Complete characterization of post-selected quantum statistics using weak measurement tomography
arXiv:0907.0533 · doi:10.1103/PhysRevA.81.012103
Abstract
The reconstruction of quantum states from a sufficient set of experimental data can be achieved with arbitrarily weak measurement interactions. Since such weak measurements have negligible back-action, the quantum state reconstruction is also valid for the post-selected sub-ensembles usually considered in weak measurement paradoxes. It is shown that post-selection can then be identified with a statistical decomposition of the initial density matrix into transient density matrices conditioned by the anticipated measurement outcomes. This result indicates that it is possible to ascribe the properties determined by the final measurement outcome to each individual quantum system before the measurement has taken place. The ``collapse'' of the pure state wavefunction in a measurement can then be understood in terms of the classical ``collapse'' of a probability distribution as new information becomes available.
Extended version (5 pages), including double slit interference as an example and the resolution of Schroedinger`s cat paradox
References in corpus (13)
- Experimentally testable state-independent quantum contextuality
- Experimental joint weak measurement on a photon pair as a probe of Hardy's Paradox
- Quantum weak values
- Complex weak values in quantum measurement
- Weak values and the Leggett-Garg inequality in solid-state qubits
- Direct observation of Hardy's paradox by joint weak measurement with an entangled photon pair
- Weak measurements are universal
- A double-slit `which-way' experiment on the complementarity--uncertainty debate
- Leggett-Garg inequality with a kicked quantum pump
- Quantum Non-demolition Measurements on Qubits
- Tomography of many-body weak values: Mach-Zehnder interferometry
- On quantum vs. classical probability
- Weak Measurements with Entangled Probes
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- Nonperturbative theory of weak pre- and post-selected measurements
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- Strange Weak Values
- Can a Future Choice Affect a Past Measurement's Outcome?
- Quasiprobabilistic Interpretation of Weak measurements in Mesoscopic Junctions
- Uncertainty limits for quantum metrology obtained from the statistics of weak measurements
- On the role of complex phases in the quantum statistics of weak measurements
- How weak values emerge in joint measurements on cloned quantum systems
- Protecting weak measurements against systematic errors
- Quasiprobabilities in quantum thermodynamics and many-body systems
- State estimation: direct state measurement vs. tomography
- Stereographical visualization of a polarization state using weak measurements with an optical-vortex beam
- Using weak values to experimentally determine "negative probabilities" in a two-photon state with Bell correlations
- Weak measurement of photon polarization by back-action induced path interference
- Noninvasiveness and time symmetry of weak measurements
- Estimation of quantum states by weak and projective measurements
- Interferometry of quantum correlation functions to access quasiprobability distribution of work
- Disturbance in weak measurements and the difference between quantum and classical weak values
- Contextuality, Coherences, and Quantum Cheshire Cats
- Direct state reconstruction with coupling-deformed pointer observables
- Direct observation of temporal coherence by weak projective measurements of photon arrival time
- Estimation of Spin-Spin Interaction by Weak Measurement Scheme
- Quantum state tomography from sequential measurement of two variables in a single setup
- Quantum process in probability representation of quantum mechanics
- Quantum uncertainty as classical uncertainty of real-deterministic variables constructed from complex weak values and a global random variable
- Delayed choice of paths selected by grin and snarl of quantum Cheshire Cat
- Experimental evaluation of non-classical correlations between measurement outcomes and target observable in a quantum measurement
- Weak values and weak coupling maximizing the output of weak measurements
- Effect of chaos on information gain in quantum tomography
- Isolating noise and amplifying signal with quantum Cheshire cat
- Weak measurement-based state estimation of Gaussian states of one-variable quantum systems
- An investigation of the transfer dynamics of quantum teleportation by weak measurement statistics
- Anomalous weak values are caused by disturbance
- Quantum tomography via Non-orthogonal basis and weak values
- Postselection induced entanglement swapping from a vacuum--excitation entangled state to separate quantum systems
- Quantum causality relations and the emergence of reality from coherent superpositions
- Statistical signatures of quantum contextuality
- Weak value as an indicator of back-action
- Exploring weak value arguments and Bargmann invariants in -level quantum systems through the Majorana symmetric representation
- Stochastic Schrödinger Equations for Quantum Reverse Diffusion
- Comparing weak and projective measurements for quantum state tomography of a single-qubit system
- Time Derivatives of Weak Values
- Characterizing entangled state update in different reference frames with weak measurements