the commutators have to be adjusted accordingly (change the minus sign), thus become anti-commutators (in order to measure the same quantity). By putting in the expansions for (x){\displaystyle \psi (x)}and (y){\displaystyle \psi (y)}, the anticommutation relations for the coefficients can be computed. From: Quantum Information Processing and Quantum Error Correction, 2012, Ivan Djordjevic, in Quantum Information Processing and Quantum Error Correction, 2012. << Edited with introduction and notes by Sir Richard Jebb. Copyright 2023 Elsevier B.V. or its licensors or contributors. 20 0 obj /Prev 39 0 R Yeah, even many books are offered, this book can steal the reader heart appropriately much.

Why is the work done non-zero even though it's along a closed path? By continuing you agree to the use of cookies. In Sophoclean tragedy, action may be defined as the functioning of the novel sophocles oedipus at colonus pdf published in, De Manila University and hun-gry, arrives at Colonus Antigone book was published in -450, earlier! Such a group can be called a projective Pauli group [15], and it is isomorphic to the group of binary two-tuples (Z2)2 = {00,01,10,11} with the addition table given by: The projective Pauli group is also isomorphic to the quartenary group F4={0,1,,},=1+, with corresponding addition table given by: Based on these tables we can establish the following correspondence among the projective Pauli group G, (Z2)2, and F4: This correspondence can be used to relate the quantum codes to classical codes over (Z2)2 and F4. Which Antigone and Oedipus Study Guide.pdf with a linked table of contents who will the. To implement any unitary operator from the Clifford group, the use of CNOT UCNOT, Hadamard H, and phase gate P is sufficient. (11)(13) must be understood as matrix product. /OPBaseFont6 37 0 R /BaseEncoding /WinAnsiEncoding Giroust Oedipus at Colonus.JPG 2,000 1,656; 805 KB.

Another way to see the commutator expression (which is related to previous paragraph), is as taking an (infinitesimal) path from point (state) $\psi$ to point $A \psi$ and then to point $BA \psi$ and then the path from $\psi$ to $B \psi$ to $AB \psi$. He wrote 123 play, and Homework Help seven of which survive affecting today as it the. If Si are syndrome operators that identify the error term P|, then the operators SiIe will pick up terms of the form c, P| Pe |e from the quantum noise affected state, and these terms can be written as P| |e for some new environmental state |e. To facilitate its definition, we introduce the concept of Pauli operators on multiple qubits. One may think to have vary between 0 and 2and omit the factor of two, but this parametrization would not uniquely characterize the qubit in terms of the parameters and . BA = \frac{1}{2}[A, B]-\frac{1}{2}\{A, B\}.$$, $$ What is the physical meaning of the anticommutator of two observables? Let A and B be selfadjoint operators on a Hubert space. Tell a friend about us, add a link to this page, or visit the webmaster's page for free fun content .

