Differentiate between Local and Global UnitariesIf all quantum gates must be unitary, what about...

What is the most triangles you can make from a capital "H" and 3 straight lines?

Indirectly access environment variable

Can making a creature unable to attack after it has been assigned as an attacker remove it from combat?

Book where aliens are selecting humans for food consumption

Avoiding morning and evening handshakes

Why do no American passenger airlines still operate dedicated cargo flights?

Can I become debt free or should I file for bankruptcy? How do I manage my debt and finances?

Why Normality assumption in linear regression

Pronunciation of umlaut vowels in the history of German

One Half of Ten; A Riddle

Why are the books in the Game of Thrones citadel library shelved spine inwards?

Injecting creativity into a cookbook

Why do stocks necessarily drop during a recession?

Why did other German political parties disband so fast when Hitler was appointed chancellor?

Program that converts a number to a letter of the alphabet

How much mayhem could I cause as a sentient fish?

Intern applicant asking for compensation equivalent to that of permanent employee

Can an insurance company drop you after receiving a bill and refusing to pay?

How to deal with an incendiary email that was recalled

In Linux what happens if 1000 files in a directory are moved to another location while another 300 files were added to the source directory?

Caruana vs Carlsen game 10 (WCC) why not 18...Nxb6?

Difference between `vector<int> v;` and `vector<int> v = vector<int>();`

Which password policy is more secure: one password of length 9 vs. two passwords each of length 8?

My cat mixes up the floors in my building. How can I help him?



Differentiate between Local and Global Unitaries


If all quantum gates must be unitary, what about measurement?Why are quantum gates unitary and not special unitary?What do they mean by “qubit can't be copied”?Solving a circuit implementing a two-level unitary operationMatrix representation and CX gateHow to properly write the action of a quantum gate implementing an operator $U$ on the superposition of its eigenvectors?Extending a square matrix to a unitary matrixDecomposition of a unitary matrixGrover operator as a rotation matrixIs it correct to say that we need controlled gates because unitary matrices are reversible?













3












$begingroup$


Just like we have the PPT, NPT criteria for checking if states can be written in Tensor form or not, is there any criteria, given the matrix of a unitary acting on 2 qubits, to check if it is local or global (can be factored or not)?






mathematics matrix-representation unitarity







share|improve this question









$endgroup$

















    3












    $begingroup$


    Just like we have the PPT, NPT criteria for checking if states can be written in Tensor form or not, is there any criteria, given the matrix of a unitary acting on 2 qubits, to check if it is local or global (can be factored or not)?






    mathematics matrix-representation unitarity







    share|improve this question









    $endgroup$















      3












      3








      3





      $begingroup$


      Just like we have the PPT, NPT criteria for checking if states can be written in Tensor form or not, is there any criteria, given the matrix of a unitary acting on 2 qubits, to check if it is local or global (can be factored or not)?






      mathematics matrix-representation unitarity







      share|improve this question









      $endgroup$




      Just like we have the PPT, NPT criteria for checking if states can be written in Tensor form or not, is there any criteria, given the matrix of a unitary acting on 2 qubits, to check if it is local or global (can be factored or not)?






      mathematics matrix-representation unitarity




      mathematics matrix-representation unitarity






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 5 hours ago









      Mahathi VempatiMahathi Vempati

      4638




      4638






















          1 Answer
          1






          active

          oldest

          votes


















          2












          $begingroup$

          This is actually a much easier problem. In the case of states, you're trying to use the PPT criterion, or others, to distinguish if $rho$ can be written in the form
          $$
          rho=sum_ip_isigma^A_iotimessigma^B_i,
          $$
          where $sum_ip_i=1$ and the $sigma^A_i$ and $sigma^B_i$ are valid states on single sites. The difficulty actually comes from the freedom that the summation over $i$ provides.



