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Practice Problem 38.) Let p= Ex Pk|eb«Xubx| be a density operator; so each |e) is a unit vector and each pk 20 with EA Pk = 1. Prove the following conditions are satisfied: (a) Tr(p) = 1. (b) p is a positive operator; that is, for any state |v), the inner product (v|plv) is a non-negative real number, (v\p|v) > 0.

Practice Problem 38.) Let p= Ex Pk|eb«Xubx| be a density operator; so each |e) is a unit vector and each pk 20 with EA Pk = 1. Prove the following conditions are satisfied: (a) Tr(p) = 1. (b) p is a positive operator; that is, for any state |v), the inner product (v|plv) is a non-negative real number, (v\p|v) > 0.

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Practice Problem 38.) Let p= Ex Pk|eb«Xubx| be a density operator; so each |e) is a unit vector and each pk 20 with EA Pk = 1. Prove the following conditions are satisfied: (a) Tr(p) = 1. (b) p is a positive operator; that is, for any state |v), the inner product (v|p|v) is a non-negative real number, (v|p|v) > 0.
Transcribed Image Text:Practice Problem 38.) Let p= Ex Pk|eb«Xubx| be a density operator; so each |e) is a unit vector and each pk 20 with EA Pk = 1. Prove the following conditions are satisfied: (a) Tr(p) = 1. (b) p is a positive operator; that is, for any state |v), the inner product (v|p|v) is a non-negative real number, (v|p|v) > 0.
1aI Mland Raum Wa can tan mid te of any berof q. Dea ay al mpinga gal miud n ons qutitaa the tle wt mhu they A lart1,. mlud an wn al t of A /-qut) N wh prtatly Tb mamprwaion h ) nal ar alelai wosld be quta tena. Themanalmaim, vry , mprand etud ued operona te ber TN. The ald dey opraica Te maris pran tady da dy ur. Te daty qprar lra puman dtnd Iapply the atury qprr Uon he D whih ha ty opar N TEAM UnG A QUENTS AND TAE FRAMEWORK OF QUAN TUM MECANCS P-la epuatikeal ta. aling Raon 4), tha pratabiliy geaing lagw ly Naken a P enaianamal mbe. Samy ter a the am dapandng imart wtn anty y h eper ter), w s wrta the prtahilty af n gvi wm the p bilon I the yy d tra a TANc) - Sinliari, Ifmma guit with dety pr p-N the protaiky of otaling he cme T onily dalag wth puman, atike arly mdunda; boe,waoder tad a auh m ie shan d abon pain Te datey qperar lr an ate of pamah a as P-AMIONI ass dapun al the nlera tamai ate the n of the pm. pla ply the untary oper U atd a dweribad ia AI wid ge the miud w hady apr No thas the sp dmity operor an be mpd ram the lp dmity qer and the umitay wite kowing e pie dompotien of the dety aprr. Cive hemiudn derbd by the deaty oper pal uuia a, nepiral the protaliliy of sang the sa TEAM UNG MOED STATES AND NERAL QUANTUM GRERATIONS S ass Prmpuing thn ia ld wia ring uy drvatle propeny da nym, al tha mun he dity operaar , and e the ci dmpaie of the daty aprr. I scer wond, ID minu wih te deaty mtianiigataleqalen (araloga the ay pan a dir anty by agetal pham amai).
Transcribed Image Text:1aI Mland Raum Wa can tan mid te of any berof q. Dea ay al mpinga gal miud n ons qutitaa the tle wt mhu they A lart1,. mlud an wn al t of A /-qut) N wh prtatly Tb mamprwaion h ) nal ar alelai wosld be quta tena. Themanalmaim, vry , mprand etud ued operona te ber TN. The ald dey opraica Te maris pran tady da dy ur. Te daty qprar lra puman dtnd Iapply the atury qprr Uon he D whih ha ty opar N TEAM UnG A QUENTS AND TAE FRAMEWORK OF QUAN TUM MECANCS P-la epuatikeal ta. aling Raon 4), tha pratabiliy geaing lagw ly Naken a P enaianamal mbe. Samy ter a the am dapandng imart wtn anty y h eper ter), w s wrta the prtahilty af n gvi wm the p bilon I the yy d tra a TANc) - Sinliari, Ifmma guit with dety pr p-N the protaiky of otaling he cme T onily dalag wth puman, atike arly mdunda; boe,waoder tad a auh m ie shan d abon pain Te datey qperar lr an ate of pamah a as P-AMIONI ass dapun al the nlera tamai ate the n of the pm. pla ply the untary oper U atd a dweribad ia AI wid ge the miud w hady apr No thas the sp dmity operor an be mpd ram the lp dmity qer and the umitay wite kowing e pie dompotien of the dety aprr. Cive hemiudn derbd by the deaty oper pal uuia a, nepiral the protaliliy of sang the sa TEAM UNG MOED STATES AND NERAL QUANTUM GRERATIONS S ass Prmpuing thn ia ld wia ring uy drvatle propeny da nym, al tha mun he dity operaar , and e the ci dmpaie of the daty aprr. I scer wond, ID minu wih te deaty mtianiigataleqalen (araloga the ay pan a dir anty by agetal pham amai).
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