Common reducing unitary subspaces and decoherence in quantum systems

2015 ◽  
Vol 30 ◽  
Author(s):  
Grzegorz Pastuszak ◽  
Andrzej Jamiołkowski
Keyword(s):  
Invariant Subspaces ◽  
Quantum Information Theory ◽  
Quantum Systems ◽  
Quantum Channels ◽  
Effective Condition ◽  
Arbitrary Dimensions ◽  
Fixed Complex ◽  
Definition Of ◽  
Dimension One ◽  
Decoherence Free Subspace

Maps of the form Phi(X) =sum_{i=1}^s A_iXA^*, where A_1, . . . ,A_s are fixed complex n by n matrices and X is any complex n by n matrix are used in quantum information theory as representations of quantum channels. This article deals with computable conditions for the existence of decoherence--free subspaces for Phi. Since the definition of decoherence-free subspace for quantum channels relies only on the matrices A1, . . . ,As, the term of common reducing unitary subspace is used instead of the original one. Among the main results of the paper, there are computable conditions for the existence of common eigenvectors. These are related to common reducing unitary subspaces of dimension one. The new results on common eigenvectors provide new effective condition for the existence of common invariant subspaces of arbitrary dimensions.

scholarly journals Indistinguishability and Negative Probabilities

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 829
Author(s):  
J. Acacio de Barros ◽  
Federico Holik
Keyword(s):  
Quantum Systems ◽  
Quantum Contextuality ◽  
No Signaling ◽  
Definition Of ◽  
Do So

In this paper, we examined the connection between quantum systems’ indistinguishability and signed (or negative) probabilities. We do so by first introducing a measure-theoretic definition of signed probabilities inspired by research in quantum contextuality. We then argue that ontological indistinguishability leads to the no-signaling condition and negative probabilities.

Separability criteria based on the Bloch representation of density matrices

2007 ◽  
Vol 7 (7) ◽  
pp. 624-638
Author(s):  
J. de Vicente
Keyword(s):  
Sufficient Conditions ◽  
Quantum Systems ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Pure Product ◽  
Separability Problem ◽  
Arbitrary Dimensions ◽  
Necessary And Sufficient ◽  
Bloch Representation

We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which we derive a necessary condition and sufficient conditions for separability. For a certain class of states the necessary condition and a sufficient condition turn out to be equivalent, therefore yielding a necessary and sufficient condition. The proofs of the sufficient conditions are constructive, thus providing decompositions in pure product states for the states that satisfy them. We provide examples that show the ability of these conditions to detect entanglement. In particular, the necessary condition is proved to be strong enough to detect bound entangled states.

Optical demonstrations of statistical decision theory for quantum systems

2004 ◽  
Vol 4 (6&7) ◽  
pp. 450-459
Author(s):  
S.M. Barnett
Keyword(s):  
Information Theory ◽  
Communication Systems ◽  
Quantum Information Theory ◽  
Quantum Systems ◽  
Quantum Limit ◽  
Statistical Decision Theory ◽  
Statistical Decision ◽  
Ideal Quantum ◽  
Optical Polarisation ◽  
The Ideal

The work of Holevo and other pioneers of quantum information theory has given us limits on the performance of communication systems. Only recently, however, have we been able to perform laboratory demonstrations approaching the ideal quantum limit. This article presents some of the known limits and bounds together with the results of our experiments based on optical polarisation.

scholarly journals NEW EXACT TREATMENT OF THE PERTURBED COULOMB INTERACTIONS

2003 ◽  
Vol 18 (36) ◽  
pp. 2581-2586 ◽  
Author(s):  
OKAN ÖZER ◽  
BÜLENT GÖNÜL
Keyword(s):  
Perturbation Theory ◽  
Exact Solutions ◽  
Quantum Systems ◽  
External Potential ◽  
Coulomb Interactions ◽  
Exact Solvability ◽  
Hydrogenic Atom ◽  
Novel Method ◽  
Arbitrary Dimensions ◽  
Analytical Expressions

A novel method for the exact solvability of quantum systems is discussed and used to obtain closed analytical expressions in arbitrary dimensions for the exact solutions of the hydrogenic atom in the external potential ΔV(r) = br + cr2, which is based on the recently introduced supersymmetric perturbation theory.