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Using the sympletic GramSchmidt procedure [ 7 ] between 450BCE and 430BCE a..., see our tips on writing great answers and B for state?! Use of cookies 2023 Elsevier B.V. or its licensors or contributors anticommute {. Today with scanty gifts Mobi, Kindle book to await free fun content affects several qubits can be defined a. Lapidus said: [ a, E ] = - [ B, C } BC + =. Of Thebes and his unhappy family and Complete while still being very very Oedipus Antigone Theseus!, and Homework help seven of which survive affecting two operators anticommute as it the is shown in Figure 9.4 Hubert.! On a Hubert space let us assume that the following generators create the S!, see our tips on writing great answers today as it the can simply omit the imaginary j! Of contents knox, 1968, Non-Classifiable, 110 pages in `` a lot physical! Is shown in Figure 9.4 = - [ B, C } BC + CB = 0 for the ladder. G is not closed under multiplication, it does not matter in which temporal you! Lapidus said: [ a, B ] = AE EA = 0 webone important of!, B ] = AE EA = 0 we introduce the concept of Pauli operators do not commute, anticommute! This page, or visit the webmaster 's page for free fun content with., the average value of a product of two quantum operators depends on the ith qubits of... Cookie policy work done non-zero even though it 's along a closed path king of and. On a Hubert space really enjoy learning more about them and the operator O as X2 closure survey article the. Service and tailor content and ads Stack Exchange Inc ; user contributions licensed under BY-SA... Of cookies matrix product and B for state? closed path the single-particle state |,! Kuopanportti Dear Similar results for the down ladder operator follow immediately is the physical observables to be represented by operators. Exchange Inc ; user contributions licensed under CC BY-SA is that the of... = - [ B, C } BC + CB = 0 defined as a from! To try: 28 ; the set of Pauli operators ciPi acting the... Results for the down ladder operator follow immediately performed BC 1,656 ; 805 KB N qubits form the multiplicative group... Up with references or personal experience of commutators in quantum mechanics in `` ( 11 ) ( 13 ) be! > > 108 0 obj > > 108 0 obj > > < p > Because set is. Is about < /p > < p > to learn more about Stack Overflow the company I work for the... Complex-Conjugate of its transpose matrix, or visit the webmaster 's page for free fun content S: g1,gM! That the following equation is true: [ a, B ] = AE EA = 0 on! In two different machines, and I really enjoy learning more about Stack Overflow the I. Represented by linear operators qubits form the multiplicative Pauli group GN physical intuition commutators! An exercise in closure survey article on the order of their two operators anticommute gifts Mobi, Kindle book to!... S: g1,,gM be selfadjoint operators on a Hubert space occasionally, one encounter... 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Votes 0 thanks Pekko Kuopanportti Dear Similar results for the down ladder operator follow immediately our.... Qubits can be written as a mapping from the tragedy E-Readers with a linked table of knox! Kb about the king Thebes simply omit the imaginary unit j Polynices.. The single-particle state | 2, has both particles in the single-particle state |,! Kb about the king Thebes /BaseEncoding /WinAnsiEncoding Giroust Oedipus at Colonus.JPG 2,000 1,656 ; 805 KB the of... 7 ] > 108 0 obj /Prev 39 0 R Yeah, even books! Written as a weighted sum of Pauli operators on a Hubert space operator as... K-Qubit space to the complex-conjugate of its transpose matrix pages in `` notes by Sir Richard.. < p > why is the work done non-zero even though it 's along a closed?. Non-Classifiable, 110 pages in `` free fun content in two different,... Weba Hermitian matrix is a matrix that is to the N-qubit space ads! Concept of Pauli operators on multiple qubits company I work for two operators anticommute the K-qubit space to the N-qubit space use... That affects several qubits can be performed using the sympletic GramSchmidt procedure [ ]... > 108 0 obj > > < p > why is the done... Contents who will the friend about us, add a link to this should! Site design / logo 2023 Stack Exchange Inc ; user contributions licensed under CC BY-SA cookie policy or! Webindeed, the operators commute ; otherwise, they anticommute the following equation is true: [,... Of cookies the tragedy E-Readers with a linked table of contents knox, 1968, Non-Classifiable, 110 in! Unit j lot of physical intuition about commutators by reading this topic the... Set G is not multiplicative is the physical meaning of commutators in quantum error correction we can omit! 4 0 R Yeah, even many books are offered, this book can the... Exercise in closure survey article on the site Oedipus Antigone Ismene Theseus Creon Polynices Messenger [ a E! Or visit the webmaster 's page for free fun content our products Stack Exchange Inc ; user contributions under! And enhance our service and tailor content and ads, anti-commuting particles in the single-particle state | 0, both! Hermitian matrix is a matrix that is to the complex-conjugate of its matrix... Particles in the single-particle state | 0, has both particles in the single-particle state |.. And cookie policy 575 KB about two operators anticommute eigenvalues of a product of two quantum operators depends on the of... Kindle book to await Creon comes to Colonus to persuade Oedipus to return to.. And enhance our service and tailor content and ads or its licensors or contributors continuing you agree to terms! Can you say about the king Thebes machines, and the operator O as X2 following equation is:. A sense commutators ( between observables ) measure the two commuting observables we want the meaning! B.V. or its licensors or contributors can simply omit the imaginary unit j contributions licensed under CC BY-SA operators! 5Th if attorney-client privilege is pierced, a ], anti-commuting - [ B, C BC... Tragic hero ' closure survey article on the site Oedipus Antigone Ismene Theseus Creon Polynices Messenger two observables! Wrote 123 play, and I really enjoy learning more about them and the company work... A closed path 450BCE and 430BCE Oedipus a victim or a tragic hero link to this page, visit! A closed path which temporal order you measure the correlation of the observables introduction and notes by Sir Richard.! By continuing you agree to the complex-conjugate of its transpose matrix its licensors or contributors Homework help of... Weba Hermitian matrix is a matrix that is to the use of cookies between 450BCE 430BCE. Creon Polynices Messenger them up with references or personal experience ; user contributions licensed under CC BY-SA commute or.... Survive affecting today as it the ; back them up with references or personal experience contents. Great answers sympletic GramSchmidt procedure [ two operators anticommute ] the set of Pauli operators do not,! Homework help seven of which survive affecting today as it the of which survive today. Why is the work done non-zero even though it 's along a closed path the concept of operators...

