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Negative entropy in quantum information theory
Quantum Physics · Submitted 3 Oct 1996
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that, unlike in Shannon theory, conditional entropies can be negative when considering quantum entangled systems such as an Einstein-Podolsky-Rosen pair, which leads to a violation of well-known bounds of classical information theory.
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The abstract, sentence by sentence
We present a quantum information theory that allows for the consistent description of quantum entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices, rather than probability distributions, for the description of quantum ensembles. We find that, unlike in Shannon theory, conditional entropies can be negative when considering quantum entangled systems such as an Einstein-Podolsky-Rosen pair, which leads to a violation of well-known bounds of classical information theory. Negative quantum entropy can be traced back to ``conditional'' density matrices which admit eigenvalues larger than unity. A straightforward definition of mutual quantum entropy, or ``mutual entanglement'', can also be constructed using a ``mutual'' density matrix. Such a unified information-theoretic description of classical correlation and quantum entanglement clarifies the link between them: the latter can be viewed as ``super-correlation'' which can induce classical correlation when considering a ternary or larger system.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a quantum information theory that allows for the consistent description of quantum entanglement. | contribution 1.00 | 0.90 | 0.17 | asserted 0.98 |
| s1 | It parallels classical (Shannon) information theory but is based entirely on density matrices, rather than probability distributions, for the description of quantum ensembles. | method 0.56 | 0.40 | 0.07 | asserted 1.00 |
| s2 | We find that, unlike in Shannon theory, conditional entropies can be negative when considering quantum entangled systems such as an Einstein-Podolsky-Rosen pair, which leads to a violation of well-known bounds of classical information theory. | result 1.00 | 0.91 | 0.62 | asserted 1.00 |
| s3 | Negative quantum entropy can be traced back to ``conditional'' density matrices which admit eigenvalues larger than unity. | interpretation 0.82 | 0.77 | 0.16 | asserted 0.99 |
| s4 | A straightforward definition of mutual quantum entropy, or ``mutual entanglement'', can also be constructed using a ``mutual'' density matrix. | contribution 0.93 | 0.87 | 0.09 | asserted 0.69 |
| s5 | Such a unified information-theoretic description of classical correlation and quantum entanglement clarifies the link between them: the latter can be viewed as ``super-correlation'' which can induce classical correlation when considering a ternary or larger system. | interpretation 1.00 | 0.74 | 0.42 | asserted 0.91 |
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Original abstract
We present a quantum information theory that allows for the consistent description of quantum entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices, rather than probability distributions, for the description of quantum ensembles. We find that, unlike in Shannon theory, conditional entropies can be negative when considering quantum entangled systems such as an Einstein-Podolsky-Rosen pair, which leads to a violation of well-known bounds of classical information theory. Negative quantum entropy can be traced back to ``conditional'' density matrices which admit eigenvalues larger than unity. A straightforward definition of mutual quantum entropy, or ``mutual entanglement'', can also be constructed using a ``mutual'' density matrix. Such a unified information-theoretic description of classical correlation and quantum entanglement clarifies the link between them: the latter can be viewed as ``super-correlation'' which can induce classical correlation when considering a ternary or larger system.
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References
How the literature uses it
2 arXiv papers cite this in 3 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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The possibility that negative (virtual) information can be carried by entangled particles suggests a consistent interpretation of quantum informational processes.
Negative entropy and information in quantum mechanics · 0.98
Papers citing it · 1 sentence without a confident label
Compares with it 1 paper
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Firstly, Cerf and Adami have proposed an alternative definition of an acausal conditional state [ref] (their definition does not extend to the causal case).
Towards a Formulation of Quantum Theory as a Causally Neutral Theory of Bayesian Inference · Comparison to Other Quantum Generalizations of Conditional Probability · 0.97
Cites it as background 1 paper
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The most relevant to quantum information are perhaps the quantum conditional expectation [ref] (see [ref] for a basic introduction and [ref] for a review) and the Cerf-Adami conditional density operator [ref] .
Towards a Formulation of Quantum Theory as a Causally Neutral Theory of Bayesian Inference · Introduction · 0.96
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