Entanglement Parameters Research Articles

Entanglement sudden death and sudden birth of an atom coupled to a bimodal lossy cavity

We propose another method for realizing entanglement sudden death and sudden birth using a single atom interacting with a bimodal cavity field in a dissipative environment. By suitably choosing the system's parameters and precisely controlling the dynamics, we find a novel connection between maximum entanglement and mixed state parameters. We discuss the intricate relationship between the entanglement dynamics and the dissipative environment.

Effect of network structure on the stress–strain behaviour of endlinked PDMS elastomers

Endlinked poly(dimethylsiloxane) (PDMS) networks synthesized from telechelic precursor chains of different molar mass were prepared with varying volume fractions of non-reactive chains acting as solvent. Uniaxial extension and compression measurements were performed on these networks to investigate their stress–strain behaviour. The effect of the network structure and of solvent on the stress–strain behaviour is examined by controlling the extent of crosslinks and entanglements during the network synthesis. The master curve of the Rubinstein and Panyukov non-affine slip-tube (NAST) model provide an adequate fit to most of the extension and compression data. Furthermore, the crosslink and entanglement parameters of the NAST model ( G c and G e) are found to be in general in reasonable agreement with the 2 C 1 and 2 C 2 parameters of the Mooney–Rivlin continuum model applied to the extension data. For high molar mass precursor chains, the entanglement contribution to the modulus surpasses the crosslink contribution.

Images in quantum entanglement

A system for classifying and quantifying entanglement in spin 1/2 pure states is presented based on simple images. From the image point of view, an entangled state can be described as a linear superposition of separable object wavefunction ΨO plus a portion of its own inverse image. Bell states can be defined in this way: . Using the method of images, the three-spin 1/2 system is discussed in some detail. This system can exhibit exclusive three-particle ν123 entanglement, two-particle entanglements ν12, ν13, ν23 and/or mixtures of all four. All four image states are orthogonal both to each other and to the object wavefunction. In general, five entanglement parameters ν12, ν13, ν23, ν123 and ϕ123 are required to define the general entangled state. In addition, it is shown that there is considerable scope for encoding numbers, at least from the classical point of view but using quantum-mechanical principles. Methods are developed for their extraction. It is shown that concurrence can be used to extract even-partite, but not odd-partite information. Additional relationships are also presented which can be helpful in the decoding process. However, in general, numerical methods are mandatory. A simple roulette method for decoding is presented and discussed. But it is shown that if the encoder chooses to use transcendental numbers for the angles defining the target function (α1, β1), etc, the method rapidly turns into the Devil's roulette, requiring finer and finer angular steps.

Communication aspects of a three-player Prisoner's Dilemma quantum game

We present a quantization scheme for a three-player Prisoner's Dilemma game. It is shown that entanglement plays a dominant role in the three-player quantum game. Four different types of payoffs are identified on the basis of different combinations of initial state and measurement basis entanglement parameters. A relation among these different payoffs is also established. We also study the communication aspects of the three-player game. By exploiting different combinations of initial state and measurement basis entanglement parameters, we establish a relationship for the information shared among the parties. It is seen that the strategies of the players act as carriers of information in quantum games.

Secure coherent-state quantum key distribution protocols with efficient reconciliation

We study the equivalence of a realistic quantum key distribution protocol using coherent states and homodyne detection with 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 entangled oscillator pair or, equivalently for the realistic protocol, more than one secret key bit per coherent state. The entanglement parameters are estimated using quantum tomography. We analyze the properties of the encoding scheme and investigate the resulting secret key rate in the important case of the attenuation channel.

Multiplayer quantum games with continuous-variable strategies

Based on the extended case of the Cournot's duopoly, we investigate a case of three firms in which the different entanglement parameters can vary arbitrarily. An analytical formula is presented and some interesting features are demonstrated from it. Furthermore, we find that the quantum entanglement can make an arbitrary number of players cooperate to the largest extent.

Qubit channels which require four inputs to achieve capacity: Implications for additivity conjectures

An example is given of a qubit quantum channel which requires four inputs to maximize the Holevo capacity. The example is one of a family of channels which are related to 3-state channels. The capacity of the product channel is studied and numerical evidence presented which strongly suggests additivity. The numerical evidence also supports a conjecture about the concavity of output entropy as a function of entanglement parameters. However, an example is presented which shows that for some channels this conjecture does not hold for all input states. A numerical algorithm for finding the capacity and optimal inputs is presented and its relation to a relative entropy optimization discussed.

Generalized schmidt decomposition and classification of three-quantum-Bit states

We prove for any pure three-quantum-bit state the existence of local bases which allow one to build a set of five orthogonal product states in terms of which the state can be written in a unique form. This leads to a canonical form which generalizes the two-quantum-bit Schmidt decomposition. It is uniquely characterized by the five entanglement parameters. It leads to a complete classification of the three-quantum-bit states. It shows that the right outcome of an adequate local measurement always erases all entanglement between the other two parties.