Characterizing mixing and measurement in quantum mechanics

Abstract

What fundamental constraints characterize the relationship between a mixture $\rho ={\sum }_i{p}_i{\rho }_i$ of quantum states, the states ${\rho }_i$ being mixed, and the probabilities $p_i$? What fundamental constraints characterize the relationship between prior and posterior states in a quantum measurement? In this paper we show that there are many surprisingly strong constraints on these mixing and measurement processes that can be expressed simply in terms of the eigenvalues of the quantum states involved. These constraints capture in a succinct fashion what it means to say that a quantum measurement acquires information about the system being measured, and considerably simplify the proofs of many results about entanglement transformation.

12 pages

References in corpus (5)

• Bell Inequalities and the Separability Criterion
• Entanglement of pure states for a single copy
• Minimal conditions for local pure-state entanglement manipulation
• A Method of Areas for Manipulating the Entanglement Properties of One Copy of a Two-Particle Pure State
• Probability distributions consistent with a mixed state

Cited by in corpus (32)

• Quantum Mechanics as Quantum Information (and only a little more)
• Fundamentals of Quantum Information Theory
• Thermal entanglement in a two-qubit Heisenberg XXZ spin chain under an inhomogeneous magnetic field
• The Uniqueness Theorem for Entanglement Measures
• A uniqueness theorem for entanglement measures
• Universal simulation of Hamiltonian dynamics for qudits
• Quantum Foundations in the Light of Quantum Information
• Quantum measurement and the first law of thermodynamics: the energy cost of measurement is the work value of the acquired information
• Majorization criterion for distillability of a bipartite quantum state
• Majorization Formulation of Uncertainty in Quantum Mechanics
• Random unistochastic matrices
• Orbits of quantum states and geometry of Bloch vectors for $N$-level systems
• An operational approach to quantum stochastic thermodynamics
• The trumping relation and the structure of the bipartite entangled states
• Relativity of pure states entanglement
• Quantum Operations, State Transformations and Probabilities
• Quantum entanglement dynamics and decoherence wave in spin chains at finite temperatures
• One-body entanglement as a quantum resource in fermionic systems
• Optimal common resource in majorization-based resource theories
• Memory compression and thermal efficiency of quantum implementations of non-deterministic hidden Markov models
• Approximate transformations of bipartite pure-state entanglement from the majorization lattice
• Many-body entanglement in fermion systems
• Efficient measurements, purification, and bounds on the mutual information
• A bound on the mutual information, and properties of entropy reduction, for quantum channels with inefficient measurements
• A geometrical description of non-Hermitian dynamics: speed limits in finite rank density operators
• Simulating Arbitrary Pair-Interactions by a Given Hamiltonian: Graph-Theoretical Bounds on the Time Complexity
• Various correlations in a Heisenberg XXZ spin chain both in thermal equilibrium and under the intrinsic decoherence
• Privacy protocols
• On a Supposed Conceptual Inadequacy of the Shannon Information in Quantum Mechanics
• Probabilistic Coherence Transformation Under Strictly Incoherent Operation
• Asymptotic Purification of Quantum Trajectories under Random Generalized Measurements
• Discrimination of Quantum States under Local Operations and Classical Communication