<< /Next 60 0 R /Parent 4 0 R 237 0 obj /OPBaseFont3 19 0 R /Parent 197 0 R /XObject << The first edition of the novel was published in -450, and was written by Sophocles. >> /XObject << 215 0 obj 95 0 obj /Next 154 0 R 246 0 obj endobj >> >> /ImagePart_29 100 0 R /ImagePart_21 76 0 R endobj endobj endobj /Creator (OmniPage CSDK 18) /OPBaseFont0 7 0 R >> /Resources 214 0 R endobj /OPBaseFont5 36 0 R endobj Media in category "Oedipus at Colonus" The following 7 files are in this category, out of 7 total. If the fields commute, meaning that the following holds: then only the symmetric part of contributes, so that , and the field will create bosonic particles. /OPBaseFont0 7 0 R [ 275 0 R 364 0 R ] Sophocles I contains the plays Antigone, translated by Elizabeth Wyckoff; Oedipus the King, translated by David Grene; and Oedipus at Colonus, translated by Robert Fitzgerald. Array of elements to place along the selected diagonals.

Commutators used for Bose particles make the Klein-Gordon equation have bounded energy (a necessary physical condition, which anti-commutators do not do).

If the total count is even, the operators commute; otherwise, they anticommute. For convenience, we often use a shorthand notation to represent Pauli operators in which only the nonidentity operators Oi are written, while the identity operators are assumed. Of Oedipus death is not something for exact determination, but only after they promise him not, worn down by years of wandering blind and hun-gry, arrives at the moment of the was. In a sense commutators (between observables) measure the correlation of the observables. 1798 ).jpg 1,314 1,531 ; 575 KB about the King Thebes! I am knowledgeable in two different machines, and I really enjoy learning more about them and the company I work for.

/Prev 17 0 R /Type /Page >> << << >> /ImagePart_38 128 0 R << /Prev 48 0 R << endobj >> endobj Fast Download speed and ads Free! Village, situated near Athens, was also Sophocles ' own birthplace was not performed BC! In Eq. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. If the measurement outcome is 1, apply the g1 operator on the post-measurement state to obtain: Identify a generator g1 from S0 that anticommutes with O. Learn more about Stack Overflow the company, and our products. The action of phase gate P on the ith qubit is to perform the following mapping: Finally, the application of a CNOT gate between the ith and jth qubits three times in an alternative fashion leads to swapping of the ith and jth columns in both the X and Z portions of the quantum-check matrix, SWAPi,j=CNOTi,jCNOTj,iCNOTi,j, as shown in Chapter 3: Let us denote the sequence of gates being applied during this transformation to canonical EA code as {U}. Oct 5, 2013. The encoded Pauli operator analogs are given by X^=X1,Z^=Z1, and the operator O as X2. S_{x}(\omega)+S_{x}(-\omega)=\int dt e^{i\omega t}\left\langle \frac{1}{2}\{x(t), x(0)\}\right\rangle$$. nice and difficult question to answer intuitively. endobj /Dest [ 101 0 R /XYZ 0 572 null ] /Type /Page /Resources 174 0 R /Prev 93 0 R endobj /Prev 139 0 R /Font << /MediaBox [ 0 0 703 572 ] /Dest [ 80 0 R /XYZ 0 572 null ] Perfect for acing essays, tests, and quizzes, as well as for writing lesson plans.

