scholarly journals CHARACTERIZING QUANTUMNESS VIA ENTANGLEMENT CREATION

2011 ◽  
Vol 09 (07n08) ◽  
pp. 1701-1713 ◽  
Author(s):  
SEVAG GHARIBIAN ◽  
MARCO PIANI ◽  
GERARDO ADESSO ◽  
JOHN CALSAMIGLIA ◽  
PAWEŁ HORODECKI
Keyword(s):  
Relative Entropy ◽  
Special Class ◽  
Entanglement Swapping ◽  
Quantum States ◽  
Bipartite Entanglement ◽  
Separable States ◽  
Classical Quantum ◽  
Qubit States

In [Piani et al., PRL106 (2011) 220403], an activation protocol was introduced which maps the general non-classical (multipartite) correlations between given systems into bipartite entanglement between the systems and local ancillae by means of a potentially highly entangling interaction. Here, we study how this activation protocol can be used to entangle the starting systems themselves via entanglement swapping through a measurement on the ancillae. Furthermore, we bound the relative entropy of quantumness (a naturally arising measure of non-classicality in the scheme of Piani et al. above) for a special class of separable states, the so-called classical–quantum states. In particular, we fully characterize the classical–quantum two-qubit states that are maximally non-classical.

scholarly journals RELATIVE ENTROPY OF ENTANGLEMENT FOR TWO-QUBIT STATE WITH z-DIRECTIONAL BLOCH VECTORS

2010 ◽  
Vol 08 (05) ◽  
pp. 869-879 ◽  
Author(s):  
DAEKIL PARK
Keyword(s):  
Relative Entropy ◽  
Qubit State ◽  
Closed Formula ◽  
Separable States ◽  
Relative Entropy Of Entanglement ◽  
Qubit States

So far there is no closed formula for relative entropy of entanglement of arbitrary two-qubit states. In this paper we present a method, which guarantees the derivation of the relative entropy of entanglement for most states that have z-directional Bloch vectors. It is shown that the closest separable states for those states also have z-directional Bloch vectors though there are few exceptions.

scholarly journals Maximizing the Divergence from a Hierarchical Model of Quantum States

2015 ◽  
Vol 22 (01) ◽  
pp. 1550006 ◽  
Author(s):  
Stephan Weis ◽  
Andreas Knauf ◽  
Nihat Ay ◽  
Ming-Jing Zhao
Keyword(s):  
Mutual Information ◽  
Maximum Entropy ◽  
Relative Entropy ◽  
Hierarchical Model ◽  
Hierarchical Models ◽  
Maximum Entropy Principle ◽  
Quantum States ◽  
Entropy Principle ◽  
Qubit States ◽  
Reduction Of Uncertainty

We study many-party correlations quantified in terms of the Umegaki relative entropy (divergence) from a Gibbs family known as a hierarchical model. We derive these quantities from the maximum-entropy principle which was used earlier to define the closely related irreducible correlation. We point out the differences between quantum states and probability vectors which exist in hierarchical models, in the divergence from a hierarchical model and in local maximizers of this divergence. The differences are, respectively, missing factorization, discontinuity and reduction of uncertainty. We discuss global maximizers of the mutual information of separable qubit states.

Symmetric and asymmetric cyclic controlled quantum teleportation via nine-qubit entangled state

2021 ◽  
pp. 2150249
Author(s):  
Vikram Verma
Keyword(s):  
Quantum Channel ◽  
Quantum Teleportation ◽  
Quantum States ◽  
Entangled State ◽  
Controlled Quantum Teleportation ◽  
Intrinsic Efficiency ◽  
Qubit States ◽  
Generalized Scheme

In this paper, by utilizing a nine-qubit entangled state as a quantum channel, we propose new schemes for symmetric and asymmetric cyclic controlled quantum teleportation (CYCQT). In our proposed schemes, four participants Alice, Bob, Charlie and David teleport their unknown quantum states cyclically among themselves with the help of a controller Eve. No participants can reconstruct the original states sent from the respective senders without the permission of the controller. Also, by considering same nine-qubit entangled state as a quantum channel, we propose a generalized scheme for CYCQT of multi-qubit states. In contrast to the previous CYCQT schemes involving three communicators and a controller, there are four communicators and a controller in the proposed schemes. Also, compared with previous CYCQT schemes, our proposed CYCQT schemes require less consumption of quantum resource and the intrinsic efficiency of the generalized scheme increases with the increase of number of qubits in the information states.

