arXiv subjects

N. J. Cerf

Publications and source records attributed to N. J. Cerf.

At least 37 records · Page 2Linked to original sources

arXiv2006

Entanglement may enhance the channel capacity in arbitrary dimensions

We consider explicitly two examples of d-dimensional quantum channels with correlated noise and show that, in agreement with previous results on Pauli qubit channels, there are situations where maximally entangled input states achieve higher values of the output mutual information than product states. We obtain a strong dependence of this effect on the nature of the noise correlations as well as on the parity of the space dimension, and conjecture that when entanglement gives an advantage in terms of mutual information, maximally entangled states achieve the channel capacity.

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arXiv2006

Entanglement enhanced classical capacity of quantum communication channels with correlated noise in arbitrary dimensions

We study the capacity of d-dimensional quantum channels with memory modeled by correlated noise. We show that, in agreement with previous results on Pauli qubit channels, there are situations where maximally entangled input states achieve higher values of mutual information than product states. Moreover, a strong dependence of this effect on the nature of the noise correlations as well as on the parity of the space dimension is found. We conjecture that when entanglement gives an advantage in terms of mutual information, maximally entangled states saturate the channel capacity.

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arXiv2006

Experimental Proof of Quantum Nonlocality without Squeezing

It is shown that the ensemble $\{p (α),|α>|α^*>\}$ where $p (α)$ is a Gaussian distribution of finite variance and $| α>$ is a coherent state can be better discriminated with an entangled measurement than with any local strategy supplemented by classical communication. Although this ensemble consists of products of quasi-classical states, it exhibits some quantum nonlocality. This remarkable effect is demonstrated experimentally by implementing the optimal local strategy together with a joint nonlocal strategy that yields a higher fidelity.

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arXiv2006

Multipartite Nonlocality without Entanglement in Many Dimensions

We present a generic method to construct a product basis exhibiting Nonlocality Without Entanglement with $n$ parties each holding a system of dimension at least $n-1$. This basis is generated via a quantum circuit made of control-Discrete Fourier Transform gates acting on the computational basis. The simplicity of our quantum circuit allows for an intuitive understanding of this new type of nonlocality. We also show how this circuit can be used to construct Unextendible Product Bases and their associated Bound Entangled States. To our knowledge, this is the first method which, given a general Hilbert space $\bigotimes_{i=1}^n {\cal H}_{d_i}$ with $d_i\le n-1$, makes it possible to construct (i) a basis exhibiting Nonlocality Without Entanglement, (ii) an Unextendible Product Basis, and (iii) a Bound Entangled state.

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arXiv2006

Universal optical amplification without nonlinearity

We propose and experimentally realize a new scheme for universal phase-insensitive optical amplification. The presented scheme relies only on linear optics and homodyne detection, thus circumventing the need for nonlinear interaction between a pump field and the signal field. The amplifier demonstrates near optimal quantum noise limited performance for a wide range of amplification factors.

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arXiv2005

Extremal quantum cloning machines

We investigate the problem of cloning a set of states that is invariant under the action of an irreducible group representation. We then characterize the cloners that are "extremal" in the convex set of group covariant cloning machines, among which one can restrict the search for optimal cloners. For a set of states that is invariant under the discrete Weyl-Heisenberg group, we show that all extremal cloners can be unitarily realized using the so-called "double-Bell states", whence providing a general proof of the popular ansatz used in the literature for finding optimal cloners in a variety of settings. Our result can also be generalized to continuous-variable optimal cloning in infinite dimensions, where the covariance group is the customary Weyl-Heisenberg group of displacements.

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arXiv2005

Separating the classical and quantum information via quantum cloning

An application of quantum cloning to optimally interface a quantum system with a classical observer is presented, in particular we describe a procedure to perform a minimal disturbance measurement on a single qubit by adopting a 1->2 cloning machine followed by a generalized measurement on a single clone and the anti-clone or on the two clones. Such scheme has been applied to enhance the transmission fidelity over a lossy quantum channel.

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arXiv2005

Reduced randomness in quantum cryptography with sequences of qubits encoded in the same basis

We consider the cloning of sequences of qubits prepared in the states used in the BB84 or 6-state quantum cryptography protocol, and show that the single-qubit fidelity is unaffected even if entire sequences of qubits are prepared in the same basis. This result is of great importance for practical quantum cryptosystems because it reduces the need for high-speed random number generation without impairing on the security against finite-size attacks.

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arXiv2005

Cloning quantum entanglement in arbitrary dimensions

We have found a quantum cloning machine that optimally duplicates the entanglement of a pair of $d$-dimensional quantum systems. It maximizes the entanglement of formation contained in the two copies of any maximally-entangled input state, while preserving the separability of unentangled input states. Moreover, it cannot increase the entanglement of formation of all isotropic states. For large $d$, the entanglement of formation of each clone tends to one half the entanglement of the input state, which corresponds to a classical behavior. Finally, we investigate a local entanglement cloner, which yields entangled clones with one fourth the input entanglement in the large-$d$ limit.