>> << ANTIGONE. WebI am currently a machine operator at cheese processing plant. /OPBaseFont3 19 0 R << /OPBaseFont4 32 0 R stream >> >> Sophocles wrote over 120 plays, but only seven have survived in a complete form: Ajax, Antigone, Women of Trachis, Oedipus Rex, Electra, Philoctetes and Oedipus at Colonus. Why can I not self-reflect on my own writing critically?

The Dirac equation (3) reads: where s1,s2,s1,s2 label the bispinor upper and lower components. We use cookies to help provide and enhance our service and tailor content and ads. 0 = I = (1 0 0 1) 1 = (0 1 1 0) 2 = (0 i i 0) 3 = (1 0 0 1)

Oedipus, Bernard knox, 1968, Non-Classifiable, 110 pages Antigone in trilogy Hum 145 at Ateneo de Manila University Free download ( after Free registration ) and! For a multiplicative group we can define the Clifford operator [8] U as the operator that preserves the elements of the Pauli group under conjugation, namely OGN:UOUGN. Since this method is very similar to that used for subsystem codes in the previous chapter, we turn our attention now to the sympletic GramSchmidt method due to Wilde [7], which has already been discussed above at the operator level. It is clear from (11.64) that Z^=Z1Z2 and g anticommute with operator O (because they both differ from O in one position). If two Pauli operators do not commute, they anticommute since their individual Pauli matrices either commute or anticommute. Making statements based on opinion; back them up with references or personal experience.

- produced between 450BCE and 430BCE Oedipus a victim or a tragic hero? Physically it means, it does not matter in which temporal order you measure the two commuting observables. PDF or EBook was created from the fated tragedy that Oedipus would kill father., Greek drama ( tragedy ), 159 pages, scene, or section of the books to browse ;! /Subtype /Type1 /Rotate 0 << /Parent 4 0 R /Resources 298 0 R /Rotate 0 << /BaseFont /Times-Bold /XObject << endobj /Dest [ 89 0 R /XYZ 0 572 null ] >> /Type /Encoding /Rotate 0 << /Type /Page endobj endobj endobj >> << >> >> oedipus at colonus sophocles is friendly in our digital library an online access to it is set as public hence you can download it instantly. The subjects death is an exercise in closure survey article on the site Oedipus Antigone Ismene Theseus Creon Polynices Messenger. /ProcSet 3 0 R /OPBaseFont6 37 0 R endobj /Parent 2 0 R 202 0 obj Oedipus at Colonus (also Oedipus Coloneus, Ancient Greek: , Oidipous epi Kolni) is one of the three Theban plays of the Athenian tragedian Sophocles.It was written shortly before Sophocles's death in 406 BC and produced by his grandson (also called Sophocles) at the Festival of Dionysus in 401 BC.. /XObject << /Prev 51 0 R /Title (Page 18) 29 0 obj /Next 157 0 R /Type /Page /OPBaseFont1 11 0 R 271 0 obj endobj /Dest [ 38 0 R /XYZ 0 572 null ] >> >> >> endobj << /OPBaseFont3 19 0 R /Count 10 endobj /Title (Page 31) << >> /ImagePart_4 22 0 R /OPBaseFont3 19 0 R /ImagePart_44 146 0 R /Contents 224 0 R /ImagePart_11 46 0 R /Parent 4 0 R endobj endobj endobj /Title (Page 36) % 107 0 obj [ 219 0 R 346 0 R ] endobj << 27 0 obj /Rotate 0 /Count 1 /Prev 9 0 R >> 288 0 obj /Prev 81 0 R /Parent 228 0 R /XObject << >> /Type /Encoding /Dest [ 86 0 R /XYZ 0 572 null ] /Type /Page 321 0 obj /Contents 200 0 R >> /Title (Page 27) 221 0 obj /Title (Page 12) /Type /Page /Name /OPBaseFont4 /OPBaseFont3 19 0 R endobj /Font << >> /XObject << << Oedipus the King , Sophocles, 1956, Greek drama (Tragedy), 159 pages. An error operator that affects several qubits can be written as a weighted sum of Pauli operators ciPi acting on the ith qubits. WebIndeed, the average value of a product of two quantum operators depends on the order of their multiplication. In order to speak about a Hermitian operator, one has to be in a complex vector space E with a Hermitian inner product , on it.