Long distance two-party quantum crypto made simple

2012 ◽  
Vol 12 (5&6) ◽  
pp. 448-460
Author(s):  
Iordanis Kerenidis ◽  
Stephanie Wehner
Keyword(s):  
Quantum Communication ◽  
Oblivious Transfer ◽  
Difficult Problem ◽  
Entanglement Swapping ◽  
Quantum States ◽  
Large Network ◽  
Long Distance ◽  
Computational Problem ◽  
Cryptographic Primitive

Any two-party cryptographic primitive can be implemented using quantum communication under the assumption that it is difficult to store a large number of quantum states perfectly. However, achieving reliable quantum communication over long distances remains a difficult problem. Here, we consider a large network of nodes with only neighboring quantum links. We exploit properties of this cloud of nodes to enable any two nodes to achieve security even if they are not directly connected. Our results are based on techniques from classical cryptography and do not resort to technologically difficult procedures like entanglement swapping. More precisely, we show that oblivious transfer can be achieved in such a network if and only if there exists a path in the network between the sender and the receiver along which all nodes are honest. Finally, we show that useful notions of security can still be achieved when we relax the assumption of an honest path. For example, we show that we can combine our protocol for oblivious transfer with computational assumptions such that we obtain security if either there exists an honest path, or, as a backup, at least the adversary cannot solve a computational problem.

Dynamics of Interacting Classical and Quantum Systems

2011 ◽  
Vol 18 (04) ◽  
pp. 339-351 ◽  
Author(s):  
Dariusz Chruściński ◽  
Andrzej Kossakowski ◽  
Giuseppe Marmo ◽  
E. C. G. Sudarshan
Keyword(s):  
Characteristic Feature ◽  
Quantum Dynamics ◽  
Quantum Discord ◽  
Main Idea ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Quantum States ◽  
Algebra Of Observables ◽  
Classical Quantum ◽  
True Quantum

We analyze the dynamics of coupled classical and quantum systems. The main idea is to treat both systems as true quantum ones and impose a family of superselection rules which imply that the corresponding algebra of observables of one subsystem is commutative and hence may be treated as a classical one. Equivalently, one may impose a special symmetry which restricts the algebra of observables to the 'classical' subalgebra. The characteristic feature of classical-quantum dynamics is that it leaves invariant a subspace of classical-quantum states, that is, it does not create quantum correlations as measured by the quantum discord.

scholarly journals Generic Entanglement Entropy for Quantum States with Symmetry

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 684
Author(s):  
Yoshifumi Nakata ◽  
Mio Murao
Keyword(s):  
Phase Transition ◽  
Information Science ◽  
Entanglement Entropy ◽  
Quantum States ◽  
Permutation Symmetry ◽  
Phase Transition Behavior ◽  
Bipartite Entanglement ◽  
Translation Symmetry ◽  
The One ◽  
Random States

When a quantum pure state is drawn uniformly at random from a Hilbert space, the state is typically highly entangled. This property of a random state is known as generic entanglement of quantum states and has been long investigated from many perspectives, ranging from the black hole science to quantum information science. In this paper, we address the question of how symmetry of quantum states changes the properties of generic entanglement. More specifically, we study bipartite entanglement entropy of a quantum state that is drawn uniformly at random from an invariant subspace of a given symmetry. We first extend the well-known concentration formula to the one applicable to any subspace and then show that 1. quantum states in the subspaces associated with an axial symmetry are still highly entangled, though it is less than that of the quantum states without symmetry, 2. quantum states associated with the permutation symmetry are significantly less entangled, and 3. quantum states with translation symmetry are as entangled as the generic one. We also numerically investigate the phase-transition behavior of the distribution of generic entanglement, which indicates that the phase transition seems to still exist even when random states have symmetry.

scholarly journals Effectively classical quantum states for open systems

2000 ◽  
Vol 273 (4) ◽  
pp. 223-231 ◽  
Author(s):  
Ph. Blanchard ◽  
R. Olkiewicz
Keyword(s):  
Open Systems ◽  
Quantum States ◽  
Classical Quantum

Entangled versus classical quantum states

2001 ◽  
Vol 280 (1-2) ◽  
pp. 7-16 ◽  
Author(s):  
Ph. Blanchard ◽  
L. Jakóbczyk ◽  
R. Olkiewicz
Keyword(s):  
Quantum States ◽  
Classical Quantum

scholarly journals Completing bases in four dimensions

2022 ◽  
Author(s):  
Hans Havlicek ◽  
Karl Svozil
Keyword(s):  
Hilbert Space ◽  
Quantum States ◽  
Four Dimensions ◽  
Separable States ◽  
Orthogonal Representation ◽  
Relational Properties ◽  
Dimensional Hilbert Space ◽  
Physical Entanglement

Abstract Criteria for the completion of an incomplete basis of, or context in, a four-dimensional Hilbert space by (in)decomposable vectors are given. This, in particular, has consequences for the task of ``completing'' one or more bases or contexts of a (hyper)graph: find a complete faithful orthogonal representation (aka coordinatization) of a hypergraph when only a coordinatization of the intertwining observables is known. In general indecomposability and thus physical entanglement and the encoding of relational properties by quantum states ``prevails'' and occurs more often than separability associated with well defined individual, separable states.

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