scholarly journals Physical Limits on Self-Replication Processes

2006 ◽  
Vol 13 (02) ◽  
pp. 113-117 ◽  
Author(s):  
Robert Alicki
Keyword(s):  
Second Law Of Thermodynamics ◽  
Entangled States ◽  
Strongly Correlated ◽  
Classical Information ◽  
Composite Systems ◽  
Classical Models ◽  
Pure States ◽  
Self Replication ◽  
Quantum And Classical Models ◽  
Homogeneous Environment

Using few very general axioms which should be satisfied by any reasonable theory consistent with the Second Law of Thermodynamics we argue that: a) "no-cloning theorem" is meaningful for a very general theoretical scheme including both quantum and classical models, b) in order to describe self-replication, Wigner's "cloning" process should be replaced by a more general "broadcasting", c) "separation of species" is possible only in a non-homogeneous environment, d) "parent" and "offspring" must be strongly correlated. Motivated by the existing results on broadcasting which show that only classical information can self-replicate perfectly we discuss briefly a classical toy model with "quantum features" — overlapping pure states and "entangled states" for composite systems.

Most robust and fragile two-qubit entangled states under deploarizing channels

2013 ◽  
Vol 13 (7&8) ◽  
pp. 645-660
Author(s):  
Chao-Qian Pang ◽  
Fu-Lin Zhang ◽  
Yue Jiang ◽  
Mai-Lin Liang ◽  
Jing-Ling Chen
Keyword(s):  
Evolution Equation ◽  
Numerical Calculations ◽  
Entangled States ◽  
Fragile States ◽  
Qubit System ◽  
Uniform Channel ◽  
Pure States ◽  
The One ◽  
Major Factors ◽  
The Impact

For a two-qubit system under local depolarizing channels, the most robust and most fragile states are derived for a given concurrence or negativity. For the one-sided channel, the pure states are proved to be the most robust ones, with the aid of the evolution equation for entanglement given by Konrad \emph{et al.} [Nat. Phys. 4, 99 (2008)]. Based on a generalization of the evolution equation for entanglement, we classify the ansatz states in our investigation by the amount of robustness, and consequently derive the most fragile states. For the two-sided channel, the pure states are the most robust for a fixed concurrence. Under the uniform channel, the most fragile states have the minimal negativity when the concurrence is given in the region $[1/2,1]$. For a given negativity, the most robust states are the ones with the maximal concurrence, and the most fragile ones are the pure states with minimum of concurrence. When the entanglement approaches zero, the most fragile states under general nonuniform channels tend to the ones in the uniform channel. Influences on robustness by entanglement, degree of mixture, and asymmetry between the two qubits are discussed through numerical calculations. It turns out that the concurrence and negativity are major factors for the robustness. When they are fixed, the impact of the mixedness becomes obvious. In the nonuniform channels, the most fragile states are closely correlated with the asymmetry, while the most robust ones with the degree of mixture.

scholarly journals Entanglement of Identical Particles

2014 ◽  
Vol 21 (01n02) ◽  
pp. 1440003 ◽  
Author(s):  
F. Benatti ◽  
R. Floreanini ◽  
K. Titimbo
Keyword(s):  
Single Particle ◽  
Entangled States ◽  
Second Quantization ◽  
Identical Particles ◽  
Nonlocal Correlation ◽  
Pure States ◽  
Bipartite States

Unlike for bipartite states consisting of distinguishable particles, in the case of identical parties the notion of entanglement is still under debate. In the following, we review two different approaches to the entanglement of systems consisting of two bosons or fermions; the first approach is based on the particle aspect typical of first quantization and identifies separable pure states as those that allow to assign two orthogonal single particle vector states to both parties. The second approach makes full use of the mode aspect of second quantization whereby separability can be formulated as absence of nonlocal correlation among two different sets of modes. While the first approach applies to pure states only, the second one is more general and characterizes generic entangled states. In the following, we shall show that the mode-based approach indeed contains the particle-based one.

Robustness of two-qubit and three-qubit states in correlated quantum channels

2022 ◽  
Author(s):  
Zhan-Yun Wang ◽  
Feng-Lin Wu ◽  
Zhen-Yu Peng ◽  
Si-Yuan Liu
Keyword(s):  
Entangled States ◽  
Fragile States ◽  
Quantum Channels ◽  
Noisy Channels ◽  
Correlated Channels ◽  
Pure States ◽  
Bit Flip ◽  
Qubit States

Abstract We investigate how the correlated actions of quantum channels affect the robustness of entangled states. We consider the Bell-like state and random two-qubit pure states in the correlated depolarizing, bit flip, bit-phase flip, and phase flip channels. It is found that the robustness of two-qubit pure states can be noticeably enhanced due to the correlations between consecutive actions of these noisy channels, and the Bell-like state is always the most robust state. We also consider the robustness of three-qubit pure states in correlated noisy channels. For the correlated bit flip and phase flip channels, the result shows that although the most robust and most fragile states are locally unitary equivalent, they exhibit different robustness in different correlated channels, and the effect of channel correlations on them is also significantly different. However, for the correlated depolarizing and bit-phase flip channels, the robustness of two special three-qubit pure states is exactly the same. Moreover, compared with the random three-qubit pure states, they are neither the most robust states nor the most fragile states.