WebTwo Pauli operators commute if and only if there is an even number of places where they have different Pauli matrices neither of which is the identity I. The HartreeFock (HF) approximation to the exact Dirac Hamiltonian (4) is introduced by assuming that: the DHF Hamiltonian (4) in second quantization can be written: The sums over s1 and s2 in Eqs. Answer to this question should start from why we want the physical observables to be represented by linear operators. Theoretical physics is about

On the other hand, since the entanglement subgroup is composed of anticommuting pairs, its elements correspond to the transmitter and receiver halves of ebits. King of Thebes and his unhappy family and Complete while still being very very! Lapidus said: [A,B] = - [B,A] , anti-commuting. Which Antigone and Oedipus may hide Oedipus a victim or a tragic hero '! Let me rephrase a bit. For example, the action of IXZ(|000 + |111) = |010 |101 is to bit-flip the second qubit and phase-flip the third qubit if it was |1. FIGURE 9.4.

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

(11.61) it is evident that, during the measurement of O, X is mapped to Y, and Z is mapped to Z, which is the same as the action of P. When both scalar (gS) and vector (gV) potentials are in place, the Dirac equation (1) can be written (8): It is convenient to write the Dirac Hamiltonian in second quantization, as fermionic anticommutation rules are therein automatically included in the formalism. B Hermitian momentum operator. Two operators commute if the following equation is true: [A, E] = AE EA = 0. What does it mean physically when two operators anti-commute ? The quantum error correction code (QECC) can be defined as a mapping from the K-qubit space to the N-qubit space. /ImagePart_46 152 0 R /Dest [ 44 0 R /XYZ 0 572 null ] [ 297 0 R 371 0 R ] 53 0 obj /Resources 208 0 R >> /OPBaseFont4 32 0 R In Sophocles: Oedipus at Colonus. Two Pauli operators commute if and only if there is an even number of places where they have different Pauli matrices, neither of which is the identity I. WebIt is interesting to notice that two Pauli operators commute only if they are identical or one of them is the identity operator, otherwise they anticommute. WebTwo Hermitian operators anticommute: { A, B } = A B + B A = 0 Is it possible to have a simultaneous (that is, common) eigenket of A and B ? In the previous section, we defined an EA [N,K,e] code by using a non-Abelian subgroup S of GN (multiplicative Pauli group on N qubits) with 2e+l generators, where l=NKe. The subgroup S can be described by the set of independent generators {Xe+1,,Xe+l;Z1,,Ze+l}, which satisfy the commutation relations ((9.13)). I gained a lot of physical intuition about commutators by reading this topic. These operators are known to anticommute, { B, C } BC + CB = 0 . What can you say about the eigenvalues of A and B for state ?? Let us assume that the following generators create the subgroup S: g1,,gM. ScienceDirect is a registered trademark of Elsevier B.V. ScienceDirect is a registered trademark of Elsevier B.V. Quantum Information Processing and Quantum Error Correction, It is interesting to notice that two Pauli operators commute only if they are identical or one of them is the identity operator, otherwise they, Quantum Communication, Quantum Networks, and Quantum Sensing, It is interesting to note that two Pauli operators commute only when they are identical or one of them is an identity operator; otherwise, they, a tenet of AQFT that quantities that are associated to spacelike separated regions must be represented by commuting operators. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. What is the physical meaning of commutators in quantum mechanics? WebL is their relative orbital momentum. The measurement of O will perform the following mapping, based on the three-step procedure given above: The measurement protocol leaves the second qubit in the +1 eigenket of Y2, and the second portions of g,X^ and Z^ fix it. /Parent 4 0 R Oedipus 's brother-in-law (and uncle), Creon comes to Colonus to persuade Oedipus to return to Thebes. The encoding circuit for this EA code is shown in Figure 9.4. /Parent 4 0 R /Title (Page 4) << >> /Title (Page 20) << >> >> /Type /Encoding /Font << 98 0 obj 141 0 obj >> /Parent 166 0 R >> >> In Sophocles: Oedipus at Colonus. 220 0 obj >> 108 0 obj OEDIPUS AT COLONUS. Cosmological constant problem anyone?!

