenberger-Horne-Zeilinger (GHZ) state. We show that before carrying out measurements on the state, the parties must make an irreversible decision about what probability distribution they want to obtain

Entanglement of coherent states and decoherence

A possibility to produce entangled superpositions of strong coherent states is discussed. A recent proposal by Howell and Yazell [Phys. Rev. A 62, 012102 (2000)] of a device which entangles two strong coherent coherent states is critically examined. A serious flaw in their design is found. New modified scheme is proposed and it is shown that it really can generate non-classical states that can violate Bell inequality. Moreover, a profound analysis of the effect of losses and decoherence on the degree of entanglement is accomplished. It reveals the high sensitivity of the device to any disturbances and the fragility of generated states

Undetermined states: how to find them and their applications

We investigate the undetermined sets consisting of two-level, multi-partite pure quantum states, whose reduced density matrices give absolutely no information of their original states. Two approached of finding these quantum states are proposed. One is to establish the relation between codewords of the stabilizer quantum error correction codes (SQECCs) and the undetermined states. The other is to study the local complementation rules of the graph states. As an application, the undetermined states can be exploited in the quantum secret sharing scheme. The security is guaranteed by their undetermineness.Comment: 6 pages, no figur

Universal cloning of continuous quantum variables

The cloning of quantum variables with continuous spectra is analyzed. A universal - or Gaussian - quantum cloning machine is exhibited that copies equally well the states of two conjugate variables such as position and momentum. It also duplicates all coherent states with a fidelity of 2/3. More generally, the copies are shown to obey a no-cloning Heisenberg-like uncertainty relation.Comment: 4 pages, RevTex. Minor revisions, added explicit cloning transformation, added reference

Optimal manipulations with qubits: Universal quantum entanglers

We analyze various scenarios for entangling two initially unentangled qubits. In particular, we propose an optimal universal entangler which entangles a qubit in unknown state $|\Psi>$ with a qubit in a reference (known) state $|0>$. That is, our entangler generates the output state which is as close as possible to the pure (symmetrized) state $(|\Psi>|0> +|0>|\Psi>)$. The most attractive feature of this entangling machine, is that the fidelity of its performance (i.e. the distance between the output and the ideally entangled -- symmetrized state) does not depend on the input and takes the constant value $F= (9+3\sqrt{2})/14\simeq 0.946$. We also analyze how to optimally generate from a single qubit initially prepared in an unknown state |\Psi\r a two qubit entangled system which is as close as possible to a Bell state $(|\Psi\r|\Psi^\perp\r+|\Psi^\perp\r|\Psi\r)$, where \l\Psi|\Psi^\perp\r =0.Comment: 11 pages, 3 eps figures, accepted for publication in Phys. Rev.

Security of quantum cryptography using balanced homodyne detection

In this paper we investigate the security of a quantum cryptographic scheme which utilizes balanced homodyne detection and weak coherent pulse (WCP). The performance of the system is mainly characterized by the intensity of the WCP and postselected threshold. Two of the simplest intercept/resend eavesdropping attacks are analyzed. The secure key gain for a given loss is also discussed in terms of the pulse intensity and threshold.Comment: RevTeX4, 8pages, 7 figure