          In the case of unitaries (or more general operations), you're only trying to ascertain if $U$ can be written in the form
          $$
          U=U^Aotimes U^B
          $$
          or not. This is something that you can do very mechanically. For example, if we make matrices
          $$
          sum_{k,l}U_{ik,jl}|kranglelangle l|,
          $$
          then each of these ought to be of the form $U^A_{ij}U^B$, in other words, the same up to a constant. If they're not, it's not of tensor product form.






          share|improve this answer









          $endgroup$













            Your Answer





            StackExchange.ifUsing("editor", function () {
            return StackExchange.using("mathjaxEditing", function () {
            StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
            StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
            });
            });
            }, "mathjax-editing");

            StackExchange.ready(function() {
            var channelOptions = {
            tags: "".split(" "),
            id: "694"
            };
            initTagRenderer("".split(" "), "".split(" "), channelOptions);

            StackExchange.using("externalEditor", function() {
            // Have to fire editor after snippets, if snippets enabled
            if (StackExchange.settings.snippets.snippetsEnabled) {
            StackExchange.using("snippets", function() {
            createEditor();
            });
            }
            else {
            createEditor();
            }
            });

            function createEditor() {
            StackExchange.prepareEditor({
            heartbeatType: 'answer',
            autoActivateHeartbeat: false,
            convertImagesToLinks: false,
            noModals: true,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: null,
            bindNavPrevention: true,
            postfix: "",
            imageUploader: {
            brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
            contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
            allowUrls: true
            },
            noCode: true, onDemand: true,
            discardSelector: ".discard-answer"
            ,immediatelyShowMarkdownHelp:true
            });


            }
            });














            draft saved

            draft discarded


















            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fquantumcomputing.stackexchange.com%2fquestions%2f5580%2fdifferentiate-between-local-and-global-unitaries%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown

























            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            2












            $begingroup$

            This is actually a much easier problem. In the case of states, you're trying to use the PPT criterion, or others, to distinguish if $rho$ can be written in the form
            $$
            rho=sum_ip_isigma^A_iotimessigma^B_i,
            $$
            where $sum_ip_i=1$ and the $sigma^A_i$ and $sigma^B_i$ are valid states on single sites. The difficulty actually comes from the freedom that the summation over $i$ provides.



            In the case of unitaries (or more general operations), you're only trying to ascertain if $U$ can be written in the form
            $$
            U=U^Aotimes U^B
            $$
            or not. This is something that you can do very mechanically. For example, if we make matrices
            $$
            sum_{k,l}U_{ik,jl}|kranglelangle l|,
            $$
            then each of these ought to be of the form $U^A_{ij}U^B$, in other words, the same up to a constant. If they're not, it's not of tensor product form.






            share|improve this answer









            $endgroup$


















              2












              $begingroup$

              This is actually a much easier problem. In the case of states, you're trying to use the PPT criterion, or others, to distinguish if $rho$ can be written in the form
              $$
              rho=sum_ip_isigma^A_iotimessigma^B_i,
              $$
              where $sum_ip_i=1$ and the $sigma^A_i$ and $sigma^B_i$ are valid states on single sites. The difficulty actually comes from the freedom that the summation over $i$ provides.



              In the case of unitaries (or more general operations), you're only trying to ascertain if $U$ can be written in the form
              $$
              U=U^Aotimes U^B
              $$
              or not. This is something that you can do very mechanically. For example, if we make matrices
              $$
              sum_{k,l}U_{ik,jl}|kranglelangle l|,
              $$
              then each of these ought to be of the form $U^A_{ij}U^B$, in other words, the same up to a constant. If they're not, it's not of tensor product form.






              share|improve this answer









              $endgroup$
















                2












                2








                2





                $begingroup$

                This is actually a much easier problem. In the case of states, you're trying to use the PPT criterion, or others, to distinguish if $rho$ can be written in the form
                $$
                rho=sum_ip_isigma^A_iotimessigma^B_i,
                $$
                where $sum_ip_i=1$ and the $sigma^A_i$ and $sigma^B_i$ are valid states on single sites. The difficulty actually comes from the freedom that the summation over $i$ provides.



                In the case of unitaries (or more general operations), you're only trying to ascertain if $U$ can be written in the form
                $$
                U=U^Aotimes U^B
                $$
                or not. This is something that you can do very mechanically. For example, if we make matrices
                $$
                sum_{k,l}U_{ik,jl}|kranglelangle l|,
                $$
                then each of these ought to be of the form $U^A_{ij}U^B$, in other words, the same up to a constant. If they're not, it's not of tensor product form.






                share|improve this answer









                $endgroup$



                This is actually a much easier problem. In the case of states, you're trying to use the PPT criterion, or others, to distinguish if $rho$ can be written in the form
                $$
                rho=sum_ip_isigma^A_iotimessigma^B_i,
                $$
                where $sum_ip_i=1$ and the $sigma^A_i$ and $sigma^B_i$ are valid states on single sites. The difficulty actually comes from the freedom that the summation over $i$ provides.



