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Equivalence of operations with respect to discriminator clones

2009
*
Discrete Mathematics
*

Moreover, we show that the smallest

doi:10.1016/j.disc.2008.01.003
fatcat:7vjtzajobjfrhhdrkdxftt6qia
*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. ...##
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Structure of minimum-error quantum state discrimination

2013
*
New Journal of Physics
*

We also introduce

doi:10.1088/1367-2630/15/7/073037
fatcat:lifavx7gcje3tm644euesfydly
*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*. ...##
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Quantum state separation, unambiguous discrimination and exact cloning

1998
*
Journal of Physics A: Mathematical and General
*

and

doi:10.1088/0305-4470/31/50/007
fatcat:tqerjizslrhsnbczu5wglqhljy
*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*...##
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A note on general no-cloning theorem for black boxes
[article]

2010
*
arXiv
*
pre-print

The paper has been withdrawn by the author due

arXiv:0908.1668v3
fatcat:e23l2dxaa5bypbtmeaor3iv3wm
*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 }. ...##
###
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*...##
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Optimal Cloning of Unitary Transformation

2008
*
Physical Review Letters
*

After proving a general no-

doi:10.1103/physrevlett.101.180504
pmid:18999806
fatcat:btp4i7eqyrd2xdvi4wzhtyv6ju
*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. ...##
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The submaximal clones on the three-element set with finitely many relative R-classes
[article]

2009
*
arXiv
*
pre-print

For each

arXiv:0905.1614v1
fatcat:dkwdwbba6remtnpips4qg6mz3m
*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 . ...##
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Large intervals in the clone lattice

2009
*
Algebra Universalis
*

, (2) the interval [C 2 , O] in the lattice

doi:10.1007/s00012-010-0047-6
fatcat:tho25wyfnrerxh4sr7ku4suhdi
*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. ...##
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Cavity broadcasting via Raman scattering
[article]

2004
*
arXiv
*
pre-print

The notion

arXiv:quant-ph/0409105v1
fatcat:l7yka5lmhzc4bfykepaizqcana
*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 . ...##
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Telecloning of qudits via partially entangled states

2016
*
Quantum Information Processing
*

It is also shown that other strategies, such as minimum error

doi:10.1007/s11128-016-1348-2
fatcat:kztwd3vobjbuhkdwr63gih4suy
*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. ...##
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Sequential state discrimination with quantum correlation

2018
*
Quantum Information Processing
*

When one considers at least one

doi:10.1007/s11128-018-2033-4
fatcat:a5rtuqw7zzb3vgsrhgxwahkoh4
*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. ...##
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Condition and capability of quantum state separation

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). ...

##
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Quantum state discrimination

2000
*
Contemporary physics (Print)
*

There are fundamental limits

doi:10.1080/00107510010002599
fatcat:kcb5afjiyjfftpqueqs4ufh2oy
*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 . ...##
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Quantum Circuit Architecture

2008
*
Physical Review Letters
*

The method allows one

doi:10.1103/physrevlett.101.060401
pmid:18764438
fatcat:lb4lhxm7qvdrhahn6rnczzknvm
*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 ...##
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Optimality of minimum-error discrimination by the no-signaling condition

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

doi:10.1103/physreva.78.022335
fatcat:lu773rcnofgrjdt7axaazynyje
*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 ...
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