Lyapunov control on quantum systems

2014 ◽  
Vol 28 (30) ◽  
pp. 1430020 ◽  
Author(s):  
L. C. Wang ◽  
X. X. Yi
Keyword(s):  
Quantum System ◽  
Open Quantum System ◽  
Open Quantum Systems ◽  
Logic Gates ◽  
Quantum Systems ◽  
Open Quantum ◽  
Quantum Operations ◽  
Lyapunov Control ◽  
Decoherence Free Subspace ◽  
General Method

We review the scheme of quantum Lyapunov control and its applications into quantum systems. After a brief review on the general method of quantum Lyapunov control in closed and open quantum systems, we apply it into controlling quantum states and quantum operations. The control of a spin-1/2 quantum system, driving an open quantum system into its decoherence free subspace (DFS), constructing single qubit and two-qubit logic gates are taken to illustrate the scheme. The optimalization of the Lyapunov control is also reviewed in this article.

Correspondence between continuous-variable and discrete quantum systems of arbitrary dimensions

2003 ◽  
Vol 68 (6) ◽  
Author(s):  
Časlav Brukner ◽  
Myungshik S. Kim ◽  
Jian-Wei Pan ◽  
Anton Zeilinger
Keyword(s):  
Continuous Variable ◽  
Quantum Systems ◽  
Arbitrary Dimensions

Measurements and Consistent Families of Quantum Channels

2011 ◽  
Vol 18 (03) ◽  
pp. 235-251
Author(s):  
Yves Le Jan ◽  
Rolando Rebolledo
Keyword(s):  
Quantum System ◽  
Moment Problem ◽  
Probability Space ◽  
Measurement Instrument ◽  
Quantum Systems ◽  
Quantum Channels ◽  
Simultaneous Observation ◽  
Classical Probability ◽  
Quantum Version ◽  
The Moment

This article introduces the notion of consistent families (Λ(n))n≥1of quantum channels. These families correspond to simultaneous observation of different copies of a given quantum system. Here, we are primarily interested in the analysis of measurements connected with them. As usual, the measurement of a quantum system requires the construction of a classical dilation of the corresponding quantum channel. In our case, the quantum systems represented by (Λ(n))n≥1are supposed to interact through the measurement instrument only. That is, we construct a classical probability space which allows to have a common dilation for all the Λ(n)' s . Doing this, we introduce and solve a quantum version of the moment problem.

scholarly journals ENTANGLEMENT SHARING: FROM QUBITS TO GAUSSIAN STATES

2006 ◽  
Vol 04 (03) ◽  
pp. 383-393 ◽  
Author(s):  
GERARDO ADESSO ◽  
FABRIZIO ILLUMINATI
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Quantum Correlations ◽  
Quantum Information Theory ◽  
Continuous Variable ◽  
Quantum Systems ◽  
Tripartite Entanglement ◽  
Gaussian States ◽  
Trade Off ◽  
Entanglement Sharing

It is a central trait of quantum information theory that there exist limitations to the free sharing of quantum correlations among multiple parties. Such monogamy constraints have been introduced in a landmark paper by Coffman, Kundu and Wootters, who derived a quantitative inequality expressing a trade-off between the couplewise and the genuine tripartite entanglement for states of three qubits. Since then, a lot of efforts have been devoted to the investigation of distributed entanglement in multipartite quantum systems. In this paper we report, in a unifying framework, a bird's eye view of the most relevant results that have been established so far on entanglement sharing in quantum systems. We will take off from the domain of N qubits, graze qudits, and finally land in the almost unexplored territory of multimode Gaussian states of continuous variable systems.

scholarly journals Entanglement May Enhance Channel Capacity in Arbitrary Dimensions

2006 ◽  
Vol 13 (04) ◽  
pp. 363-372 ◽  
Author(s):  
E. Karpov ◽  
D. Daems ◽  
N. J. Cerf
Keyword(s):  
Mutual Information ◽  
Channel Capacity ◽  
Space Dimension ◽  
Strong Dependence ◽  
Entangled States ◽  
Correlated Noise ◽  
Quantum Channels ◽  
Maximally Entangled States ◽  
Arbitrary Dimensions

We consider explicitly two examples of d-dimensional quantum channels with correlated noise and show that, in agreement with previous results on Pauli qubit channels, there are situations where maximally entangled input states achieve higher values of the output mutual information than product states. We obtain a strong dependence of this effect on the nature of the noise correlations as well as on the parity of the space dimension, and conjecture that when entanglement gives an advantage in terms of mutual information, maximally entangled states achieve the channel capacity.

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