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Mixed states for reference frames transformations
Quantum Physics · Submitted 8 Jul 2025 · Published version
abstract compiled · 2026-10-20 · no language-model review
The authors' main claim This gives rise to interesting consequences: the state of a system can be pure with respect to a reference frame and mixed with respect to another; we concretely discuss this in the framework of Galilei transformations in 1+1 dimensions.
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The abstract, sentence by sentence
We discuss the concept of transformations among reference frames (classical or quantum). Usually transformations among classical reference frames have sharply defined parameters; geometrically they can be considered as {pure states in the parameters' space, and they form a group. It is however possible that the distributions in the parameters' space are mixed states; such states form a semigroup. Similarly, transformations among quantum reference frames can be either pure or mixed. This gives rise to interesting consequences: the state of a system can be pure with respect to a reference frame and mixed with respect to another; we concretely discuss this in the framework of Galilei transformations in 1+1 dimensions. In particular, if the state of a reference frame with respect to another frame is thermal at some temperature, a quantum particle in the pure (improper) rest state with respect to the first frame will appear in a thermal state with a related nonzero temperature with respect to the other. This can also be discussed in relation to the time/energy uncertainty relation.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We discuss the concept of transformations among reference frames (classical or quantum). | background 0.67 | 0.63 | 0.03 | unclear 0.58 |
| s1 | Usually transformations among classical reference frames have sharply defined parameters; geometrically they can be considered as {pure states in the parameters' space, and they form a group. | background 1.00 | 0.07 | 0.04 | asserted 0.96 |
| s2 | It is however possible that the distributions in the parameters' space are mixed states; such states form a semigroup. | background 0.53 | 0.22 | 0.15 | hedged possibility 0.81 |
| s3 | Similarly, transformations among quantum reference frames can be either pure or mixed. | background 0.62 | 0.21 | 0.07 | asserted 0.86 |
| s4 | This gives rise to interesting consequences: the state of a system can be pure with respect to a reference frame and mixed with respect to another; we concretely discuss this in the framework of Galilei transformations in 1+1 dimensions. | contribution 0.45 | 0.75 | 0.33 | asserted 0.95 |
| s5 | In particular, if the state of a reference frame with respect to another frame is thermal at some temperature, a quantum particle in the pure (improper) rest state with respect to the first frame will appear in a thermal state with a related nonzero temperature with respect to the other. | result 0.93 | 0.69 | 0.46 | asserted 0.94 |
| s6 | This can also be discussed in relation to the time/energy uncertainty relation. | interpretation 0.97 | 0.28 | 0.04 | hedged possibility 0.85 |
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Original abstract
We discuss the concept of transformations among reference frames (classical or quantum). Usually transformations among classical reference frames have sharply defined parameters; geometrically they can be considered as {pure states in the parameters' space, and they form a group. It is however possible that the distributions in the parameters' space are mixed states; such states form a semigroup. Similarly, transformations among quantum reference frames can be either pure or mixed. This gives rise to interesting consequences: the state of a system can be pure with respect to a reference frame and mixed with respect to another; we concretely discuss this in the framework of Galilei transformations in 1+1 dimensions. In particular, if the state of a reference frame with respect to another frame is thermal at some temperature, a quantum particle in the pure (improper) rest state with respect to the first frame will appear in a thermal state with a related nonzero temperature with respect to the other. This can also be discussed in relation to the time/energy uncertainty relation.
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It has been developed from different perspectives including quantum foundations, quantum information, quantum gravity, and mathematical physics (see, for instance, [ref] ).
Universal $T$-matrices for quantum Poincar\'e groups: contractions and quantum reference frames · Introduction · 0.96
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