| Topic: |
Science > Physics |
| User: |
"David McAnally" |
| Date: |
19 Feb 2006 08:32:39 AM |
| Object: |
Trace of product of density operators |
Does anybody know of a physical interpretation of the trace of the product
of two density operators in quantum mechanics (i.e. a physical
interpretation of the trace of the product of two self-adjoint operators,
each with trace 1, in quantum mechanics)?
If one of the density operators represents a pure state, then the trace of
the product has the interpretation of a probability (suppose that \rho_1 =
|i><i| - let A be a physical observable with with a as a nondegenerate
eigenvalue, with corresponding eigenvector |i> (so that A|i> = a|i>), and
let the system be in the state \rho_2, then tr(\rho_1 \rho_2) is the
probability that a is returned as the value when A is measured).
This means that the case of interest is when both density operators
represent mixed states.
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| User: "David McAnally" |
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| Title: Re: Trace of product of density operators |
19 Feb 2006 09:56:26 AM |
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D.McAnally@i'm_a_gnu.uq.net.au (David McAnally) writes:
Does anybody know of a physical interpretation of the trace of the product
of two density operators in quantum mechanics (i.e. a physical
interpretation of the trace of the product of two self-adjoint operators,
each with trace 1, in quantum mechanics)?
That part in brackets should have read:
i.e. a physical interpretation of the trace of the product of two
positive self-adjoint operators, each with trace 1, in quantum
mechanics
If one of the density operators represents a pure state, then the trace of
the product has the interpretation of a probability (suppose that \rho_1 =
|i><i| - let A be a physical observable with with a as a nondegenerate
eigenvalue, with corresponding eigenvector |i> (so that A|i> = a|i>), and
let the system be in the state \rho_2, then tr(\rho_1 \rho_2) is the
probability that a is returned as the value when A is measured).
This means that the case of interest is when both density operators
represent mixed states.
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