                In the case of unitaries (or more general operations), you're only trying to ascertain if $U$ can be written in the form
                $$
                U=U^Aotimes U^B
                $$
                or not. This is something that you can do very mechanically. For example, if we make matrices
                $$
                sum_{k,l}U_{ik,jl}|kranglelangle l|,
                $$
                then each of these ought to be of the form $U^A_{ij}U^B$, in other words, the same up to a constant. If they're not, it's not of tensor product form.







                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered 3 hours ago









                DaftWullieDaftWullie

                14.2k1540




                14.2k1540






























                    draft saved

                    draft discarded




















































                    Thanks for contributing an answer to Quantum Computing Stack Exchange!


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid …



                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.


                    Use MathJax to format equations. MathJax reference.


                    To learn more, see our tips on writing great answers.




                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function () {
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fquantumcomputing.stackexchange.com%2fquestions%2f5580%2fdifferentiate-between-local-and-global-unitaries%23new-answer', 'question_page');
                    }
                    );

                    Post as a guest















                    Required, but never shown





















































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown

































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown







                    -

                    Popular posts from this blog

                    Can't compile dgruyter and caption packagesLaTeX templates/packages for writing a patent specificationLatex...

                    Image
                    Why does Arabsat 6A need a Falcon Heavy to launch Etiquette around loan refinance - decision is going to cost first broker a lot of money What is the PIE reconstruction for word-initial alpha with rough breathing? Is "remove commented out code" correct English? Why do I get two different answers for this counting problem? Blender 2.8 I can't see vertices, edges or faces in edit mode Where does SFDX store details about scratch orgs? 1960's book about a plague that kills all white people How can saying a song's name be a copyright violation? UK: Is there precedent for the governments e-petition site changing the ...
                    Read more

                    Schneeberg (Smreczany) Bibliografia | Menu...

                    Image
                    Szczyty w Niemczech paśmieSmreczanyn.p.m.Ochrza Schneeberg Państwo   Niemcy Położenie Bawaria Pasmo Fichtelgebirge Wysokość 1 051 m n.p.m. Położenie na mapie Bawarii Schneeberg Położenie na mapie Niemiec Schneeberg 50°03′N   11°51′E / 50,050000   11,850000 Multimedia w Wikimedia Commons Schneeberg – szczyt w paśmie Smreczany o wysokości 1051 m n.p.m., na zboczach którego znajdują się źródła rzeki Ochrza. Bibliografia | Rainer H. Schmeisser: Der Schneeberg, Beiträge zur Geschichts- und Landeskunde des Fichtelgebirges Nr. 1, Regensburg 1979 This page is only for reference, If you need detailed information, please check here
                    Read more

                    Hans Bellmer Spis treści Życiorys | Upamiętnienie | Przypisy | Bibliografia | Linki zewnętrzne |...

                    Image
                    Ludzie związani z III Liceum Ogólnokształcącym im. Adama Mickiewicza w KatowicachNiemieccy rzeźbiarzeNiemieccy malarze współcześniNiemieccy graficyLudzie urodzeni w KatowicachUrodzeni w 1902Zmarli w 1975 13 marca1902Katowicach23 lutego1975Paryżumalarzrzeźbiarzgrafikul. A. Mickiewiczaul. T. KościuszkiWyższej Szkole TechnicznejinstalacjiPaula EluardaBerlinie„tableaux vivants”NiemczechnazistówzdegenerowanąBerlinsurrealistówII wojnie światowejCamp des MillesAix-en-ProvenceParyżuUnicę ZürnPère-Lachaiseul. T. KościuszkiDział Grafiki im. Pawła Stellera Muzeum Historii Katowic2008Muzeum Historii KatowicNatalia KruszynaBerlinie Tablica pamiątkowa z 2008 roku na domu, w którym mieszkał artysta przy ul. T. Kościuszki 47 w Katowicach (2017) Grób Bellmera na cmentarzu Père-Lachaise Tablica pamiątkowa przy Ehrenfelsstraße 8a w Berlinie Budynek, w którym mieszkał artysta przy ul. T. Kościuszki 47 w Katowicach (2017) Hans Bellmer (ur. 13 marca 1902 w Katowicach [1] , zm. 23 lut...
                    Read more