Secure quantum key distribution using squeezed states

We prove the security of a quantum key distribution scheme based on transmission of squeezed quantum states of a harmonic oscillator. Our proof employs quantum error-correcting codes that encode a finite-dimensional quantum system in the infinite-dimensional Hilbert space of an oscillator, and protect against errors that shift the canonical variables p and q. If the noise in the quantum channel is weak, squeezing signal states by 2.51 dB (a squeeze factor e^r=1.34) is sufficient in principle to ensure the security of a protocol that is suitably enhanced by classical error correction and privacy amplification. Secure key distribution can be achieved over distances comparable to the attenuation length of the quantum channel.Comment: 19 pages, 3 figures, RevTeX and epsf, new section on channel losse

Decoherence and Entanglement in Two-mode Squeezed Vacuum States

I investigate the decoherence of two-mode squeezed vacuum states by analyzing the relative entropy of entanglement. I consider two sources of decoherence: (i) the phase damping and (ii) the amplitude damping due to the coupling to the thermal environment. In particular, I give the exact value of the relative entropy of entanglement for the phase damping model. For the amplitude damping model, I give an upper bound for the relative entropy of entanglement, which turns out to be a good approximation for the entanglement measure in usual experimental situations.Comment: 5 pages, RevTex, 3 eps figure

Correlated Errors in Quantum Error Corrections

We show that errors are not generated correlatedly provided that quantum bits do not directly interact with (or couple to) each other. Generally, this no-qubits-interaction condition is assumed except for the case where two-qubit gate operation is being performed. In particular, the no-qubits-interaction condition is satisfied in the collective decoherence models. Thus, errors are not correlated in the collective decoherence. Consequently, we can say that current quantum error correcting codes which correct single-qubit-errors will work in most cases including the collective decoherence.Comment: no correction, 3 pages, RevTe

Characterizing the entanglement of bipartite quantum systems

We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria.Comment: 5 pages, 2 figures. Revised versio

Geometric entangling gates for coupled cavity system in decoherence-free subspaces

We propose a scheme to implement geometric entangling gates for two logical qubits in a coupled cavity system in decoherence-free subspaces. Each logical qubit is encoded with two atoms trapped in a single cavity and the geometric entangling gates are achieved by cavity coupling and controlling the external classical laser fields. Based on the coupled cavity system, the scheme allows the scalability for quantum computing and relaxes the requirement for individually addressing atoms.Comment: 6 pages, 1 figur

Robustness of Decoherence-Free Subspaces for Quantum Computation

It was shown recently [D.A. Lidar et al., Phys. Rev. Lett. 81, 2594 (1998)] that within the framework of the semigroup Markovian master equation, decoherence-free (DF) subspaces exist which are stable to first order in time to a perturbation. Here this result is extended to the non-Markovian regime and generalized. In particular, it is shown that within both the semigroup and the non-Markovian operator sum representation, DF subspaces are stable to all orders in time to a symmetry-breaking perturbation. DF subspaces are thus ideal for quantum memory applications. For quantum computation, however, the stability result does not extend beyond the first order. Thus, to perform robust quantum computation in DF subspaces, they must be supplemented with quantum error correcting codes.Comment: 16 pages, no figures. Several changes, including a clarification of the derivation of the Lindblad equation from the operator sum representation. To appear in Phys. Rev

A framework for bounding nonlocality of state discrimination

We consider the class of protocols that can be implemented by local quantum operations and classical communication (LOCC) between two parties. In particular, we focus on the task of discriminating a known set of quantum states by LOCC. Building on the work in the paper "Quantum nonlocality without entanglement" [BDF+99], we provide a framework for bounding the amount of nonlocality in a given set of bipartite quantum states in terms of a lower bound on the probability of error in any LOCC discrimination protocol. We apply our framework to an orthonormal product basis known as the domino states and obtain an alternative and simplified proof that quantifies its nonlocality. We generalize this result for similar bases in larger dimensions, as well as the "rotated" domino states, resolving a long-standing open question [BDF+99].Comment: 33 pages, 7 figures, 1 tabl

Detecting genuine multipartite continuous-variable entanglement

We derive necessary conditions in terms of the variances of position and momentum linear combinations for all kinds of separability of a multi-party multi-mode continuous-variable state. Their violations can be sufficient for genuine multipartite entanglement, provided the combinations contain both conjugate variables of all modes. Hence a complete state determination, for example by detecting the entire correlation matrix of a Gaussian state, is not needed.Comment: 13 pages, 3 figure

Entanglement concentration of continuous variable quantum states

We propose two probabilistic entanglement concentration schemes for a single copy of two-mode squeezed vacuum state. The first scheme is based on the off-resonant interaction of a Rydberg atom with the cavity field while the second setup involves the cross Kerr interaction, auxiliary mode prepared in a strong coherent state and a homodyne detection. We show that the continuous-variable entanglement concentration allows us to improve the fidelity of teleportation of coherent states.Comment: 7 pages, 7 figure

Creating Bell states and decoherence effects in quantum dots system

We show how to improve the efficiency for preparing Bell states in coupled two quantum dots system. A measurement to the state of driven quantum laser field leads to wave function collapse. This results in highly efficiency preparation of Bell states. The effect of decoherence on the efficiency of generating Bell states is also discussed in this paper. The results show that the decoherence does not affect the relative weight of $|00>$ and $|11>$ in the output state, but the efficiency of finding Bell states.Comment: 4 pages, 2figures, corrected some typo