Qubits, Qutrits and Gaussian states in Noisy Quantum Channels

2007 ◽  
Author(s):  
K. Wódkiewicz
Keyword(s):  
Quantum Channels ◽  
Gaussian States

Linear bosonic quantum channels defined by superpositions

2018 ◽  
Vol 18 (5&6) ◽  
pp. 481-496
Author(s):  
T.J. Volkoff
Keyword(s):  
Optical Element ◽  
Single Mode ◽  
Coherent System ◽  
Closed Convex Hull ◽  
Quantum Channels ◽  
Quantum Superposition ◽  
Nonclassical State ◽  
Gaussian States ◽  
System 2 ◽  
Energy Quantum

A minimal energy quantum superposition of two maximally distinguishable, isoenergetic single mode Gaussian states is used to construct the system-environment representation of a class of linear bosonic quantum channels acting on a single bosonic mode. The quantum channels are further defined by unitary dynamics of the system and environment corresponding to either a passive linear optical element U_{BS} or two-mode squeezing U_{TM}. The notion of nonclassicality distance is used to show that the initial environment superposition state becomes maximally nonclassical as the constraint energy is increased. When the system is initially prepared in a coherent state, application of the quantum channel defined by U_{BS} results in a nonclassical state for all values of the environment energy constraint. We also discuss the following properties of the quantum channels: 1) the maximal noise that a coherent system can tolerate, beyond which the linear bosonic attenuator channel defined by U_{BS} cannot impart nonclassical correlations to the system, 2) the noise added to a coherent system by the phase-preserving linear amplification channel defined by U_{TM}, and 3) a generic lower bound for the trace norm contraction coefficient on the closed, convex hull of energy-constrained Gaussian states.

Cohering power and decohering power of Gaussian unitary operations

2019 ◽  
Vol 19 (7&8) ◽  
pp. 575-586
Author(s):  
Yangyang Wang ◽  
Xiaofei Qi ◽  
Jinchuan Hou ◽  
Rufen Ma
Keyword(s):  
Relative Entropy ◽  
Continuous Variable ◽  
Quantum States ◽  
Entropy Measure ◽  
Quantum Channels ◽  
Gaussian States ◽  
Basic Properties ◽  
Suitable Measure

Having a suitable measure to quantify the coherence of quantum states, a natural task is to evaluate the power of quantum channels for creating or destroying the coherence of input quantum states. In the present paper, by introducing the maximal coherent Gaussian states based on the relative entropy measure of coherence, we propose the (generalized) cohering power and the (generalized) decohering power of Gaussian unitary operations for continuous-variable systems. Some basic properties are obtained and the cohering power and decohering power of two special kinds of Gaussian unitary operations are calculated.

scholarly journals Jordan products of quantum channels and their compatibility

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Mark Girard ◽  
Martin Plávala ◽  
Jamie Sikora
Keyword(s):  
Quantum State ◽  
Sufficient Conditions ◽  
The Other ◽  
Independent Interest ◽  
Quantum Channels ◽  
Semidefinite Programs ◽  
Jordan Product ◽  
Marginal Problem ◽  
Jordan Products ◽  
Product Of Matrices

AbstractGiven two quantum channels, we examine the task of determining whether they are compatible—meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting the output of the other channel). Here, we present several results concerning this task. First, we show it is equivalent to the quantum state marginal problem, i.e., every quantum state marginal problem can be recast as the compatibility of two channels, and vice versa. Second, we show that compatible measure-and-prepare channels (i.e., entanglement-breaking channels) do not necessarily have a measure-and-prepare compatibilizing channel. Third, we extend the notion of the Jordan product of matrices to quantum channels and present sufficient conditions for channel compatibility. These Jordan products and their generalizations might be of independent interest. Last, we formulate the different notions of compatibility as semidefinite programs and numerically test when families of partially dephasing-depolarizing channels are compatible.

scholarly journals Maximum relative entropy of coherence for quantum channels

2021 ◽  
Vol 64 (8) ◽  
Author(s):  
Zhi-Xiang Jin ◽  
Long-Mei Yang ◽  
Shao-Ming Fei ◽  
Xianqing Li-Jost ◽  
Zhi-Xi Wang ◽  
...  
Keyword(s):  
Relative Entropy ◽  
Quantum Channels ◽  
Relative Entropy Of Coherence

scholarly journals Polarization of Quantum Channels using Clifford-based Channel Combining

2021 ◽  
pp. 1-1
Author(s):  
Frederic Dupuis ◽  
Ashutosh Goswami ◽  
Mehdi Mhalla ◽  
Valentin Savin
Keyword(s):  
Quantum Channels

scholarly journals One-particle and two-particle visibilities in bipartite entangled Gaussian states

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Danko Georgiev ◽  
Leon Bello ◽  
Avishy Carmi ◽  
Eliahu Cohen
Keyword(s):  
Gaussian States

scholarly journals Absorption in Invariant Domains for Semigroups of Quantum Channels

2021 ◽  
Author(s):  
Raffaella Carbone ◽  
Federico Girotti
Keyword(s):  
Hilbert Space ◽  
Ergodic Theory ◽  
Markov Processes ◽  
Separable Hilbert Space ◽  
Quantum Channels ◽  
Quantum Markov Processes ◽  
Positive Recurrent ◽  
Markov Evolution ◽  
Absorption Probabilities ◽  
Invariant Domains

AbstractWe introduce a notion of absorption operators in the context of quantum Markov processes. The absorption problem in invariant domains (enclosures) is treated for a quantum Markov evolution on a separable Hilbert space, both in discrete and continuous times: We define a well-behaving set of positive operators which can correspond to classical absorption probabilities, and we study their basic properties, in general, and with respect to accessibility structure of channels, transience and recurrence. In particular, we can prove that no accessibility is allowed between the null and positive recurrent subspaces. In the case, when the positive recurrent subspace is attractive, ergodic theory will allow us to get additional results, in particular about the description of fixed points.

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