The DOI matches its Crossref record; 12 of the 12 references it cites were found in a registry or an index; none of the 4 sources its claims cite is checked for support yet.
Completely positive linear maps on complex matrices
Open accessOverview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
14 No basis given · 2 Sources not found · 2 Own interpretation
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“For some improvement, we may require {u:} to be linearly independent, then {Vi} must be linearly independent too.”
§ Completely Positive Linear Maps on Complex Matrices > Abstract
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“Q : !JXn,+9Xm is hermitian-preserving iff @ admits an expression @(A) = Zei V;CAV, where ei = + 1, Vi are n X m matrices.”
§ Completely Positive Linear Maps on Complex Matrices > Abstract
What the sources say
- Not matchedcites [7, p. 134, Theorem 2.11]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [5, p. 259, Theorem 21]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“For a linear map a: 9JIm,-+Izll,, it is obvious that Q is hermitian-preserving iff (@(Eik))jk is hermitian.”
§ Completely Positive Linear Maps on Complex Matrices > Abstract
boostedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“THEOREM 2. Let Cp be a linear map from %!, to %Q,,,.Then @ is completely positive iff (@(Ejk))lG i,k9n is positiue.”
§ Completely Positive Linear Maps on Complex Matrices > Abstract
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Let { W,}; be a class of n X m matrices, then Q, has the expression @(A) = X;W:AWp iff there exists an isometric I! ' x E matrix (@Pi, such that Wp = Zipppi Vi for all p.”
§ Completely Positive Linear Maps on Complex Matrices > Abstract
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Let Q,: 9.Rm,41Qm,.Then ip is extreme in CP[ZRn, VA!,; K] iff @ admits an expression @(A)=ZiVFAVi for all A in 9X,,, where y are n X m matrices, Xi VF Vi = K, and { y vi} ii is a linearly independent set.”
§ Completely Positive Linear Maps on Complex Matrices > Abstract
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: unclear — It is unclear why the paper says it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“THEOREM 1 . Let Q, : !J.R,+!&,,.Then CD is completely positive iff Q is of the form ia = ZiVTAV for all A in 92, where Vi are n X m matrices.”
§ Completely Positive Linear Maps on Complex Matrices > Abstract
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Rests on an assumption: Every positive matrix can be expressed as a sum of rank-one positive matrices (vectors).
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“THEOREM 7 . Zf @:!!JL&lR,,, is positive, then there exist 2Xm matrices y such that Q(A) =ZiVi*AVi for all 2X2 symmetric A.”
§ Completely Positive Linear Maps on Complex Matrices > Additional information
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“Let F be an mm,-coefficient quadratic form F(s, t) = B,?+ B,st + B,t2 with real indeterminates s, t.If F(s, t) is positive for all s, t, then there exist k X m matrices C, D, such that F(s, t) = (Cs + Dt)*(Cs + Dt).(k is a certain integer.)”
§ Completely Positive Linear Maps on Complex Matrices > Additional information
What the sources say
- Not matchedcites [3,Theorem 21]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [6, Appendix III]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“For each n urn matrix V, it is evident that the map: %!,-+m,,, with A + V* A V is completely positive.”
§ Completely Positive Linear Maps on Complex Matrices > Abstract
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- It may state two separate claims as one. 6
- Probably not a substantial claim. 1
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Endowed with the natural ordering induced by !TQ,(!lP,J, the class of hermitian-preserving maps is a partially ordered vector space over the reals, while the class of completely positive linear maps is just the positive cone.”
§ Completely Positive Linear Maps on Complex Matrices > Abstract
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Suppose a: YJ?”+%P, is completely positive.From Remark 4, we can write 0 in the form O(A) = Z,!VTAVi where { Vi} f is a class of linearly independent n X m matrices; hence e < nm.”
§ Completely Positive Linear Maps on Complex Matrices > Additional information
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Moreover, if { W,}; is also a linearly independent set, then F ' = I', and ( ppJpi is unitary.”
§ Completely Positive Linear Maps on Complex Matrices > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In the proof of Theorem 1, the expression (@(Ejk))+ = Xi”* q is not unique, hence ( Vi} is not uniquely determined.”
§ Completely Positive Linear Maps on Complex Matrices > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“It is evident that CP[!&, iDi!,; K] is a convex set, hence it is the convex hull of its extreme points.”