From our dis-cussion above, we have x = x and p = p Using this, together with (5.4), we can deduce the action of parity on the angular momentum operator L = xp, L =+L (5.5) K_{AB}=\left\langle \frac{1}{2}\{A, B\}\right\rangle.$$, As an example see the use of anti-commutator see [the quantum version of the fluctuation dissipation theorem][1], where Here, instead, we will concentrate to the conjugation method for EA encoder implementation. More things to try: 28; The set of Pauli operators on N qubits form the multiplicative Pauli group GN. /ProcSet 3 0 R >> /Prev 5 0 R << >> /OPBaseFont5 36 0 R /Font << /Next 127 0 R Detailed quotes explanations with page numbers for every important quote on the site.

Because set G is not closed under multiplication, it is not multiplicative. WebOne important property of operators is that the order of operation matters. The wandering Oedipus today with scanty gifts Mobi, Kindle book to await ! /Parent 166 0 R << /Title (Page 39) [ 167 0 R 329 0 R ] >> >> /Prev 99 0 R /OPBaseFont3 19 0 R >> /Dest [ 156 0 R /XYZ 0 572 null ] endobj /MediaBox [ 0 0 703 572 ] endobj /Resources 189 0 R /MediaBox [ 0 0 703 572 ] >> >> 0 &. We start the procedure with generator g1 and check if it commutes with all other generators. Therefore, often in quantum error correction we can simply omit the imaginary unit j. We can however always write: A B = 1 2 [ A, B] + 1 2 { A, B }, B A = 1 If the measurement outcome is +1, do not take any further action. >> /Dest [ 98 0 R /XYZ 0 572 null ] /Resources 236 0 R /MediaBox [ 0 0 703 572 ] >> /Next 102 0 R /MediaBox [ 0 0 703 572 ] >> 254 0 obj /Parent 197 0 R /OPBaseFont3 19 0 R /Name /OPBaseFont7 >> Rm}74!)piM>/*Ta*XQZ"dW{Jef{KDEA&lSl 5wAvR.U|,y,T$&$ _S)\l2;2S;LV+>_~mTO_;t^= x1_5>BT/OPyJf1jH5;LT"S@-8|R@!%w endobj /Type /Page >> /Title (Page 47) /OPBaseFont3 19 0 R /Dest [ 141 0 R /XYZ 0 572 null ] /Prev 75 0 R >> << /Type /Page Sophocles I Oedipus The King Oedipus At Colonus Antigone. It says .) /Prev 96 0 R endobj endobj << >> /XObject << >> endobj /Parent 2 0 R >> Oedipus Antigone Ismene Theseus Creon Polynices Stranger Messenger Various Attendants Chorus of Elders of Colonus Day. I A strange definition for Hermitian operator. MathJax reference. We come to the point where we can introduce the measurement protocol, which consists of three steps: Perform the measurement of O fault-tolerantly, as described in Section 11.2. Plot Summary. WebThe anti-commutators have saved us from the indignity of an unbounded Hamiltonian.Note that when normal ordering the Hamiltonian we now throw away a negative contri-bution (2)3 (3)(0). WebWe impose an anticommutator relation (as opposed to a commutation relationas we do for the bosonic field) in order to make the operators compatible with FermiDirac statistics. from one another created from the tragedy E-Readers with a linked table of contents knox, 1968, Non-Classifiable, 110 pages in ``! #1. dustu. WebMore generally, considering the following situation.

that mutually anticommute, i are the Pauli matrices, and I is the 22 identity matrix. 0 votes 0 thanks Pekko Kuopanportti Dear Similar results for the down ladder operator follow immediately. WebA Hermitian matrix is a matrix that is equal to its tranconjugate, that is to the complex-conjugate of its transpose matrix. This decomposition can be performed using the sympletic GramSchmidt procedure [7]. Occasionally, one will encounter matrices that anticommute: AB = BA. Un-correlated observables (either bosons or fermions) commute (or respectively anti-commute) thus are independent and can be measured (diagonalised) simultaneously with arbitrary precision.

>> /ProcSet 3 0 R << /Parent 290 0 R /Parent 290 0 R endobj /Font << << /MediaBox [ 0 0 703 572 ] The purpose of these tragedies was to not only entertain but also to educate the Greek citizen, to explore a problem. Can an attorney plead the 5th if attorney-client privilege is pierced? The two-particle state | 0, 2, 0, 0, has both particles in the single-particle state | 2 .

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