scholarly journals Direct Measurement of Nonlinear Properties of Bipartite Quantum States

2006 ◽  
Vol 13 (03) ◽  
pp. 281-289
Author(s):  
F. A. Bovino ◽  
G. Castagnoli ◽  
A. Ekert ◽  
C. Moura Alves ◽  
P. Horodecki ◽  
...  
Keyword(s):  
Information Science ◽  
Quantum States ◽  
Full Description ◽  
Entangled Photons ◽  
Entanglement Witness ◽  
Entropic Inequalities ◽  
Nonlinear Properties ◽  
Local Measurements ◽  
Marking Technique ◽  
Chsh Inequalities

Nonlinear properties of quantum states, such as entropy or entanglement, quantify important physical resources and are frequently used in quantum information science. They are usually calculated from a full description of a quantum state, even though they depend only on a small number of parameters that specify the state. Here we extract a nonlocal and a nonlinear quantity, namely the Renyi entropy, from local measurements on two pairs of polarization entangled photons. We also introduce a "phase marking" technique which allows to select uncorrupted outcomes even with nondeterministic sources of entangled photons. We use our experimental data to demonstrate the violation of entropic inequalities. They are examples of a nonlinear entanglement witness and their power exceeds all linear tests for quantum entanglement based on all possible Bell-CHSH inequalities.

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 Direct Measurement of Nonlinear Properties of Bipartite Quantum States

2005 ◽  
Vol 95 (24) ◽  
Author(s):  
Fabio Antonio Bovino ◽  
Giuseppe Castagnoli ◽  
Artur Ekert ◽  
Paweł Horodecki ◽  
Carolina Moura Alves ◽  
...  
Keyword(s):  
Direct Measurement ◽  
Quantum States ◽  
Nonlinear Properties

scholarly journals Quantum Rayleigh Annihilation of Entangled Photons

2018 ◽  
Author(s):  
Andre Vatarescu
Keyword(s):  
Physical Reality ◽  
Quantum States ◽  
Entangled States ◽  
Entangled Photons ◽  
Dielectric Media ◽  
Quantum Phenomenon ◽  
Quantum Non Locality ◽  
Linearly Polarized ◽  
Photonic States ◽  
Non Locality

The interpretation of published experimental results intended to prove the existence of a quantum phenomenon of non-locality involving photonic entangled states did not take into consideration the existence of the quantum Rayleigh conversion of photons in dielectric media. This phenomenon leads to the existence of high levels of correlations between two independent photonic and linearly polarized quantum states generated after the entangled photons have been absorbed through the quantum Rayleigh conversion. Both pure and mixed individual states of polarization result in expressions normally associated with entangled photonic states, providing support for the view that the physical reality of quantum non-locality is highly questionable.

scholarly journals Locally restricted measurements on a multipartite quantum system: data hiding is generic

2015 ◽  
pp. 513-540
Author(s):  
Guillaume Aubrun ◽  
Cecilia Lancien
Keyword(s):  
Quantum System ◽  
Data Hiding ◽  
Quantum Measurements ◽  
Quantum States ◽  
Classical Communication ◽  
Substantial Loss ◽  
Local Measurements ◽  
System Data

We study the distinguishability norms associated to families of locally restricted POVMs on multipartite systems. These norms (introduced by Matthews, Wehner and Winter) quantify how quantum measurements, subject to locality constraints, perform in the task of discriminating two multipartite quantum states. We mainly address the following question regarding the behaviour of these distinguishability norms in the highdimensional regime: On a bipartite space, what are the relative strengths of standard classes of locally restricted measurements? We show that the class of PPT measurements typically performs almost as well as the class of all measurements whereas restricting to local measurements and classical communication, or even just to separable measurements, implies a substantial loss. We also provide examples of state pairs which can be perfectly distinguished by local measurements if (one-way) classical communication is allowed between the parties, but very poorly without it. Finally, we study how many POVMs are needed to distinguish almost perfectly any pair of states on C^d, showing that the answer is exp(Θ(d^2 )).

