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Equivalence of operations with respect to discriminator clones

Erkko Lehtonen, Ágnes Szendrei
2009 Discrete Mathematics  
Moreover, we show that the smallest discriminator clone is minimal with respect to this finiteness property.  ...  For each clone C on a set A there is an associated equivalence relation, called C-equivalence, on the set of all operations on A, which relates two operations iff each one is a substitution instance of  ...  Acknowledgements This work was initiated while the first author was visiting the University of Waterloo. He is indebted to Professors Ian Goulden and Bruce Richmond for helpful discussions.  ... 
doi:10.1016/j.disc.2008.01.003 fatcat:7vjtzajobjfrhhdrkdxftt6qia

Structure of minimum-error quantum state discrimination

Joonwoo Bae
2013 New Journal of Physics  
We also introduce equivalent classes of sets of quantum states in terms of minimum-error discrimination: sets of quantum states in an equivalence class share the same guessing probability.  ...  In particular, for qubit states where the state geometry is found with the Bloch sphere, we illustrate that for an arbitrary set of qubit states, the minimum-error state discrimination with equal prior  ...  Finally, we consider results obtained in state discrimination in the context of its equivalence to asymptotic quantum cloning.  ... 
doi:10.1088/1367-2630/15/7/073037 fatcat:lifavx7gcje3tm644euesfydly

Quantum state separation, unambiguous discrimination and exact cloning

Anthony Chefles, Stephen M Barnett
1998 Journal of Physics A: Mathematical and General  
and cloning are special cases of this general bound.  ...  Unambiguous discrimination and exact cloning reduce the square-overlap between quantum states, exemplifying the more general type of procedure we term state separation.  ...  The discrimination limit P IDP and the infinite cloning bound P 1∞ (or, for that matter, the maximum discrimination probability with M copies of the state, and P M∞ ), are equal due to the equivalence  ... 
doi:10.1088/0305-4470/31/50/007 fatcat:tqerjizslrhsnbczu5wglqhljy

A note on general no-cloning theorem for black boxes [article]

Alexey E. Rastegin
2010 arXiv   pre-print
The paper has been withdrawn by the author due to unhappy mistake in the initial scope of the work.  ...  [10] with respect to probabilistic cloning operations. a i . So, the diagonal elements of output E(A) are expressed as  ...  Suppose that positive operator A with eigenvalues a i is diagonal with respect to the basis {|i }.  ... 
arXiv:0908.1668v3 fatcat:e23l2dxaa5bypbtmeaor3iv3wm

Page 6794 of Mathematical Reviews Vol. , Issue 87m [page]

1987 Mathematical Reviews  
An algebra & on A is semi-affine if there exists an abelian group 6 such that every basic operation of & is affine with respect to 6.  ...  This discussion leads to a proof of Palfy’s theorem: A finite algebra % = (A, F) with |A| > 3 is polynomially equivalent to a vector space if and only if every nonconstant unary polynomial operation of  ... 

Optimal Cloning of Unitary Transformation

Giulio Chiribella, Giacomo Mauro D'Ariano, Paolo Perinotti
2008 Physical Review Letters  
After proving a general no-cloning theorem for black boxes, we derive the optimal universal cloning of unitary transformations, from one to two copies.  ...  The optimal cloner is realized by quantum channels with memory, and greately outperforms the optimal measure-and-reprepare cloning strategy.  ...  GC is grateful to M. Murao, M. Hayashi, and A. Winter for useful and enjoyable discussions on possible applications/variations of the channel cloning problem.  ... 
doi:10.1103/physrevlett.101.180504 pmid:18999806 fatcat:btp4i7eqyrd2xdvi4wzhtyv6ju

The submaximal clones on the three-element set with finitely many relative R-classes [article]

Erkko Lehtonen, Agnes Szendrei
2009 arXiv   pre-print
For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A if and only if each one is a substitution instance of the other  ...  We study the maximal and submaximal clones on a three-element set and determine which of them have only finitely many relative R-classes.  ...  Acknowledgements We would like to thank Miguel Couceiro for helpful discussions concerning the clones in lines 34 and 35 of Table 2 .  ... 
arXiv:0905.1614v1 fatcat:dkwdwbba6remtnpips4qg6mz3m

Large intervals in the clone lattice

Martin Goldstern, Saharon Shelah
2009 Algebra Universalis  
, (2) the interval [C 2 , O] in the lattice of local clones is isomorphic to the congruence lattice of an arbitrary semilattice, (3) the interval [C 3 , O] in the lattice of all clones is isomorphic to  ...  Specifically, we will exhibit clones C 1 , C 2 , C 3 such that: (1) the interval [C 1 , O] in the lattice of local clones is (as a lattice) isomorphic to {0, 1, 2, . . .} under the divisibility relation  ...  Acknowledgement We are grateful to the referee for pointing out Pixley's theorem, which led to essential simplifications of our proofs.  ... 
doi:10.1007/s00012-010-0047-6 fatcat:tho25wyfnrerxh4sr7ku4suhdi