§ Completely Positive Linear Maps on Complex Matrices > Abstract
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Each linear map Q, : !IR2,-+'171, is determined by its values on Eik.Hence ip is completely determined by the single element (@(Ejk))l < i, k G n E 9JIm, (TRJ.”
§ Completely Positive Linear Maps on Complex Matrices > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In particular, if m = I, we obtain the well-known fact that @ is a 'pure state' (an extreme identity-preserving positive functional) on YJ$, iff @ is a 'vector state' (i.e., there exists a unit vector u such that Q(A) = v*Av for all A).”
§ Completely Positive Linear Maps on Complex Matrices > Additional information
boostedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper relies on this without support.
Every positive matrix can be expressed as a sum of rank-one positive matrices (vectors).
“As (E&< i,kGn is positive, so P(EjJ)r< j,k(n E !I&, (!l.R,J is positive; thus there exist vectors vi” (regarded as nm x 1 matrices) such that (Q(Ejk))jk =Z,uFvi.”
The paper relies on this without support.
Theorem 7 is not valid for higher order matrices.
“We remark that Theorem 7 is not valid for higher order matrices.This is just because the quoted result for an mm,-coefficient quadratic form cannot be generalized to the case of more than 2 real indeterminates, as will be shown in a forthcoming paper.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“E (t,t 1 ) ⊗ 1 1 (| |) 1 = 1 iff E (t,t 1 ) is CP, > 1 otherwise.”
From Quantum non-Markovianity: characterization, quantification and detection (2014) · cites this paper as [19]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“Complete positive maps are much easier to characterize than maps that are merely positive [19,20]; they admit the so-called Kraus representation,”
From Quantum non-Markovianity: characterization, quantification and detection (2014) · cites this paper as [19]
The check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“For this, typical methods used to generate hybrid entangled states using q-plates [46] and static meta-surfaces [47,48] will not suffice, hence we make use of an all-digital SPC approach [49]”
From Non-local skyrmions as topologically resilient quantum entangled states of light (2024) · cites this paper as [48]
Experimental — accuracy not yet measuredIn the citing paper
“for a Hilbert space with finite dimension N S = dim H S complete positivity is equivalent to N S -positivity [13].”
From Foundations and measures of quantum non-Markovianity (2012) · cites this paper as [13]
In the citing paper
“Theorem 5. A linear map : M n → M n is completely positive if and only if ⊗ I M n is positivity-preserving on M n ⊗ M n or equivalently, if and only if the matrix”
From An analysis of completely-positive trace-preserving maps on M2 (2002) · cites this paper as [4]
In the citing paper
“Lemma 10.The minimal number of Kraus operators A k needed to represent a completely positive map in the form (1) is rank[β( )].”
From An analysis of completely-positive trace-preserving maps on M2 (2002) · cites this paper as [4]
In the citing paper
“Lemma 9. A stochastic map is an extreme point of S if and only if it can be written in the form (1) (necessarily with k A k A † k = I ), so that the set of matrices {A j A † k } is linearly independent.”
From An analysis of completely-positive trace-preserving maps on M2 (2002) · cites this paper as [4]
In the citing paper
“After the results were first published, it was shown by Gottesman[32] that fault tolerant procedures for the universal set of gates introduced by Shor can be constructed for any stabilizer code, using basically the same technique as presented by Shor for the CSS codes, a result which was generalized to qupits[33].”
From Fault-Tolerant Quantum Computation with Constant Error Rate (2008) · cites this paper as [32]
In the citing paper
“qPCA for quantum states can be extended to quantum processes by using the Choi-Jamiolkowski state (1/d) ij |i j| ⊗ S(|i j|) for a completely positive map S (ref.22).”
From Quantum principal component analysis (2014) · cites this paper as [22]
In the citing paper
“qPCA can then be used to construct the eigenvectors corresponding to the dominant eigenvalues of this state: the resulting spectral decomposition in turn encapsulates many of the most important properties of the channel 22 .”
From Quantum principal component analysis (2014) · cites this paper as [22]
Citations
Cites
Arveson, W. (1969) · Acta Mathematica · doi:10.1007/bf02392388 · Cited by 1,107
Positive functions on 𝐶*-algebras
Stinespring, W. F. (1955) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-1955-0069403-4 · Cited by 1,085
Positive Functions on C ∗ -Algebras
Stinespring, W. F. (1955) · Proceedings of the American Mathematical Society · doi:10.2307/2032342 · Cited by 753
Positive Linear Maps of Operator Algebras
Størmer, E. (2012) · Springer monographs in mathematics · doi:10.1007/978-3-642-34369-8 · Cited by 428
Arveson, W. (1972) · Acta Mathematica · doi:10.1007/bf02392166 · Cited by 382
Positive linear maps of operator algebras
Størmer, E. (1963) · Acta Mathematica · doi:10.1007/bf02391860 · Cited by 354
Positive Linear Maps on C*-Algebras
Choi, M.-D. (1972) · Canadian Journal of Mathematics · doi:10.4153/cjm-1972-044-5 · Cited by 239
Self-citationLinear transformations which preserve hermitian and positive semidefinite operators
de Pillis, J. (1967) · Pacific Journal of Mathematics · doi:10.2140/pjm.1967.23.129 · Cited by 188
On subalgebras of $C^*$-algebras
Arveson, W. (1969) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1969-12293-7 · Cited by 144
Synthesis of Finite Passive n-Ports with Prescribed Positive Real Matrices of Several Variables
Koga, T. (1968) · IEEE Transactions on Circuit Theory · doi:10.1109/tct.1968.1082780 · Cited by 91
Cited by
Sorted by citations
Items 1,601–1,700 of 2,678
Yang, S., Zheng, J.-H., & Yang, T. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.134436 · Cited by 4
Yoneya, T., Fujimoto, K., & Kawaguchi, Y. (2025) · Annals of Physics · doi:10.1016/j.aop.2025.170072 · Cited by 10
A mirrored pair of optimal non-decomposable entanglement witnesses for two qudits does exist
Chruściński, D., Bera, A., Bae, J., et al. (2025) · Scientific Reports · doi:10.1038/s41598-025-10985-0 · Cited by 4
Effective conformal field theory generated from pure and dephased Chern insulator
Sarma, A., Bao, Y., Myerson-Jain, N. E., et al. (2025) · Physical review. B./Physical review. B · doi:10.1103/nn2m-w4vk · Cited by 4
Entanglement-breaking channels are a quantum memory resource
Vieira, L. B., Ku, H.-Y., & Budroni, C. (2025) · Physical Review Research · doi:10.1103/r8lf-bb4p · Cited by 3
Spacetime density matrix: formalism and properties
Guo, W.-Z. (2026) · Journal of High Energy Physics · doi:10.1007/jhep01(2026)128 · Cited by 4
Notes on entropic characteristics of quantum channels
Rastegin, A. E. (2012) · Open Physics · doi:10.2478/s11534-012-0134-8 · Cited by 4
Experimental characterization of a non-local convertor for quantum photonic networks
Mičuda, M., Stárek, R., Marek, P., Miková, M., Straka, I., Ježek, M., Tashima, T., Özdemir, Ş. K., & Tame, M. (2017) · Optics Express · doi:10.1364/oe.25.007839 · Cited by 5
Hertz, A., Arnhem, M., Asadian, A., et al. (2021) · Physical Review A · doi:10.1103/physreva.104.022427 · Cited by 4
Deep Reinforcement Learning Quantum Control on IBMQ Platforms and Qiskit Pulse
Semola, R., Moro, L. D., Bacciu, D., & Prati, E. (2022) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce53715.2022.00108 · Cited by 4
Strategies for single-shot discrimination of process matrices
Lewandowska, P., Pawela, Ł., & Puchała, Z. (2023) · Scientific Reports · doi:10.1038/s41598-023-30191-0 · Cited by 7
Delocalized and dynamical catalytic randomness and information flow
Lie, S. H., & Jeong, H. (2023) · Physical Review A · doi:10.1103/physreva.107.042430 · Cited by 5
Wieśniak, M. (2023) · Scientific Reports · doi:10.1038/s41598-023-46337-z · Cited by 4
Reversibility-unitality-disturbance tradeoff in quantum channels
Sun, Y., & Li, N. (2024) · Physical Review A · doi:10.1103/physreva.109.012407 · Cited by 4
C⁎-extreme entanglement breaking maps on operator systems
Balasubramanian, S., & Hotwani, N. (2024) · Linear Algebra and its Applications · doi:10.1016/j.laa.2024.01.004 · Cited by 5
Benchmarking of universal qutrit gates
Amaro-Alcalá, D., Sanders, B. C., & de Guise, H. (2024) · Physical Review A · doi:10.1103/physreva.109.012621 · Cited by 4
Quantifying the irreversibility of channels
Luo, S., & Sun, Y. (2024) · Theoretical and Mathematical Physics · doi:10.1134/s004057792403005x · Cited by 5
Influence of initial states on memory effects: A study of early-time superradiance
Hou, S. C., Shuai, G. Q., Zhang, X. Y., Shen, J.-K., & Yi, X. X. (2024) · Physical Review A · doi:10.1103/physreva.109.053708 · Cited by 4
Error suppression in multicomponent cat codes with photon subtraction and teleamplification
Shringarpure, S. U., Teo, Y. S., & Jeong, H. (2024) · Optics Express · doi:10.1364/oe.519638 · Cited by 4
Roy, A. K., Srivastava, V., Mahanti, S., Giarmatzi, C., & Gilchrist, A. (2024) · Physical Review A · doi:10.1103/physreva.110.012608 · Cited by 4
Extending quantum detailed balance through optimal transport
Duvenhage, R., Skosana, S., & Snyman, M. (2024) · Reviews in Mathematical Physics · doi:10.1142/s0129055x24500405 · Cited by 4
Characterization of k-Positive Maps
Młynik, T., Osaka, H., & Marciniak, M. (2025) · Communications in Mathematical Physics · doi:10.1007/s00220-025-05250-4 · Cited by 4
Power of quantum measurement in simulating unphysical operations
Zhao, X., Zhang, L., Zhao, B., & Wang, X. (2025) · Physical Review Research · doi:10.1103/physrevresearch.7.013334 · Cited by 9
Efficient Pauli Channel Estimation with Logarithmic Quantum Memory
Chen, S., & Gong, W. (2025) · PRX Quantum · doi:10.1103/prxquantum.6.020323 · Cited by 26
Noise-adapted quantum error correction for non-Markovian noise
Biswas, D., Utagi, S., & Mandayam, P. (2025) · Physical Review A · doi:10.1103/physreva.111.052413 · Cited by 4
Universality of sudden death of entanglement
Fanchini, F. F., Mendonça, P. E. M. F., & Napolitano, R. D. J. (2011) · Quantum Information and Computation · doi:10.26421/qic11.7-8-9 · Cited by 5
On Kadison-Schwarz Type Quantum Quadratic Operators on
Mukhamedov, F., & Abduganiev, A. (2013) · Abstract and Applied Analysis · doi:10.1155/2013/278606 · Cited by 5
Deb, P., & Banik, M. (2015) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/48/18/185303 · Cited by 4
Exotic one-parameter semigroups of endomorphisms of a symmetric cone
Kuzma, B., Omladič, M., Šivic, K., et al. (2015) · Linear Algebra and its Applications · doi:10.1016/j.laa.2015.03.006 · Cited by 4
Searching for evolutions from pure states into mixed states with entangled neutral kaons
Gerber, H.-J. (2004) · The European Physical Journal C · doi:10.1140/epjc/s2003-01382-2 · Cited by 4
Generalised quantum weakest preconditions
Gielerak, R., & Sawerwain, M. (2009) · Quantum Information Processing · doi:10.1007/s11128-009-0151-8 · Cited by 4
How two spins can thermalize a third spin
Kleinbölting, S., & Klesse, R. (2015) · Physical Review E · doi:10.1103/physreve.91.052101 · Cited by 4
Tensor powers of 2-positive maps
Størmer, E. (2010) · Journal of Mathematical Physics · doi:10.1063/1.3497628 · Cited by 4
Quantum controlled- Z gate for weakly interacting qubits
Mičuda, M., Stárek, R., Straka, I., Miková, M., Dušek, M., Ježek, M., Filip, R., & Fiurášek, J. (2015) · Physical Review A · doi:10.1103/physreva.92.022341 · Cited by 4
Bruns, D., Sperling, J., & Scheel, S. (2016) · Physical Review A · doi:10.1103/physreva.93.032132 · Cited by 4
Indecomposability of entanglement witnesses
Qi, X., & Hou, J. (2015) · Quantum Information and Computation · doi:10.26421/qic15.5-6-7 · Cited by 4
An Invitation to Quantum Information Theory
Parthasarathy, K. R. (2009) · Statistical science and interdisciplinary research · doi:10.1142/9789814273633_0010 · Cited by 4
Extension properties of some completely positive maps
Sun, X.-H., & Li, Y. (2016) · Linear and Multilinear Algebra · doi:10.1080/03081087.2016.1238032 · Cited by 4
Average entropy of a subsystem over a global unitary orbit of a mixed bipartite state
Zhang, L., & Xiang, H. (2017) · Quantum Information Processing · doi:10.1007/s11128-017-1570-6 · Cited by 4
All unital qubit channels are 4-noisy operations
Müller‐Hermes, A., & Perry, C. (2018) · Letters in Mathematical Physics · doi:10.1007/s11005-018-1104-x · Cited by 4
Spin Polarization-Scaling Quantum Maps and Channels
Filippov, S. N., & Magadov, K. Y. (2018) · Lobachevskii Journal of Mathematics · doi:10.1134/s1995080218010109 · Cited by 5
Translations and reflections on the torus: identities for discrete Wigner functions and transforms
Saraceno, M., & de Almeida, A. M. O. (2019) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/aafdc2 · Cited by 4
Matrix N-dilations of quantum channels
Levick, J., & Martin, R. T. W. (2018) · Operators and Matrices · doi:10.7153/oam-2018-12-59 · Cited by 4
Some trace inequalities for exponential and logarithmic functions
Carlen, E. A., & Lieb, É. H. (2018) · Bulletin of Mathematical Sciences · doi:10.1007/s13373-018-0123-3 · Cited by 4
Double-trace deformation in open quantum field theory
Meng, X. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.104.016016 · Cited by 6
Fate of symmetry protected coherence in open quantum system
Deng, T.-S., & Pan, L. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.094306 · Cited by 4
Entanglement breaking channels, stochastic matrices, and primitivity
Ahiable, J., Kribs, D. W., Levick, J., et al. (2021) · Linear Algebra and its Applications · doi:10.1016/j.laa.2021.08.013 · Cited by 4
Trace class operators via OPV-frames
Bhardwaj, R., Sharma, S., & Kaushik, S. K. (2021) · Filomat · doi:10.2298/fil2113353b · Cited by 4
Robust observable control of open and closed quantum systems
Bhutoria, V., Koswara, A., & Chakrabarti, R. (2022) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ac623f · Cited by 4
Causal and Causally Separable Processes
Giarmatzi, C. (2019) · Springer theses · doi:10.1007/978-3-030-31930-4_2 · Cited by 4
Role of matter coherence in entanglement due to gravity
Matsumura, A. (2022) · Quantum · doi:10.22331/q-2022-10-11-832 · Cited by 4
Linear Maps as Sufficient Criteria for Entanglement Depth and Compatibility in Many-Body Systems
Lewenstein, M., Müller-Rigat, G., Tura, J., et al. (2022) · Open Systems & Information Dynamics · doi:10.1142/s1230161222500111 · Cited by 4
Quantum-Dynamical Semigroups and the Church of the Larger Hilbert Space
Ende, F. V. (2023) · Open Systems & Information Dynamics · doi:10.1142/s1230161223500038 · Cited by 4
System–environment dynamics of GHZ-like states in noninertial frames
Zhang, T., Yang, H., & Fei, S.-M. (2023) · Quantum Information Processing · doi:10.1007/s11128-023-04081-3 · Cited by 4
Multi-agent blind quantum computation without universal cluster states
Cao, S. (2023) · New Journal of Physics · doi:10.1088/1367-2630/acfab6 · Cited by 7
Identification of Quantum Change Points for Hamiltonians
Nakahira, K. (2023) · Physical Review Letters · doi:10.1103/physrevlett.131.210804 · Cited by 4
Petz recovery maps for qudit quantum channels
Lautenbacher, L., Jagadish, V., Petruccione, F., & Bernardes, N. K. (2024) · Physics Letters A · doi:10.1016/j.physleta.2024.129583 · Cited by 4
Sun, R.-Y., Shirakawa, T., & Yunoki, S. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.085149 · Cited by 4
Fixed points of trace preserving completely positive maps
Zhang, H., & Xue, M. (2015) · Linear and Multilinear Algebra · doi:10.1080/03081087.2015.1043718 · Cited by 4
Horodeckis criterion of separability of mixed states in von Neumann and C*-algebras
Miller, M., & Olkiewicz, R. (2014) · Infinite Dimensional Analysis Quantum Probability and Related Topics · doi:10.1142/s0219025714500283 · Cited by 4
Fixed Points Associated to Power of Normal Completely Positive Maps*
Zhang, H., & Si, H. (2016) · Journal of Applied Mathematics and Physics · doi:10.4236/jamp.2016.45101 · Cited by 4
Symmetry in the open-system dynamics of quantum correlations
Lyyra, H., Karpat, G., Li, C.-F., Guo, G.-C., Piilo, J., & Maniscalco, S. (2017) · Scientific Reports · doi:10.1038/s41598-017-08457-1 · Cited by 6
Two Definitions of the Gell-Mann Channels—A Comparative Analysis
Siudzińska, K. (2018) · Reports on Mathematical Physics · doi:10.1016/s0034-4877(18)30051-x · Cited by 4
A Proof for the Existence of Nonsquare Unextendible Maximally Entangled Bases
Liu, F. (2018) · International Journal of Theoretical Physics · doi:10.1007/s10773-018-3771-x · Cited by 4
Xie, W. D., Wang, X., & Duan, R. (2018) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2018.8437766 · Cited by 4
Sargolzahi, I., & Mirafzali, S. Y. (2019) · Physical Review A · doi:10.1103/physreva.100.042121 · Cited by 4
On the Complexity of Finding the Maximum Entropy Compatible Quantum State
Giorgio, S. D., & Mateus, P. (2021) · Mathematics · doi:10.3390/math9020193 · Cited by 4
Transition probabilities and transition rates in discrete phase space
Braasch, W. F., & Wootters, W. K. (2020) · Physical Review A · doi:10.1103/physreva.102.052204 · Cited by 4
The End of a Classical Ontology for Quantum Mechanics?
Evans, P. W. (2020) · Entropy · doi:10.3390/e23010012 · Cited by 6
Confidence polytopes for quantum process tomography
Kiktenko, E. O., Norkin, D. O., & Fedorov, A. K. (2021) · New Journal of Physics · doi:10.1088/1367-2630/ac3cf7 · Cited by 4
Efficient quantum state tracking in noisy environments
Rambach, M., Youssry, A., Tomamichel, M., & Romero, J. (2022) · Quantum Science and Technology · doi:10.1088/2058-9565/aca049 · Cited by 4
The Pitfalls of Deciding Whether a Quantum Channel is (Conjugate) Degradable and How to Avoid Them
Brádler, K. (2015) · Open Systems & Information Dynamics · doi:10.1142/s1230161215500262 · Cited by 5
Detailed balance as a quantum-group symmetry of Kraus operators
Andersson, A. (2018) · Journal of Mathematical Physics · doi:10.1063/1.5023900 · Cited by 4
Applications of the joint angular field of values
Barker, G. P. (1984) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-1984-0744623-x · Cited by 4
Generalized interlacing inequalities
Li, C.-K., Poon, Y., & Sze, N.-S. (2011) · Linear and Multilinear Algebra · doi:10.1080/03081087.2011.619534 · Cited by 4
Parametric quantum search algorithm by CP maps: algebraic, geometric and complexity aspects
Ellinas, D., & Konstandakis, C. (2013) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/46/41/415303 · Cited by 4
Quantum channel negativity as a measure of system-bath coupling and correlation
McCracken, J. M. (2013) · Physical Review A · doi:10.1103/physreva.88.032103 · Cited by 4
On the cone of completely positive linear transformations
Yopp, D. A., & Hill, R. D. (2000) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(99)00209-8 · Cited by 4
Loewy, R. (1992) · Linear and Multilinear Algebra · doi:10.1080/03081089208818179 · Cited by 4
Directed quantum communication
Åberg, J., Hengl, S., & Renner, R. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/3/033025 · Cited by 4
Ambrozie, C.-G., & Gheondea, A. (2014) · Linear and Multilinear Algebra · doi:10.1080/03081087.2014.903253 · Cited by 4
Decoherence induced spontaneous symmetry breaking
Karpat, G., & Gedik, Z. (2009) · Optics Communications · doi:10.1016/j.optcom.2009.07.066 · Cited by 4
Algebraic and quantum theoretical approach to coding on wiretap channels
Hamada, M. (2008) · International Symposium on Communications, Control and Signal Processing · doi:10.1109/isccsp.2008.4537281 · Cited by 4
Efficient Monte Carlo characterization of quantum operations for qudits
Gualdi, G., Licht, D., Reich, D. M., & Koch, C. P. (2014) · Physical Review A · doi:10.1103/physreva.90.032317 · Cited by 5
Control and enhancement of interferometric coupling between two photonic qubits
Stárek, R., Mičuda, M., Straka, I., Miková, M., Ježek, M., Filip, R., & Fiurášek, J. (2016) · Physical Review A · doi:10.1103/physreva.93.042321 · Cited by 4
Optimizing nontrivial quantum observables using coherence
Tan, K. C., Choi, S., & Jeong, H. (2019) · New Journal of Physics · doi:10.1088/1367-2630/ab0430 · Cited by 4
User-specified random sampling of quantum channels and its applications
Sim, J. Y., Suzuki, J., Englert, B., & Ng, H. K. (2020) · Physical Review A · doi:10.1103/physreva.101.022307 · Cited by 3
Contexts in Quantum Measurement Theory
Gudder, S. (2019) · Foundations of Physics · doi:10.1007/s10701-019-00235-5 · Cited by 4
Quantifying entanglement preservability of experimental processes
Chen, S.-H., Ng, M.-L., & Li, C. (2021) · Physical Review A · doi:10.1103/physreva.104.032403 · Cited by 3
Coherent information of a quantum channel or its complement is generically positive
Singh, S., & Datta, N. (2022) · Quantum · doi:10.22331/q-2022-08-11-775 · Cited by 5
Carroll, C. J. F., & Braunecker, B. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.245134 · Cited by 4
A unified framework for graph algebras and quantum causal historiesPreprint
Kribs, D. W. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.math/0501087 · Cited by 4
Quantum error correction and generalized numerical rangesPreprint
Li, C.-K., & Poon, Y. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0812.4772 · Cited by 5
Non-completely positive maps: properties and applicationsPreprint
Wood, C. J. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0911.3199 · Cited by 9
Interpolation problems by completely positive mapsPreprint
Li, C.-K., & Poon, Y. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1012.1675 · Cited by 4
Unital q-positive maps on M_2(\C) and a related E_0-semigroup resultPreprint
Jankowski, C. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1005.4404 · Cited by 4
Nuclearity and the C*-algebraic flip
Effros, E. G. (2008) · Springer eBooks · doi:10.1007/3-540-08853-9_13 · Cited by 4
Information Rates Achievable with Algebraic Codes on Quantum Discrete Memoryless ChannelsPreprint
Hamada, M. (2002) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0207113 · Cited by 4
Expressiveness and Learning of Hidden Quantum Markov ModelsPreprint
Adhikary, S., Srinivasan, S., Gordon, G., & Boots, B. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1912.02098 · Cited by 8
Randomized Partial Decoupling Unifies One-Shot Quantum Channel CapacitiesPreprint
Wakakuwa, E., & Nakata, Y. (2020) · arXiv (Cornell University) · Cited by 4
Metadata
- Authors
- Choi, M.-D.
- Affiliations
- University of California, Berkeley (US)
- Corresponding author
- Choi, Man-Duen
- Venue
- Linear Algebra and its Applications
- Publisher
- Elsevier BV
- Published
- 1975-06
- Volume
- 10
- Issue
- 3
- Pages
- 285-290
- ISSN
- 0024-3795 (ISSN-L)
- OpenAlex
- W2116102644
- Cited by
- 2,659
- References
- 12
- Citations by year
- 2026: 122 · 2025: 216 · 2024: 189 · 2023: 205 · 2022: 161 · 2021: 167 · 2020: 132 · 2019: 152 · 2018: 112 · 2017: 98 · 2016: 95 · 2015: 100 · 2014: 93 · 2013: 90 · 2012: 97
- FWCI
- 4.55
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Linear Algebra and its Applications (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Keywords
- complex matrices, matrix algebra, positive linear maps, operator algebras
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-11, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-11 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
