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Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy, and the uncertainty principle and is generally used in single-body systems. Use the quantum-field-theory tag for the theory of many-body quantum-mechanical systems.
2
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Is there a formula for the eigenvalues of $\rho_A,\rho_B$ in terms of those of $\rho_{AB}$?
Let $\rho_{AB}$ be a bipartite density matrix with marginal states $\rho_A=\text{tr}_B(\rho_{AB})$ and $\rho_B=\text{tr}_A(\rho_{AB})$. In such a case, is there a formula for the eigenvalues of $\rho_ …
9
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Are two states with the same measurement probabilities necessarily equal up to unitary equiv...
Let $\rho$ and $\rho'$ be $n\times n$ density matrices, and suppose that for every observable $A$ and every $\lambda$ in the spectrum of $A$ we have
$$
\text{tr}(\rho P_{\lambda})=\text{tr}(\rho' P_{\ …