Additive Extensions of a Quantum Channel

We study extensions of a quantum channel whose one-way capacities are described by a single-letter formula. This provides a simple technique for generating powerful upper bounds on the capacities of a general quantum channel. We apply this technique to two qubit channels of particular interest--the depolarizing channel and the channel with independent phase and amplitude noise. Our study of the latter demonstrates that the key rate of BB84 with one-way post-processing and quantum bit error rate q cannot exceed H(1/2-2q(1-q)) - H(2q(1-q)).Comment: 6 pages, one figur

Superadditivity in trade-off capacities of quantum channels

In this article, we investigate the additivity phenomenon in the dynamic capacity of a quantum channel for trading classical communication, quantum communication and entanglement. Understanding such additivity property is important if we want to optimally use a quantum channel for general communication purpose. However, in a lot of cases, the channel one will be using only has an additive single or double resource capacity, and it is largely unknown if this could lead to an superadditive double or triple resource capacity. For example, if a channel has an additive classical and quantum capacity, can the classical-quantum capacity be superadditive? In this work, we answer such questions affirmatively. We give proof-of-principle requirements for these channels to exist. In most cases, we can provide an explicit construction of these quantum channels. The existence of these superadditive phenomena is surprising in contrast to the result that the additivity of both classical-entanglement and classical-quantum capacity regions imply the additivity of the triple capacity region.Comment: 15 pages. v2: typo correcte

Fundamental limits on key rates in device-independent quantum key distribution

In this paper, we introduce intrinsic non-locality as a quantifier for Bell non-locality, and we prove that it satisfies certain desirable properties such as faithfulness, convexity, and monotonicity under local operations and shared randomness. We then prove that intrinsic non-locality is an upper bound on the secret-key-agreement capacity of any device-independent protocol conducted using a device characterized by a correlation $p$. We also prove that intrinsic steerability is an upper bound on the secret-key-agreement capacity of any semi-device-independent protocol conducted using a device characterized by an assemblage $\hat{\rho}$. We also establish the faithfulness of intrinsic steerability and intrinsic non-locality. Finally, we prove that intrinsic non-locality is bounded from above by intrinsic steerability.Comment: 44 pages, 4 figures, final version accepted for publication in New Journal of Physic

Forgetfulness of continuous Markovian quantum channels

The notion of forgetfulness, used in discrete quantum memory channels, is slightly weakened in order to be applied to the case of continuous channels. This is done in the context of quantum memory channels with Markovian noise. As a case study, we apply the notion of weak-forgetfulness to a bosonic memory channel with additive noise. A suitable encoding and decoding unitary transformation allows us to unravel the effects of the memory, hence the channel capacities can be computed using known results from the memoryless setting.Comment: 6 pages, 2 figures, comments are welcome. Minor corrections and acknoledgment adde

Uncertainty, Monogamy, and Locking of Quantum Correlations

Squashed entanglement and entanglement of purification are quantum mechanical correlation measures and defined as certain minimisations of entropic quantities. We present the first non-trivial calculations of both quantities. Our results lead to the conclusion that both measures can drop by an arbitrary amount when only a single qubit of a local system is lost. This property is known as "locking" and has previously been observed for other correlation measures, such as the accessible information, entanglement cost and the logarithmic negativity. In the case of squashed entanglement, the results are obtained with the help of an inequality that can be understood as a quantum channel analogue of well-known entropic uncertainty relations. This inequality may prove a useful tool in quantum information theory. The regularised entanglement of purification is known to equal the entanglement needed to prepare a many copies of quantum state by local operations and a sublinear amount of communication. Here, monogamy of quantum entanglement (i.e., the impossibility of a system being maximally entangled with two others at the same time) leads to an exact calculation for all quantum states that are supported either on the symmetric or on the antisymmetric subspace of a dxd-dimensional system.Comment: 7 pages revtex4, no figures. v2 has improved presentation and a couple of references adde

"Squashed Entanglement" - An Additive Entanglement Measure

In this paper, we present a new entanglement monotone for bipartite quantum states. Its definition is inspired by the so-called intrinsic information of classical cryptography and is given by the halved minimum quantum conditional mutual information over all tripartite state extensions. We derive certain properties of the new measure which we call "squashed entanglement": it is a lower bound on entanglement of formation and an upper bound on distillable entanglement. Furthermore, it is convex, additive on tensor products, and superadditive in general. Continuity in the state is the only property of our entanglement measure which we cannot provide a proof for. We present some evidence, however, that our quantity has this property, the strongest indication being a conjectured Fannes type inequality for the conditional von Neumann entropy. This inequality is proved in the classical case.Comment: 8 pages, revtex4. v2 has some more references and a bit more discussion, v3 continuity discussion extended, typos correcte

A Stochastic Liouville Equation Approach for the Effect of Noise in Quantum Computations

We propose a model based on a generalized effective Hamiltonian for studying the effect of noise in quantum computations. The system-environment interactions are taken into account by including stochastic fluctuating terms in the system Hamiltonian. Treating these fluctuations as Gaussian Markov processes with zero mean and delta function correlation times, we derive an exact equation of motion describing the dissipative dynamics for a system of n qubits. We then apply this model to study the effect of noise on the quantum teleportation and a generic quantum controlled-NOT (CNOT) gate. For the quantum CNOT gate, we study the effect of noise on a set of one- and two-qubit quantum gates, and show that the results can be assembled together to investigate the quality of a quantum CNOT gate operation. We compute the averaged gate fidelity and gate purity for the quantum CNOT gate, and investigate phase, bit-flip, and flip-flop errors during the CNOT gate operation. The effects of direct inter-qubit coupling and fluctuations on the control fields are also studied. We discuss the limitations and possible extensions of this model. In sum, we demonstrate a simple model that enables us to investigate the effect of noise in arbitrary quantum circuits under realistic device conditions.Comment: 36 pages, 6 figures; to be submitted to Phys. Rev.