Cavity broadcasting via Raman scattering [article]

Moorad Alexanian
2004 arXiv   pre-print
The notion of broadcasting is extended to include the case where an arbitrary input density state of a two-mode radiation field gives rise to an output state with identical marginal states for the respective  ...  This extended notion of broadcasting suggests a possible way of discriminating between two noncommuting quantum states.  ...  σ A = |Φ σ >< Φ σ | and |Φ σ > is given by (18) with expectation values taken with respect to σ i rather than ρ i .  ... 
arXiv:quant-ph/0409105v1 fatcat:l7yka5lmhzc4bfykepaizqcana

Telecloning of qudits via partially entangled states

Gabriel Araneda, Nataly Cisternas, Aldo Delgado
2016 Quantum Information Processing  
It is also shown that other strategies, such as minimum error discrimination, lead to a decrease in the fidelity of the copies and that certain partially entangled pure states with maximal Schmidt rank  ...  This process efficiently mixes optimal universal symmetric cloning with quantum teleportation.  ...  with respect to the input state.  ... 
doi:10.1007/s11128-016-1348-2 fatcat:kztwd3vobjbuhkdwr63gih4suy

Sequential state discrimination with quantum correlation

Jin-Hua Zhang, Fu-Lin Zhang, Mai-Lin Liang
2018 Quantum Information Processing  
When one considers at least one of the parties succeeds, the protocol with probabilistic cloning is superior to others, which is not observed in the special case with equal prior probabilities.  ...  The left and right discords correspond to the part of information extracted by the first observer and the part left to his successor respectively.  ...  Charlie performs a similar joint unitary operation Uc between it and his qutrit C and then makes an optimal unambiguous discrimination measurement [18] on C. qutrit with respect to the basis.  ... 
doi:10.1007/s11128-018-2033-4 fatcat:a5rtuqw7zzb3vgsrhgxwahkoh4

Condition and capability of quantum state separation

Yuan Feng, Runyao Duan, Zhengfeng Ji
2005 Physical Review A. Atomic, Molecular, and Optical Physics  
cloning and quantum discrimination.  ...  To be specific, if a system is prepared in a state secretly chosen from a linearly independent pure state set, then any quantum state separation can be physically realized with a positive probability.  ...  Duan acknowledges the financial support of Tsinghua University (Grant No. 052420003).  ... 
doi:10.1103/physreva.72.012313 fatcat:v4lbpmw4pneqvmizn525ncyjca

Quantum state discrimination

Anthony Chefles
2000 Contemporary physics (Print)  
There are fundamental limits to the accuracy with which one can determine the state of a quantum system. I give an overview of the main approaches to quantum state discrimination.  ...  In addition to reviewing these various strategies, I describe connections between state discrimination, the manipulation of quantum entanglement, and quantum cloning.  ...  I would also like to thank him, Erling Riis and the Journal of Modern Optics for permission to use Figure 3 .  ... 
doi:10.1080/00107510010002599 fatcat:kcb5afjiyjfftpqueqs4ufh2oy

Quantum Circuit Architecture

G. Chiribella, G. M. D'Ariano, P. Perinotti
2008 Physical Review Letters  
The method allows one to efficiently address novel kinds of quantum information processing tasks, such as storing-retrieving, and cloning of channels.  ...  The method is based on the notion of "quantum comb", which describes a circuit board in which one can insert variable subcircuits.  ...  A quantum comb with N slots is clearly equivalent to a concatenation of N 1 channels with memory, which is in turn equivalent to a causal network, namely, a network where the quantum state of the output  ... 
doi:10.1103/physrevlett.101.060401 pmid:18764438 fatcat:lb4lhxm7qvdrhahn6rnczzknvm

Optimality of minimum-error discrimination by the no-signaling condition

Joonwoo Bae, Jae-Weon Lee, Jaewan Kim, Won-Young Hwang
2008 Physical Review A. Atomic, Molecular, and Optical Physics  
In this work we relate the well-known no-go theorem that two non-orthogonal (mixed) quantum states cannot be perfectly discriminated, to the general principle in physics, the no-signalling condition.  ...  In fact, we derive the minimum error in discrimination between two quantum states, using the no-signalling condition.  ...  This leads to one of the well-known no-go theorems, that quantum states cannot be copied with certainty [1] , although approximate quantum cloning is possible with the use of quantum operations and ancillary  ... 
doi:10.1103/physreva.78.022335 fatcat:lu773rcnofgrjdt7axaazynyje
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