Devastating Effects of Quantum Noises and Noisy Quantum Operations on Entanglement and Quantum Information Protocols

2011 ◽  
Author(s):  
Ye Yeo ◽  
Timothy Ralph ◽  
Ping Koy Lam
Keyword(s):  
Quantum Information ◽  
Quantum Operations ◽  
Quantum Noises

scholarly journals Effects of quantum noises and noisy quantum operations on entanglement and special dense coding

2010 ◽  
Vol 81 (2) ◽  
Author(s):  
Sylvanus Quek ◽  
Ziang Li ◽  
Ye Yeo
Keyword(s):  
Dense Coding ◽  
Quantum Operations ◽  
Quantum Noises

Stochastic Resonance with Unital Quantum Noise

2019 ◽  
Vol 18 (03) ◽  
pp. 1950015 ◽  
Author(s):  
Nicolas Gillard ◽  
Étienne Belin ◽  
François Chapeau-Blondeau
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Stochastic Resonance ◽  
Quantum Noise ◽  
Quantum Information Processing ◽  
Broad Class ◽  
Resonance Effects ◽  
Estimation Efficiency ◽  
Bit Flip ◽  
Quantum Noises

The fundamental quantum information processing task of estimating the phase of a qubit is considered. Following quantum measurement, the estimation efficiency is evaluated by the classical Fisher information which determines the best performance limiting any estimator and achievable by the maximum likelihood estimator. The estimation process is analyzed in the presence of decoherence represented by essential quantum noises that can affect the qubit and belonging to the broad class of unital quantum noises. Such a class especially contains the bit-flip, the phase-flip, the depolarizing noises, or the whole family of Pauli noises. As the level of noise is increased, we report the possibility of non-standard behaviors where the estimation efficiency does not necessarily deteriorate uniformly, but can experience non-monotonic variations. Regimes are found where higher noise levels prove more favorable to estimation. Such behaviors are related to stochastic resonance effects in signal estimation, shown here feasible for the first time with unital quantum noises. The results provide enhanced appreciation of quantum noise or decoherence, manifesting that it is not always detrimental for quantum information processing.

scholarly journals Entangling capacities and the geometry of quantum operations

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Jhih-Yuan Kao ◽  
Chung-Hsien Chou
Keyword(s):  
Quantum Information ◽  
Physical Significance ◽  
Quantum States ◽  
Important Class ◽  
Quantum Operation ◽  
Positive Partial Transpose ◽  
Quantum Operations ◽  
Partial Transpose ◽  
Ppt States

Abstract Quantum operations are the fundamental transformations on quantum states. In this work, we study the relation between entangling capacities of operations, geometry of operations, and positive partial transpose (PPT) states, which are an important class of states in quantum information. We show a method to calculate bounds for entangling capacity, the amount of entanglement that can be produced by a quantum operation, in terms of negativity, a measure of entanglement. The bounds of entangling capacity are found to be associated with how non-PPT (PPT preserving) an operation is. A length that quantifies both entangling capacity/entanglement and PPT-ness of an operation or state can be defined, establishing a geometry characterized by PPT-ness. The distance derived from the length bounds the relative entangling capability, endowing the geometry with more physical significance. We also demonstrate the equivalence of PPT-ness and separability for unitary operations.

Maximally coherent states

2015 ◽  
Vol 15 (15&16) ◽  
pp. 1355-1364
Author(s):  
Zhaofang Bai ◽  
Shuanping Du
Keyword(s):  
Quantum Information ◽  
Coherent State ◽  
Relative Entropy ◽  
Quantum Correlation ◽  
Coherent States ◽  
Entropy Measure ◽  
Product State ◽  
Quantum Operations ◽  
Maximal Entanglement

The relative entropy measure quantifying coherence, a key property of quantum system, is proposed recently. In this note, we firstly investigate structural characterization of maximally coherent states with respect to the relative entropy measure. It is shown that mixed maximally coherent states do not exist and every pure maximally coherent state has the form U|ψihψ|U† , |ψi = √1 d Pd k=1 |ki, U is diagonal unitary. Based on the characterization of pure maximally coherent states, for a bipartite maximally coherent state with dA = dB, we obtain that the super-additivity equality of relative entropy measure holds if and only if the state is a product state of its reduced states. From the viewpoint of resource in quantum information, we find there exists a maximally coherent state with maximal entanglement. Originated from the behaviour of quantum correlation under the influence of quantum operations, we further classify the incoherent operations which send maximally coherent states to themselves.