scholarly journals Quantum Rayleigh Annihilation of Entangled Photons

2018 ◽  
Author(s):  
Andre Vatarescu
Keyword(s):  
Physical Reality ◽  
Quantum States ◽  
Entangled States ◽  
Entangled Photons ◽  
Dielectric Media ◽  
Quantum Phenomenon ◽  
Quantum Non Locality ◽  
Linearly Polarized ◽  
Photonic States ◽  
Non Locality

The interpretation of published experimental results intended to prove the existence of a quantum phenomenon of non-locality involving photonic entangled states did not take into consideration the existence of the quantum Rayleigh conversion of photons in dielectric media. This phenomenon leads to the existence of high levels of correlations between two independent photonic and linearly polarized quantum states generated after the entangled photons have been absorbed through the quantum Rayleigh conversion. Both pure and mixed individual states of polarization result in expressions normally associated with entangled photonic states, providing support for the view that the physical reality of quantum non-locality is highly questionable.

Is absolute separability determined by the partial transpose?

2015 ◽  
Vol 15 (7&8) ◽  
pp. 694-720 ◽  
Author(s):  
Srinivasan Arunachalam ◽  
Nathaniel Johnston ◽  
Vincent Russo
Keyword(s):  
Quantum States ◽  
Entanglement Witness ◽  
Unitary Matrices ◽  
Positive Partial Transpose ◽  
Entanglement Witnesses ◽  
The Family ◽  
Separability Criteria ◽  
Separability Problem ◽  
Partial Transpose

The absolute separability problem asks for a characterization of the quantum states $\rho \in M_m\otimes M_n$ with the property that $U\rho U^\dagger$ is separable for all unitary matrices $U$. We investigate whether or not it is the case that $\rho$ is absolutely separable if and only if $U\rho U^\dagger$ has positive partial transpose for all unitary matrices $U$. In particular, we develop an easy-to-use method for showing that an entanglement witness or positive map is unable to detect entanglement in any such state, and we apply our method to many well-known separability criteria, including the range criterion, the realignment criterion, the Choi map and its generalizations, and the Breuer--Hall map. We also show that these two properties coincide for the family of isotropic states, and several eigenvalue results for entanglement witnesses are proved along the way that are of independent interest.

Entanglement

Quantum 20/20 ◽  
2019 ◽  
pp. 151-162
Author(s):  
Ian R. Kenyon
Keyword(s):  
Quantum States ◽  
Entangled States ◽  
Entangled State ◽  
Entangled Photons ◽  
Photon State ◽  
Full Knowledge ◽  
Quantum Entangled States ◽  
The Individual ◽  
Down Conversion ◽  
Individual Particles

The distiction between classical product states and quantum entangled states is disclosed with examples. Spontaneous parametric down conversion as a source of entangled photons is described. The action of a perfect beam splitter is analysed using creation and annihilation operators. The HOM interferometer is described. Its use in demonstrating the indistinguishability of photons and in measuring bandwidth of sources at the level of femtoseconds is recounted. Two particle entanglement is analysed using the Bloch sphere representation showing how the full knowledge of the entangled state does not fix the state of the individual particles. The four Bell states, eigenstates of two particle entanglement, are introduced. Teleportation of a photon state using entangled photons is described, and an experiment to entangle the quantum states of atoms at space-like separation outlined.

scholarly journals DISTINGUISHING UNENTANGLED STATES WITH AN UNENTANGLED MEASUREMENT

2006 ◽  
Vol 04 (01) ◽  
pp. 219-232 ◽  
Author(s):  
WILLIAM K. WOOTTERS
Keyword(s):  
Tensor Product ◽  
Quantum States ◽  
Local Measurements ◽  
The Individual

In a 1991 paper, Asher Peres and the author theoretically analyzed a set of unentangled bipartite quantum states that could apparently be distinguished better by a global measurement than by any sequence of local measurements on the individual subsystems. The present paper returns to the same example, and shows that the best result so far achieved can alternatively be attained by a measurement that, while still global, is "unentangled" in the sense that the operator associated with each measurement outcome is a tensor product.

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