Entanglement

2009 ◽  
Author(s):  
Stephen Barnett
Keyword(s):  
Density Operator ◽  
Superposition Principle ◽  
Quantum Systems ◽  
Entangled States ◽  
Weighted Sum ◽  
Finite Velocity ◽  
Density Operators ◽  
Two Systems ◽  
Pure States ◽  
The One

We have seen, in Section 2.5, how the superposition principle leads to the existence of entangled states of two or more quantum systems. Such states are characterized by the existence of correlations between the systems, the form of which cannot be satisfactorily accounted for by any classical theory. These have played a central role in the development of quantum theory since early in its development, starting with the famous paradox or dilemma of Einstein, Podolsky, and Rosen (EPR). No less disturbing than the EPR dilemma is the problem of Schrödinger’s cat, an example of the apparent absurdity of following entanglement into the macroscopic world. It was Schrödinger who gave us the name entanglement; he emphasized its fundamental significance when he wrote, ‘I would call this not one but the characteristic trait of quantum mechanics, the one that enforces the entire departure from classical thought’. The EPR dilemma represents a profound challenge to classical reasoning in that it seems to present a conflict between the ideas of the reality of physical properties and the locality imposed by the finite velocity of light. This challenge and the developments that followed have served to refine the concept of entanglement and will be described in the first section of this chapter. We start by recalling that a state of two quantum systems is entangled if its density operator cannot be written as a product of density operators for the two systems, or as a probability-weighted sum of such products. For pure states, the condition for entanglement can be stated more simply: a pure state of two quantum systems is not entangled only if the state vector can be written as a product of state vectors for the two systems. In the discipline of quantum information, entanglement is viewed as a resource to be exploited. We shall find, both here and in the subsequent chapters, that our subject owes much of its distinctive flavour to the utilization of entanglement.

scholarly journals Optimal verification of general bipartite pure states

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Xiao-Dong Yu ◽  
Jiangwei Shang ◽  
Otfried Gühne
Keyword(s):  
Quantum Information ◽  
Quantum Information Processing ◽  
Optimization Problems ◽  
Optimal Strategies ◽  
Adaptive Strategies ◽  
Quantum States ◽  
Entangled States ◽  
Classical Communication ◽  
Pure States ◽  
Projective Measurements

AbstractThe efficient and reliable verification of quantum states plays a crucial role in various quantum information processing tasks. We consider the task of verifying entangled states using one-way and two-way classical communication and completely characterize the optimal strategies via convex optimization. We solve these optimization problems using both analytical and numerical methods, and the optimal strategies can be constructed for any bipartite pure state. Compared with the nonadaptive approach, our adaptive strategies significantly improve the efficiency of quantum state verification. Moreover, these strategies are experimentally feasible, as only few local projective measurements are required.

Efficient simultaneous dense coding and teleportation with two-photon four-qubit cluster states

2016 ◽  
Vol 14 (05) ◽  
pp. 1650023 ◽  
Author(s):  
Cai Zhang ◽  
Haozhen Situ ◽  
Qin Li ◽  
Guang Ping He
Keyword(s):  
Degrees Of Freedom ◽  
Quantum States ◽  
Degree Of Freedom ◽  
Generation Rate ◽  
Entangled States ◽  
Dense Coding ◽  
Cluster States ◽  
Two Degrees Of Freedom ◽  
Classical Information ◽  
Two Photon

We firstly propose a simultaneous dense coding protocol with two-photon four-qubit cluster states in which two receivers can simultaneously get their respective classical information sent by a sender. Because each photon has two degrees of freedom, the protocol will achieve a high transmittance. The security of the simultaneous dense coding protocol has also been analyzed. Secondly, we investigate how to simultaneously teleport two different quantum states with polarization and path degree of freedom using cluster states to two receivers, respectively, and discuss its security. The preparation and transmission of two-photon four-qubit cluster states is less difficult than that of four-photon entangled states, and it has been experimentally generated with nearly perfect fidelity and high generation rate. Thus, our protocols are feasible with current quantum techniques.

scholarly journals Tensor network representations from the geometry of entangled states

2020 ◽  
Vol 9 (3) ◽  
Author(s):  
Matthias Christandl ◽  
Angelo Lucia ◽  
Peter Vrana ◽  
Albert H. Werner
Keyword(s):  
General Setting ◽  
Entangled States ◽  
Strongly Correlated ◽  
Effective Dimension ◽  
Tensor Networks ◽  
Tensor Network ◽  
Correlated Quantum Systems ◽  
Network States ◽  
Tensor Network States ◽  
Entanglement Structure

Tensor networks provide descriptions of strongly correlated quantum systems based on an underlying entanglement structure given by a graph of entangled states along the edges that identify the indices of the local tensors to be contracted. Considering a more general setting, where entangled states on edges are replaced by multipartite entangled states on faces, allows us to employ the geometric properties of multipartite entanglement in order to obtain representations in terms of superpositions of tensor network states with smaller effective dimension, leading to computational savings.

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