Computing stabilized norms for quantum operations

2009 ◽  
Vol 9 (1&2) ◽  
pp. 16-36
Author(s):  
N. Johnston ◽  
D.W. Kribs ◽  
V.I. Paulsen
Keyword(s):  
Quantum Information ◽  
Information Science ◽  
Distance Measures ◽  
Quantum Information Science ◽  
Linear Map ◽  
Quantum Operations ◽  
Linear Maps

The diamond and completely bounded norms for linear maps play an increasingly important role in quantum information science, providing fundamental stabilized distance measures for differences of quantum operations. We give a brief introduction to the theory of completely bounded maps. Based on this theory, we formulate an algorithm to compute the norm of an arbitrary linear map. We present an implementation of the algorithm via MATLAB, discuss its efficiency, and consider the case of differences of unitary maps.

Distinguishing quantum operations having few Kraus operators

2008 ◽  
Vol 8 (8&9) ◽  
pp. 819-833
Author(s):  
J. Watrous
Keyword(s):  
Quantum Information ◽  
Auxiliary System ◽  
Alternate Proof ◽  
Auxiliary Space ◽  
Input Space ◽  
Quantum Operations ◽  
The Difference ◽  
Kraus Operators

Entanglement is sometimes helpful in distinguishing between quantum operations, as differences between quantum operations can become magnified when their inputs are entangled with auxiliary systems. Bounds on the dimension of the auxiliary system needed to optimally distinguish quantum operations are known in several situations. For instance, the dimension of the auxiliary space never needs to exceed the dimension of the input space of the operations for optimal distinguishability, while no auxiliary system whatsoever is needed to optimally distinguish unitary operations. Another bound, which follows from work of R. Timoney , is that optimal distinguishability is always possible when the dimension of the auxiliary system is twice the number of operators needed to express the difference between the quantum operations in Kraus form. This paper provides an alternate proof of this fact that is based on concepts and tools that are familiar to quantum information theorists.

scholarly journals An introductory review on resource theories of generalized nonclassical light

2021 ◽  
Vol 2038 (1) ◽  
pp. 012008
Author(s):  
Sanjib Dey
Keyword(s):  
Quantum Information ◽  
Quantum Physics ◽  
Quantum Effect ◽  
Resource Theory ◽  
Standard Quantum ◽  
Quantum Operations ◽  
Quantum Phenomena ◽  
Quantum Optical ◽  
Oscillator Quantum ◽  
Free Set

Abstract Quantum resource theory is perhaps the most revolutionary framework that quantum physics has ever experienced. It plays vigorous roles in unifying the quantification methods of a requisite quantum effect as wells as in identifying protocols that optimize its usefulness in a given application in areas ranging from quantum information to computation. Moreover, the resource theories have transmuted radical quantum phenomena like coherence, nonclassicality and entanglement from being just intriguing to being helpful in executing realistic thoughts. A general quantum resource theoretical framework relies on the method of categorization of all possible quantum states into two sets, namely, the free set and the resource set. Associated with the set of free states there is a number of free quantum operations emerging from the natural constraints attributed to the corresponding physical system. Then, the task of quantum resource theory is to discover possible aspects arising from the restricted set of operations as resources. Along with the rapid growth of various resource theories corresponding to standard harmonic oscillator quantum optical states, significant advancement has been expedited along the same direction for generalized quantum optical states. Generalized quantum optical framework strives to bring in several prosperous contemporary ideas including nonlinearity, PT -symmetric non-Hermitian theories, q-deformed bosonic systems, etc., to accomplish similar but elevated objectives of the standard quantum optics and information theories. In this article, we review the developments of nonclassical resource theories of different generalized quantum optical states and their usefulness in the context of quantum information theories.

