Entangled inputs cannot make imperfect quantum channels perfect

Entangled inputs can enhance the capacity of quantum channels, this being one of the consequences of the celebrated result showing the non-additivity of several quantities relevant for quantum information science. In this work, we answer the converse question (whether entangled inputs can ever render noisy quantum channels have maximum capacity) to the negative: No sophisticated entangled input of any quantum channel can ever enhance the capacity to the maximum possible value; a result that holds true for all channels both for the classical as well as the quantum capacity. This result can hence be seen as a bound as to how "non-additive quantum information can be". As a main result, we find first practical and remarkably simple computable single-shot bounds to capacities, related to entanglement measures. As examples, we discuss the qubit amplitude damping and identify the first meaningful bound for its classical capacity.Comment: 5 pages, 2 figures, an error in the argument on the quantum capacity corrected, version to be published in the Physical Review Letter

Parmenidean Monism and The Routes of Being

Resum

Perspectivism and Conciliation in the Reading of Plato’s Dialogues

In recent decades, a growing number of scholars have questioned the developmental approach to Plato that dominated scholarship during the 20th century. In this context, old strategies of reading the dialogues have been renewed and new approaches proposed. Basically, three different reading strategies the dialogues have been advocated: the still dominant Developmentalism, Unitarianism, and the Literary (or Dramatic) reading. These different approaches are still largely taken as competitors and there seems to be no methodology available that systematically integrates these different readings. In this paper, I work upon the “Perspective reading” proposed by Kahn (2005), and Gonzales (2016) in order to present a methodology that integrates some aspects of these different approaches in a systematic and coherent way. -- Original in English.In recent decades, a growing number of scholars have questioned the developmental approach to Plato that dominated scholarship during the 20th century. In this context, old strategies of reading the dialogues have been renewed and new approaches proposed. Basically, three different reading strategies the dialogues have been advocated: the still dominant Developmentalism, Unitarianism, and the Literary (or Dramatic) reading. These different approaches are still largely taken as competitors and there seems to be no methodology available that systematically integrates these different readings. In this paper, I work upon the “Perspective reading” proposed by Kahn (2005), and Gonzales (2016) in order to present a methodology that integrates some aspects of these different approaches in a systematic and coherent way. Perspectivismo e Conciliação na Leitura dos Diálogos de Platão Nas últimas décadas, a abordagem desenvolvimentista da obra de Platão, que dominou a academia durante o século XX, tem sido progressivamente questionada. Nesse contexto, antigas estratégias de leitura dos diálogos foram renovadas e novas abordagens, propostas. Basicamente, três estratégias de leitura dos diálogos foram defendidas: a, ainda dominante, leitura desenvolvimentista, o unitarismo e a leitura literária (ou dramática). Essas diferentes abordagens ainda são amplamente consideradas como concorrentes e parece não haver metodologia disponível que integre essas diferentes leituras. Neste artigo, desenvolvo a “leitura de perspectivista” proposta por Kahn (2005) e Gonzales (2016), a fim de apresentar uma metodologia que integre aspectos importantes das três abordagens acima citadas de maneira sistemática e coerente. -- Original em inglês. &nbsp

Witnessed Entanglement

We present a new measure of entanglement for mixed states. It can be approximately computable for every state and can be used to quantify all different types of multipartite entanglement. We show that it satisfies the usual properties of a good entanglement quantifier and derive relations between it and other entanglement measures.Comment: Revised version. 7 pages and one figur

Are all maximally entangled states pure?

We study if all maximally entangled states are pure through several entanglement monotones. In the bipartite case, we find that the same conditions which lead to the uniqueness of the entropy of entanglement as a measure of entanglement, exclude the existence of maximally mixed entangled states. In the multipartite scenario, our conclusions allow us to generalize the idea of monogamy of entanglement: we establish the \textit{polygamy of entanglement}, expressing that if a general state is maximally entangled with respect to some kind of multipartite entanglement, then it is necessarily factorized of any other system.Comment: 5 pages, 1 figure. Proof of theorem 3 corrected e new results concerning the asymptotic regime include

Schmidt balls around the identity

Robustness measures as introduced by Vidal and Tarrach [PRA, 59, 141-155] quantify the extent to which entangled states remain entangled under mixing. Analogously, we introduce here the Schmidt robustness and the random Schmidt robustness. The latter notion is closely related to the construction of Schmidt balls around the identity. We analyse the situation for pure states and provide non-trivial upper and lower bounds. Upper bounds to the random Schmidt-2 robustness allow us to construct a particularly simple distillability criterion. We present two conjectures, the first one is related to the radius of inner balls around the identity in the convex set of Schmidt number n-states. We also conjecture a class of optimal Schmidt witnesses for pure states.Comment: 7 pages, 1 figur

Separable Multipartite Mixed States - Operational Asymptotically Necessary and Sufficient Conditions

We introduce an operational procedure to determine, with arbitrary probability and accuracy, optimal entanglement witness for every multipartite entangled state. This method provides an operational criterion for separability which is asymptotically necessary and sufficient. Our results are also generalized to detect all different types of multipartite entanglement.Comment: 4 pages, 2 figures, submitted to Physical Review Letters. Revised version with new calculation

On Hastings' counterexamples to the minimum output entropy additivity conjecture

Hastings recently reported a randomized construction of channels violating the minimum output entropy additivity conjecture. Here we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact probability distribution of the Schmidt coefficients of a random bipartite pure state, as in the original proof, but rather derive the necessary large deviation bounds by a concentration of measure argument. Furthermore, we prove non-additivity for the overwhelming majority of channels consisting of a Haar random isometry followed by partial trace over the environment, for an environment dimension much bigger than the output dimension. This makes Hastings' original reasoning clearer and extends the class of channels for which additivity can be shown to be violated.Comment: 17 pages + 1 lin

Quantum Speed-ups for Semidefinite Programming

We give a quantum algorithm for solving semidefinite programs (SDPs). It has worst case running time n^(1/2)m^(1/2)S^2 poly(log(n), log(m), R, r, 1/δ), with n and s the dimension and sparsity of the input matrices, respectively, m the number of constraints, δ the accuracy of the solution, and R, r upper bounds on the size of the optimal primal and dual solutions. This gives a square-root unconditional speed-up over any classical method for solving SDPs both in n and m. We prove the algorithm cannot be substantially improved giving a Ω(n^(1/2) + m^(1/2)) quantum lower bound for solving semidefinite programs with constant s, R, r and δ. We then argue that in some instances the algorithm offer even exponential speed-ups. This is the case whenever the quantum Gibbs states of Hamiltonians given by linear combinations of the input matrices of the SDP can be prepared efficiently on a quantum computer. An example are SDPs in which the input matrices have low-rank: For SDPs with the maximum rank of any input matrix bounded by rank, we show the quantum algorithm runs in time poly(log(n), log(m), rank, r, R, δ)m^(1/2). The quantum algorithm is constructed by a combination of quantum Gibbs sampling and the multiplicative weight method. In particular it is based on an classical algorithm of Arora and Kale for approximately solving SDPs. We present a modification of their algorithm to eliminate the need of solving an inner linear program which may be of independent interest