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arXiv2004

The optimal cloning of quantum coherent states is non-Gaussian

We consider the optimal cloning of quantum coherent states with single-clone and joint fidelity as figures of merit. Both optimal fidelities are attained for phase space translation covariant cloners. Remarkably, the joint fidelity is maximized by a Gaussian cloner, whereas the single-clone fidelity can be enhanced by non-Gaussian operations: a symmetric non-Gaussian 1-to-2 cloner can achieve a single-clone fidelity of approximately 0.6826, perceivably higher than the optimal fidelity of 2/3 in a Gaussian setting. This optimal cloner can be realized by means of an optical parametric amplifier supplemented with a particular source of non-Gaussian bimodal states. Finally, we show that the single-clone fidelity of the optimal 1-to-infinity cloner, corresponding to a measure-and-prepare scheme, cannot exceed 1/2. This value is achieved by a Gaussian scheme and cannot be surpassed even with supplemental bound entangled states.

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arXiv2004

Multipartite Asymmetric Quantum Cloning

We investigate the optimal distribution of quantum information over multipartite systems in asymmetric settings. We introduce cloning transformations that take $N$ identical replicas of a pure state in any dimension as input, and yield a collection of clones with non-identical fidelities. As an example, if the clones are partitioned into a set of $M_A$ clones with fidelity $F^A$ and another set of $M_B$ clones with fidelity $F^B$, the trade-off between these fidelities is analyzed, and particular cases of optimal $N \to M_A+M_B$ cloning machines are exhibited. We also present an optimal $1 \to 1+1+1$ cloning machine, which is the first known example of a tripartite fully asymmetric cloner. Finally, it is shown how these cloning machines can be optically realized.

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arXiv2004

Asymmetric phase-covariant d-dimensional cloning

We consider cloning transformations of d-dimensional states of the form e^{iϕ_0}|0> + e^{iϕ_1}|1> +...+ e^{iϕ_{d-1}}|d-1> that are covariant with respect to rotations of the phases ϕ_i's. The optimal cloning maps are easily obtained using a well-defined general characterization of state-dependent 1 -> 2 cloning transformations in arbitrary dimensions. Our results apply to symmetric as well as asymmetric cloners, so that the balance between the fidelity of the two clones can be analyzed.

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arXiv2004

Secure Coherent-state Quantum Key Distribution Protocols with Efficient Reconciliation

We study the equivalence between a realistic quantum key distribution protocol using coherent states and homodyne detection and a formal entanglement purification protocol. Maximally-entangled qubit pairs that one can extract in the formal protocol correspond to secret key bits in the realistic protocol. More specifically, we define a qubit encoding scheme that allows the formal protocol to produce more than one entangled qubit pair per coherent state, or equivalently for the realistic protocol, more than one secret key bit. The entanglement parameters are estimated using quantum tomography. We analyze the properties of the encoding scheme and investigate its application to the important case of the attenuation channel.

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arXiv2004

Quantum entanglement can be simulated without communication

It has recently been shown that all causal correlations between two parties which output each one bit, a and b, when receiving each one bit, x and y, can be expressed as convex combinations of local correlations (i.e., correlations that can be simulated with local random variables) and non-local correlations of the form a+b=xy mod 2. We show that a single instance of the latter elementary non-local correlation suffices to simulate exactly all possible projective measurements that can be performed on the singlet state of two qubits, with no communication needed at all. This elementary non-local correlation thus defines some unit of non-locality, which we call a nl-bit.

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arXiv2004

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.

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arXiv2004

Pulsed squeezed vacuum characterization without homodyning

Direct photon detection is experimentally implemented to measure the squeezing and purity of a single-mode squeezed vacuum state without an interferometric homodyne detection. Following a recent theoretical proposal [arXiv quant-ph/0311119], the setup only requires a tunable beamsplitter and a single-photon detector to fully characterize the generated Gaussian states. The experimental implementation of this procedure is discussed and compared with other reference methods.

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arXiv2004

Proposal for a loophole-free Bell test using homodyne detection

We propose a feasible optical setup allowing for a loophole-free Bell test with efficient homodyne detection. A non-gaussian entangled state is generated from a two-mode squeezed vacuum by subtracting a single photon from each mode, using beamsplitters and standard low-efficiency single-photon detectors. A Bell violation exceeding 1% is achievable with 6-dB squeezed light and an homodyne efficiency around 95%. A detailed feasibility analysis, based upon the recent generation of single-mode non-gaussian states, confirms that this method opens a promising avenue towards a complete experimental Bell test.

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arXiv2004

Experimental Purification of Single Qubits

We report the experimental realization of the purification protocol for single qubits sent through a depolarization channel. The qubits are associated with polarization encoded photon particles and the protocol is achieved by means of passive linear optical elements. The present approach may represent a convenient alternative to the distillation and error correction protocols of quantum information.

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