Sandu Popescu

Bio: Sandu Popescu is an academic researcher from University of Bristol. The author has contributed to research in topics: Quantum entanglement & Quantum nonlocality. The author has an hindex of 66, co-authored 226 publications receiving 24018 citations. Previous affiliations of Sandu Popescu include University of South Carolina & Chapman University.

Concentrating partial entanglement by local operations

Abstract: If two separated observers are supplied with entanglement, in the form of n pairs of particles in identical partly entangled pure states, one member of each pair being given to each observer, they can, by local actions of each observer, concentrate this entanglement into a smaller number of maximally entangled pairs of particles, for example, Einstein-Podolsky-Rosen singlets, similarly shared between the two observers. The concentration process asymptotically conserves entropy of entanglement---the von Neumann entropy of the partial density matrix seen by either observer---with the yield of singlets approaching, for large n, the base-2 entropy of entanglement of the initial partly entangled pure state. Conversely, any pure or mixed entangled state of two systems can be produced by two classically communicating separated observers, drawing on a supply of singlets as their sole source of entanglement. \textcopyright{} 1996 The American Physical Society.

Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels

Abstract: Two separated observers, by applying local operations to a supply of not-too-impure entangled states (e.g., singlets shared through a noisy channel), can prepare a smaller number of entangled pairs of arbitrarily high purity (e.g., near-perfect singlets). These can then be used to faithfully teleport unknown quantum states from one observer to the other, thereby achieving faithful transmission of quantum information through a noisy channel. We give upper and lower bounds on the yield $D\left(M\right)$ of pure singlets $(|{\ensuremath{\Psi}}^{\ensuremath{-}}〉)$ distillable from mixed states $M$, showing $D\left(M\right)g0$ if $〈{\ensuremath{\Psi}}^{\ensuremath{-}}|M|{\ensuremath{\Psi}}^{\ensuremath{-}}〉g\frac{1}{2}$.

Quantum nonlocality as an axiom

Abstract: In the conventional approach to quantum mechanics, indeterminism is an axiom and nonlocality is a theorem. We consider inverting the logical order, making nonlocality an axiom and indeterminism a theorem. Nonlocal “superquantum” correlations, preserving relativistic causality, can violate the CHSH inequality more strongly than any quantum correlations.

Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels

Abstract: We report on a quantum optical experimental implementation of teleportation of unknown pure quantum states. This realizes all of the nonlocal aspects of the original scheme proposed by Bennett et al. and is equivalent to it up to a local operation. We exhibit results for the teleportation of a linearly polarized state and of an elliptically polarized state. We show that the experimental results cannot be explained in terms of a classical channel alone. The Bell measurement in our experiment can distinguish between all four Bell states simultaneously allowing, in the ideal case, a 100% success rate of teleportation. [S0031-9007(97)05275-7]

Quantum Privacy Amplification and the Security of Quantum Cryptography over Noisy Channels

Abstract: Existing quantum cryptographic schemes are not, as they stand, operable in the presence of noise on the quantum communication channel. Although they become operable if they are supplemented by classical privacy-amplification techniques, the resulting schemes are difficult to analyze and have not been proved secure. We introduce the concept of quantum privacy amplification and a cryptographic scheme incorporating it which is provably secure over a noisy channel. The scheme uses an “entanglement purification” procedure which, because it requires only a few quantum controllednot and single-qubit operations, could be implemented using technology that is currently being developed. [S0031-9007(96)01288-4] Quantum cryptography [1 ‐ 3] allows two parties (traditionally known as Alice and Bob) to establish a secure random cryptographic key if, first, they have access to a quantum communication channel, and second, they can exchange classical public messages which can be monitored but not altered by an eavesdropper (Eve). Using such a key, a secure message of equal length can be transmitted over the classical channel. However, the security of quantum cryptography has so far been proved only for the idealized case where the quantum channel, in the absence of eavesdropping, is noiseless. That is because, under existing protocols, Alice and Bob detect eavesdropping by performing certain quantum measurements on transmitted batches of qubits and then using statistical tests to determine, with any desired degree of confidence, that the transmitted qubits are not entangled with any third system such as Eve. The problem is that there is in principle no way of distinguishing entanglement with an eavesdropper (caused by her measurements) from entanglement with the environment caused by innocent noise, some of which is presumably always present. This implies that all existing protocols are, strictly speaking, inoperable in the presence of noise, since they require the transmission of messages to be suspended whenever an eavesdropper (or, therefore, noise) is detected. Conversely, if we want a protocol that is secure in the presence of noise, we must find one that allows secure transmission to continue even in the presence of eavesdroppers. To this end, one might consider modifying the existing pro

Quantum Computation and Quantum Information

Abstract: Part I. Fundamental Concepts: 1. Introduction and overview 2. Introduction to quantum mechanics 3. Introduction to computer science Part II. Quantum Computation: 4. Quantum circuits 5. The quantum Fourier transform and its application 6. Quantum search algorithms 7. Quantum computers: physical realization Part III. Quantum Information: 8. Quantum noise and quantum operations 9. Distance measures for quantum information 10. Quantum error-correction 11. Entropy and information 12. Quantum information theory Appendices References Index.

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

Abstract: A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and which have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored.

Entanglement of Formation of an Arbitrary State of Two Qubits

Abstract: The entanglement of a pure state of a pair of quantum systems is defined as the entropy of either member of the pair. The entanglement of formation of a mixed state $\ensuremath{\rho}$ is the minimum average entanglement of an ensemble of pure states that represents \ensuremath{\rho}. An earlier paper conjectured an explicit formula for the entanglement of formation of a pair of binary quantum objects (qubits) as a function of their density matrix, and proved the formula for special states. The present paper extends the proof to arbitrary states of this system and shows how to construct entanglement-minimizing decompositions.

Quantum entanglement

Abstract: All our former experience with application of quantum theory seems to say: {\it what is predicted by quantum formalism must occur in laboratory} But the essence of quantum formalism - entanglement, recognized by Einstein, Podolsky, Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a new resource as real as energy This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including ``canonical'' ones: quantum cryptography, quantum teleportation and dense coding However, it appeared that this new resource is very complex and difficult to detect Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying In particular, the authors discuss various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, quantum cryptography and point out some interrelations They also discuss a basic role of entanglement in quantum communication within distant labs paradigm and stress some peculiarities such as irreversibility of entanglement manipulations including its extremal form - bound entanglement phenomenon A basic role of entanglement witnesses in detection of entanglement is emphasized

Quantum Cryptography

Abstract: Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues.