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 1,401–1,500 of 2,678
Timelike correlations and quantum tensor product structure
Sen, S., Lobo, E. P., Patra, R. K., Naik, S. G., Bhowmik, A. D., Alimuddin, M., & Banik, M. (2022) · Physical Review A · doi:10.1103/physreva.106.062406 · Cited by 6
Convergence criterion for quantum relative entropy and its use
Широков, М. Е. (2022) · Sbornik Mathematics · doi:10.4213/sm9794e · Cited by 6
Noisy Werner-Holevo channel and its properties
Roofeh, S., & Karimipour, V. (2024) · Physical Review A · doi:10.1103/physreva.109.052620 · Cited by 8
Extracting dynamical maps of non-Markovian open quantum systems
Strachan, D. J., Purkayastha, A., & Clark, S. R. L. (2024) · The Journal of Chemical Physics · doi:10.1063/5.0228428 · Cited by 6
Exploring non-Markovianity in ergodic channels: Measuring memory retention through ergotropy
Basu, R., Chakraborty, A., Badhani, H., Alimuddin, M., & Bhattacharya, S. (2025) · Physical Review A · doi:10.1103/physreva.111.032416 · Cited by 8
Theory of Free Fermions Dynamics under Partial Postselected Monitoring
Leung, C. Y., Meidan, D., & Romito, A. (2025) · Physical Review X · doi:10.1103/physrevx.15.021020 · Cited by 6
Optimal indecomposable witnesses without extremality or the spanning property
Ha, K.-C., & Yu, H. (2012) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/45/39/395307 · Cited by 6
Cohen, S. M. (2014) · Journal of Mathematical Physics · doi:10.1063/1.4883400 · Cited by 6
Approximate broadcasting of quantum correlations
Xie, W. D., Fang, K., Wang, X., & Duan, R. (2017) · Physical Review A · doi:10.1103/physreva.96.022302 · Cited by 6
Operator valued frames and applications to quantum channels
Poumai, K. T., Kaushik, S. K., & Djordjević, S. V. (2017) · International Conference on Sampling Theory and Applications · doi:10.1109/sampta.2017.8024361 · Cited by 7
Distinguishing between statistical and systematic errors in quantum process tomography
Wölk, S., Sriarunothai, T., Giri, G. S., & Wunderlich, C. (2018) · New Journal of Physics · doi:10.1088/1367-2630/aaf5f2 · Cited by 7
Entanglement properties of a measurement-based entanglement distillation experiment
Jeng, H., Tserkis, S., Haw, J. Y., Chrzanowski, H. M., Janoušek, J., Ralph, T. C., Lam, P. K., & Assad, S. M. (2019) · Physical Review A · doi:10.1103/physreva.99.042304 · Cited by 6
Symmetry-Like Relation of Relative Entropy Measure of Quantum Coherence
Zhang, C., Guo, Z., & Cao, H. (2020) · Entropy · doi:10.3390/e22030297 · Cited by 6
Higher rank matricial ranges and hybrid quantum error correction
Cao, N., Kribs, D. W., Li, C.-K., Nelson, M. I., Poon, Y., & Zeng, B. (2020) · Linear and Multilinear Algebra · doi:10.1080/03081087.2020.1748852 · Cited by 10
On characteristic forms of positive vector bundles, mixed discriminants, and pushforward identities
Finski, S. (2022) · Journal of the London Mathematical Society · doi:10.1112/jlms.12605 · Cited by 6
Variational certification of quantum devices
Kundu, A., & Miszczak, J. A. (2022) · Quantum Science and Technology · doi:10.1088/2058-9565/ac8572 · Cited by 6
Tensor Products of Quantum Mappings
Filippov, S. N. (2020) · Journal of Mathematical Sciences · doi:10.1007/s10958-020-05146-9 · Cited by 6
Interpolating between Positive and Completely Positive Maps: A New Hierarchy of Entangled States
Siudzińska, K., Chakraborty, S., & Chruściński, D. (2021) · Entropy · doi:10.3390/e23050625 · Cited by 6
Quantum and classical dynamical semigroups of superchannels and semicausal channels
Hasenöhrl, M., & Caro, M. C. (2022) · Journal of Mathematical Physics · doi:10.1063/5.0070635 · Cited by 6
Maximal Gap Between Local and Global Distinguishability of Bipartite Quantum States
Corrêa, W. H. G., Lami, L., & Palazuelos, C. (2022) · IEEE Transactions on Information Theory · doi:10.1109/tit.2022.3186428 · Cited by 5
Path-entangling evolution and quantum gravitational interaction
Matsumura, A. (2022) · Physical Review A · doi:10.1103/physreva.105.042425 · Cited by 6
Semantics of quantum programming languages: Classical control, quantum control
Valiron, B. (2022) · Journal of Logical and Algebraic Methods in Programming · doi:10.1016/j.jlamp.2022.100790 · Cited by 6
Select Topics in Open Quantum Systems
Krishna, M., Solanki, P., & Vinjanampathy, S. (2022) · Journal of the Indian Institute of Science · doi:10.1007/s41745-022-00338-5 · Cited by 6
Bounds on the breaking time for entanglement-breaking channels
Sakuldee, F., & Rudnicki, Ł. (2023) · Physical Review A · doi:10.1103/physreva.107.022430 · Cited by 6
Dynamical signatures of the Liouvillian flat band
Liu, Y.-G., & Chen, S. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.134307 · Cited by 6
Unraveling-paired dynamical maps recover the input of quantum channels
Donvil, B., & Muratore-Ginanneschi, P. (2023) · New Journal of Physics · doi:10.1088/1367-2630/acd4dc · Cited by 6
Physical realization of realignment criteria using the structural physical approximation
Aggarwal, S., Kumari, A., & Adhikari, S. (2023) · Physical Review A · doi:10.1103/physreva.108.012422 · Cited by 6
A Survey of Universal Quantum von Neumann Architecture
Liu, Y., Wang, K., Liu, Y., & Wang, D. (2023) · Entropy · doi:10.3390/e25081187 · Cited by 5
Measurement sharpness and disturbance tradeoff
Saberian, N., Akhtarshenas, S. J., & Shahbeigi, F. (2024) · Physical Review A · doi:10.1103/physreva.109.012201 · Cited by 6
Stabilizer Formalism for Operator Algebra Quantum Error Correction
Dauphinais, G., Kribs, D. W., & Vasmer, M. (2024) · Quantum · doi:10.22331/q-2024-02-21-1261 · Cited by 6
Complete positivity violation of the reduced dynamics in higher-order quantum adiabatic elimination
Tokieda, M., Elouard, C., Sarlette, A., et al. (2024) · Physical Review A · doi:10.1103/physreva.109.062206 · Cited by 6
Understanding and Generalizing Unique Decompositions of Generators of Dynamical Semigroups
Ende, F. V. (2024) · Open Systems & Information Dynamics · doi:10.1142/s1230161224500070 · Cited by 7
Quantum thermodynamics of the spin-boson model using the principle of minimal dissipation
Gatto, S., Colla, A., Breuer, H., & Thoss, M. (2024) · Physical Review A · doi:10.1103/physreva.110.032210 · Cited by 7
Delocalization of skin steady states
Feng, X., & Chen, S. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.144305 · Cited by 6
Observational entropy with general quantum priors
Bai, G., Šafránek, D., Schindler, J., Buscemi, F., & Scarani, V. (2024) · Quantum · doi:10.22331/q-2024-11-14-1524 · Cited by 6
Role of interference in quantum cloning
Roubert, B., & Braun, D. (2008) · Physical Review A · doi:10.1103/physreva.78.042311 · Cited by 6
Stability of positive linear switched systems on ordered Banach spaces
Doan, T. S., Kalauch, A., Klose, M., et al. (2014) · Systems & Control Letters · doi:10.1016/j.sysconle.2014.10.004 · Cited by 6
A Quantum Representation for Involution Groups
Crowder, T. (2011) · Electronic Notes in Theoretical Computer Science · doi:10.1016/j.entcs.2011.09.019 · Cited by 6
Zhang, J., Piani, M., & Caves, C. M. (2012) · Quantum Information Processing · doi:10.1007/s11128-012-0500-x · Cited by 6
Constructing all entanglement witnesses from density matrices
Wang, B.-H., & Long, D. (2011) · Physical Review A · doi:10.1103/physreva.84.014303 · Cited by 6
Completely positive interpolations of compact, trace-class and Schatten-p class operators
Hsu, M., Kuo, D. L.-W., & Tsai, M.-C. (2014) · Journal of Functional Analysis · doi:10.1016/j.jfa.2014.05.013 · Cited by 6
Unital Positive Maps and Quantum States
Asorey, M., Kossakowski, A., Marmo, G., et al. (2008) · Open Systems & Information Dynamics · doi:10.1142/s1230161208000110 · Cited by 6
Some Remarks on the Role of Minimal Length of Positive Maps in Constructing Entanglement Witnesses
Jamiołkowski, A. (2004) · Open Systems & Information Dynamics · doi:10.1007/s11080-004-6629-z · Cited by 6
Spectral conditions for positive maps and entanglement witnesses
Chruściński, D., & Kossakowski, A. (2011) · Journal of Physics Conference Series · doi:10.1088/1742-6596/284/1/012017 · Cited by 6
Existence and construction of a quantum channel with given inputs and outputs
Guo, Z., & Cao, H. (2012) · Chinese Science Bulletin · doi:10.1007/s11434-012-5506-3 · Cited by 6
Singal, T. (2016) · Physical Review A · doi:10.1103/physreva.93.030301 · Cited by 6
Rational Inner Functions on a Square-Matrix Polyball
Grinshpan, A., Kaliuzhnyi-Verbovetskyi, D. S., Vinnikov, V., et al. (2017) · Association for Women in Mathematics series · doi:10.1007/978-3-319-51593-9_10 · Cited by 6
Representation of superoperators in double phase space
Saraceno, M., & de Almeida, A. M. O. (2016) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/49/14/145302 · Cited by 6
Understanding Equipartition and Thermalization from Decoupling
Hutter, A. (2011) · Cited by 6
Appearance of causality in process matrices when performing fixed-basis measurements for two parties
Baumann, V., & Brukner, Č. (2016) · Physical Review A · doi:10.1103/physreva.93.062324 · Cited by 6
Algorithmic complexity of quantum capacity
Oskouei, S. K., & Mancini, S. (2018) · Quantum Information Processing · doi:10.1007/s11128-018-1859-0 · Cited by 6
Infinite-Dimensionality in Quantum Foundations: W*-algebras as Presheaves over Matrix Algebras
Rennela, M., Staton, S., & Furber, R. (2017) · Electronic Proceedings in Theoretical Computer Science · doi:10.4204/eptcs.236.11 · Cited by 6
Direct quantum process tomography with coupling-deformed pointer observables
Zhang, Y.-X., Zhu, X., Wu, S., & Chen, Z. (2017) · Annals of Physics · doi:10.1016/j.aop.2016.12.034 · Cited by 7
Entropy exchange for infinite-dimensional systems
Duan, Z., & Hou, J. (2017) · Scientific Reports · doi:10.1038/srep41692 · Cited by 6
Channel discrimination power of bipartite quantum states
Caiaffa, M., & Piani, M. (2018) · Physical Review A · doi:10.1103/physreva.97.032334 · Cited by 7
Approximating quantum channels by completely positive maps with small Kraus rank
Lancien, C., & Winter, A. (2024) · Quantum · doi:10.22331/q-2024-04-30-1320 · Cited by 6
Chruściński, D., Marciniak, M., & Rutkowski, A. (2018) · Acta Mathematica Vietnamica · doi:10.1007/s40306-018-0272-1 · Cited by 6
Sinkhorn–Knopp theorem for rectangular positive maps
Cariello, D. (2018) · Linear and Multilinear Algebra · doi:10.1080/03081087.2018.1491524 · Cited by 6
Factorizable Maps and Traces on the Universal Free Product of Matrix Algebras
Musat, M., & Rørdam, M. (2019) · International Mathematics Research Notices · doi:10.1093/imrn/rnz312 · Cited by 6
Geometry on the manifold of Gaussian quantum channels
Siudzińska, K., Luoma, K., & Strunz, W. T. (2019) · Physical Review A · doi:10.1103/physreva.100.062308 · Cited by 6
Modeling Quantum Devices and the Reconstruction of Physics in Practical Systems
Ren, H., & Li, Y. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.140405 · Cited by 6
Entangling capacities and the geometry of quantum operations
Kao, J.-Y., & Chou, C.-H. (2020) · Scientific Reports · doi:10.1038/s41598-020-72881-z · Cited by 6
Tensor network approach to thermalization in open quantum many-body systems
Nakano, H., Shirai, T., & Mori, T. (2021) · Physical review. E · doi:10.1103/physreve.103.l040102 · Cited by 6
Lindblad Dynamics and Disentanglement in Multi-Mode Bosonic Systems
Kiselev, A. D., Ali, R., & Rybin, A. V. (2021) · Entropy · doi:10.3390/e23111409 · Cited by 6
Sample-Optimal Quantum Process Tomography with non-adaptive Incoherent Measurements
Oufkir, A. (2023) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit54713.2023.10206538 · Cited by 12
Monotone metric tensors in quantum information geometry
Ciaglia, F. M., Cosmo, F. D., Nocera, F. D., & Vitale, P. (2023) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887824400048 · Cited by 10
A class of generalized positive linear maps on matrix algebras
Li, X., & Wu, W. (2013) · Linear Algebra and its Applications · doi:10.1016/j.laa.2013.08.029 · Cited by 6
Generalizations of 2-Dimensional Diagonal Quantum Channels with Constant Frobenius Norm
Sergeev, I. (2019) · Reports on Mathematical Physics · doi:10.1016/s0034-4877(19)30055-2 · Cited by 6
A no-go theorem for superpositions of causal orders
Costa, F. (2022) · Quantum · doi:10.22331/q-2022-03-01-663 · Cited by 6
BLOOMFIELD-WATSON-KNOTT TYPE INEQUALITIES FOR EIGENVALUES
Andô, T. (2001) · Taiwanese Journal of Mathematics · doi:10.11650/tjm.5.2001.1237 · Cited by 6
A Hierarchy of Quantum Semantics
Perdrix, S. (2008) · Electronic Notes in Theoretical Computer Science · doi:10.1016/j.entcs.2008.10.028 · Cited by 6
BLOOMFIELD-WATSON-KNOTT TYPE INEQUALITIES FOR EIGENVALUES
Ando, T. (2001) · Taiwanese Journal of Mathematics · doi:10.11650/twjm/1500574942 · Cited by 6
SU(2)-Irreducibly covariant and EPOSIC channelsPreprint
Nuwairan, M. A. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1306.5321 · Cited by 6
Abstract Interpretation Techniques for Quantum Computation
Jorrand, P., & Perdrix, S. (2009) · Cambridge University Press eBooks · doi:10.1017/cbo9781139193313.007 · Cited by 13
Criteria and new classes of k-positive mapsPreprint
Hou, J., Li, C.-K., Poon, Y., et al. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1211.0386 · Cited by 6
On Positive Maps, Entanglement and Quantization
Majewski, W. A. (2004) · Open Systems & Information Dynamics · doi:10.1023/b:opsy.0000024754.43298.95 · Cited by 6
Quaternions and Quantum Theory
Graydon, M. A. (2011) · UWSpace (University of Waterloo) · Cited by 6
Separable states and the SPA of a positive mapPreprint
Størmer, E. (2012) · arXiv (Cornell University) · Cited by 6
Performance of stochastic clocks in the Alternate Ticks GamePreprint
Stupar, S., Klumpp, C., Renner, R., et al. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1806.08812 · Cited by 6
Li, C.-K., Lyles, S., & Poon, Y. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1905.10228 · Cited by 6
Quantum Interactive Proofs with Short Messages
Beigi, S., Shor, P. W., & Watrousw, J. (2011) · doi:10.21236/ada585814 · Cited by 6
MAPPING CONES ARE OPERATOR SYSTEMSPreprint
Johnston, N., & Størmer, E. (2016) · Cited by 6
Complete positivity of the map from a basis to its dual basisPreprint
Paulsen, V. I., & Shultz, F. (2013) · Cited by 6
Contextuality and the fundamental theorems of quantum mechanics
Döring, A., & Frembs, M. (2022) · Journal of Mathematical Physics · doi:10.1063/5.0012855 · Cited by 14
Topology of Discrete Quantum Feedback Control
Nakagawa, M., & Ueda, M. (2025) · Physical Review X · doi:10.1103/physrevx.15.021016 · Cited by 10
Quantifying magic resource for quantum channels via channel-state duality
Li, X., Luo, S., & Zhang, Z. (2025) · Physical Review A · doi:10.1103/physreva.111.052420 · Cited by 5
Investigating Non-Markovian Effects on Quantum Dynamics in Open Quantum Systems
Ivanchenko, M., Walters, P., & Wang, F. (2025) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.4c01632 · Cited by 5
Topological modes in monitored quantum dynamics
Pan, H., Shapourian, H., & Jian, C. (2025) · Physical review. B./Physical review. B · doi:10.1103/r8mr-zbx1 · Cited by 5
Thermalization in Open Many-Body Systems and KMS Detailed Balance
Scandi, M., & Alhambra, A. M. (2025) · Physical Review X · doi:10.1103/sfp3-3sqf · Cited by 8
Chen, C., Zhao, Q., Zhou, M., Niyato, D. T., He, Z., & Situ, H. (2026) · npj Quantum Information · doi:10.1038/s41534-026-01188-0 · Cited by 7
Storage and retrieval of von Neumann measurements
Lewandowska, P., Kukulski, R., Pawela, Ł., & Puchała, Z. (2022) · Physical Review A · doi:10.1103/physreva.106.052423 · Cited by 7
Faithfulness and Sensitivity for Ancilla-Assisted Process Tomography
Lie, S. H., & Jeong, H. (2023) · Physical Review Letters · doi:10.1103/physrevlett.130.020802 · Cited by 5
All Incompatible Measurements on Qubits Lead to Multiparticle Bell Nonlocality
Plávala, M., Gühne, O., & Quintino, M. T. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.200201 · Cited by 6
Machine learning of reduced quantum channels on noisy intermediate-scale quantum devices
Cemin, G., Cech, M., Weiss, E., Sołtan, S., Braun, D., Lesanovsky, I., & Carollo, F. (2024) · Physical Review A · doi:10.1103/physreva.110.052418 · Cited by 10
Hiesmayr, B. C., Popp, C., & Sutter, T. C. (2025) · International Journal of Quantum Information · doi:10.1142/s0219749925300037 · Cited by 18
Hryniuk, D. A., & Szymańska, M. H. (2024) · Quantum · doi:10.22331/q-2024-09-17-1475 · Cited by 8
Exploring the non-Markovian dynamics in depolarizing maps
Abu-Nada, A., Banerjee, S., & Sabale, V. B. (2024) · Physical Review A · doi:10.1103/physreva.110.052209 · Cited by 5
Emergent geometry from quantum probability
Ahmad, S. A., & Klinger, M. S. (2025) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.111.105015 · Cited by 17
Scheme to Detect the Strong-to-Weak Symmetry Breaking via Randomized Measurements
Sun, N. G., Zhang, P., & Feng, L. (2025) · Physical Review Letters · doi:10.1103/7p5x-7yqb · Cited by 8
Geometry of Entanglement Witnesses Parametrized by SO (3) Group
Chruściński, D., & Wudarski, F. A. (2012) · Open Systems & Information Dynamics · doi:10.1142/s1230161212500205 · Cited by 5
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