INSIGHTS AND IMPLICATIONS FROM A BAYESIAN APPROACH TO QUANTUM INFORMATION

2005 ◽  
Vol 03 (01) ◽  
pp. 233-237 ◽  
Author(s):  
CHRISTOPHER A. FUCHS ◽  
MARCOS PÉREZ-SUÁREZ ◽  
DAVID J. SANTOS
Keyword(s):  
Quantum Theory ◽  
Quantum Information ◽  
Bayesian Approach ◽  
Stochastic Matrix ◽  
Quantum States ◽  
Structural Elements ◽  
Quantum Operation ◽  
Quantum Operations

Providing quantum theory, and thus quantum information, with some meaning, can only be the result of adopting a well-defined approach to the notion of probability. From a subjectivistic Bayesian approach to the latter, it follows that not only quantum states, but also quantum operations, are structural elements of a subjective nature. Furthermore, we provide a representation of any quantum operation as a stochastic matrix.

scholarly journals Robustly decorrelating errors with mixed quantum gates

2021 ◽  
Author(s):  
Anthony Polloreno ◽  
Kevin Young
Keyword(s):  
Optimal Control ◽  
Quantum Information ◽  
Marked Reduction ◽  
Quantum Circuit ◽  
Physical Review ◽  
Quantum Gates ◽  
Superconducting Qubit ◽  
Convex Programs ◽  
Quantum Operations ◽  
Quantum Optimal Control

Abstract Coherent errors in quantum operations are ubiquitous. Whether arising from spurious environmental couplings or errors in control fields, such errors can accumulate rapidly and degrade the performance of a quantum circuit significantly more than an average gate fidelity may indicate. As shown by Hastings [1] and Campbell [2], by replacing the deterministic implementation of a quantum gate with a randomized ensemble of implementations, one can dramatically suppress coherent errors. Our work begins by reformulating the results of Hastings and Campbell as a quantum optimal control problem. We then discuss a family of convex programs able to solve this problem, as well as a set of secondary objectives designed to improve the performance, implementability, and robustness of the resulting mixed quantum gates. Finally, we implement these mixed quantum gates on a superconducting qubit and discuss randomized benchmarking results consistent with a marked reduction in the coherent error. [1] M. B. Hastings, Quantum Information & Computation 17, 488 (2017). [2] E. Campbell, Physical Review A 95, 042306 (2017).

Monotonicity of quantum relative entropy and recoverability

2015 ◽  
Vol 15 (15&16) ◽  
pp. 1333-1354 ◽  
Author(s):  
Mario Berta ◽  
Marius Lemm ◽  
Mark M. Wilde
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Relative Entropy ◽  
Remainder Term ◽  
Conditional Entropy ◽  
Quantum Information Theory ◽  
Partial Trace ◽  
Quantum Operations ◽  
Strong Subadditivity ◽  
Joint Convexity

The relative entropy is a principal measure of distinguishability in quantum information theory, with its most important property being that it is non-increasing with respect to noisy quantum operations. Here, we establish a remainder term for this inequality that quantifies how well one can recover from a loss of information by employing a rotated Petz recovery map. The main approach for proving this refinement is to combine the methods of [Fawzi and Renner, 2014] with the notion of a relative typical subspace from [Bjelakovic and Siegmund-Schultze, 2003]. Our paper constitutes partial progress towards a remainder term which features just the Petz recovery map (not a rotated Petz map), a conjecture which would have many consequences in quantum information theory. A well known result states that the monotonicity of relative entropy with respect to quantum operations is equivalent to each of the following inequalities: strong subadditivity of entropy, concavity of conditional entropy, joint convexity of relative entropy, and monotonicity of relative entropy with respect to partial trace. We show that this equivalence holds true for refinements of all these inequalities in terms of the Petz recovery map. So either all of these refinements are true or all are false.

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