Probabilistic quantum multimeters

We propose quantum devices that can realize probabilistically different projective measurements on a qubit. The desired measurement basis is selected by the quantum state of a program register. First we analyze the phase-covariant multimeters for a large class of program states, then the universal multimeters for a special choice of program. In both cases we start with deterministic but erroneous devices and then proceed to devices that never make a mistake but from time to time they give an inconclusive result. These multimeters are optimized (for a given type of a program) with respect to the minimum probability of inconclusive result. This concept is further generalized to the multimeters that minimize the error rate for a given probability of an inconclusive result (or vice versa). Finally, we propose a generalization for qudits.Comment: 12 pages, 3 figure

Optimal multicopy asymmetric Gaussian cloning of coherent states

We investigate the asymmetric Gaussian cloning of coherent states which produces M copies from N input replicas, such that the fidelity of all copies may be different. We show that the optimal asymmetric Gaussian cloning can be performed with a single phase-insensitive amplifier and an array of beam splitters. We obtain a simple analytical expression characterizing the set of optimal asymmetric Gaussian cloning machines.Comment: 7 pages, 2 figures, RevTeX

Minimal disturbance measurement for coherent states is non-Gaussian

In standard coherent state teleportation with shared two-mode squeezed vacuum (TMSV) state there is a trade-off between the teleportation fidelity and the fidelity of estimation of the teleported state from results of the Bell measurement. Within the class of Gaussian operations this trade-off is optimal, i.e. there is not a Gaussian operation which would give for a given output fidelity a larger estimation fidelity. We show that this trade-off can be improved by up to 2.77% if we use a suitable non-Gaussian operation. This operation can be implemented by the standard teleportation protocol in which the shared TMSV state is replaced with a suitable non-Gaussian entangled state. We also demonstrate that this operation can be used to enhance the transmission fidelity of a certain noisy channel.Comment: submitted to Physical Review A, new results added, 7 pages, 4 figure

Virtual noiseless amplification and Gaussian post-selection in continuous-variable quantum key distribution

The noiseless amplification or attenuation are two heralded filtering operations that enable respectively to increase or decrease the mean field of any quantum state of light with no added noise, at the cost of a small success probability. We show that inserting such noiseless operations in a transmission line improves the performance of continuous-variable quantum key distribution over this line. Remarkably, these noiseless operations do not need to be physically implemented but can simply be simulated in the data post-processing stage. Hence, virtual noiseless amplification or attenuation amounts to perform a Gaussian post-selection, which enhances the secure range or tolerable excess noise while keeping the benefits of Gaussian security proofs.Comment: 8 pages, 5 figure

A No-Go Theorem for Gaussian Quantum Error Correction

It is proven that Gaussian operations are of no use for protecting Gaussian states against Gaussian errors in quantum communication protocols. Specifically, we introduce a new quantity characterizing any single-mode Gaussian channel, called entanglement degradation, and show that it cannot decrease via Gaussian encoding and decoding operations only. The strength of this no-go theorem is illustrated with some examples of Gaussian channels.Comment: 4 pages, 2 figures, REVTeX

Optimal partial estimation of quantum states from several copies

We derive analytical formula for the optimal trade-off between the mean estimation fidelity and the mean fidelity of the qubit state after a partial measurement on N identically prepared qubits. We also conjecture analytical expression for the optimal fidelity trade-off in case of a partial measurement on N identical copies of a d-level system.Comment: 5 pages, 2 figures, RevTeX

Loophole-free test of quantum non-locality using high-efficiency homodyne detectors

We provide a detailed analysis of the recently proposed setup for a loophole-free test of Bell inequality using conditionally generated non-Gaussian states of light and balanced homodyning. In the proposed scheme, a two-mode squeezed vacuum state is de-gaussified by subtracting a single photon from each mode with the use of an unbalanced beam splitter and a standard low-efficiency single-photon detector. We thoroughly discuss the dependence of the achievable Bell violation on the various relevant experimental parameters such as the detector efficiencies, the electronic noise and the mixedness of the initial Gaussian state. We also consider several alternative schemes involving squeezed states, linear optical elements, conditional photon subtraction and homodyne detection.Comment: 13 pages, 14 figures, RevTeX

On the distillation and purification of phase-diffused squeezed states

Recently it was discovered that non-Gaussian decoherence processes, such as phase-diffusion, can be counteracted by purification and distillation protocols that are solely built on Gaussian operations. Here, we make use of this experimentally highly accessible regime, and provide a detailed experimental and theoretical analysis of several strategies for purification/distillation protocols on phase-diffused squeezed states. Our results provide valuable information for the optimization of such protocols with respect to the choice of the trigger quadrature, the trigger threshold value and the probability of generating a distilled state

Optimal Cloning and Singlet Monogamy

The inability to produce two perfect copies of an unknown state is inherently linked with the inability to produce maximal entanglement between multiple spins. Despite this, there is no quantitative link between how much entanglement can be generated between spins (known as monogamy), and how well an unknown state can be cloned. This situation is remedied by giving a set of sufficient conditions such that the optimal Completely Positive map can be implemented as a teleportation operation into a standard, reference, state. The case of arbitrary 1 to N asymmetric cloning of d-dimensional spins can then be solved exactly, yielding the concept of `singlet monogamy'. The utility of this relation is demonstrated by calculating properties of Heisenberg systems, and contrasting them with the results from standard monogamy arguments.Comment: 4 pages, 1 figure. v2: conjecture upgraded to proof and generalized to arbitrary local hilbert space dimensions. v3: published versio

Optimal probabilistic cloning and purification of quantum states

We investigate the probabilistic cloning and purification of quantum states. The performance of these probabilistic operations is quantified by the average fidelity between the ideal and actual output states. We provide a simple formula for the maximal achievable average fidelity and we explictly show how to construct a probabilistic operation that achieves this fidelity. We illustrate our method on several examples such as the phase covariant cloning of qubits, cloning of coherent states, and purification of qubits transmitted via depolarizing channel and amplitude damping channel. Our examples reveal that the probabilistic cloner may yield higher fidelity than the best deterministic cloner even when the states that should be cloned are linearly dependent and are drawn from a continuous set.Comment: 9 pages, 2 figure