Multiple-time states and multiple-time measurements in quantum mechanics

Abstract

We discuss experimental situations that consist of multiple preparation and measurement stages. This leads us to a new approach to quantum mechanics. In particular, we introduce the idea of multi-time quantum states which are the appropriate tools for describing these experimental situations. We also describe multi-time measurements and discuss their relation to multi-time states. A consequence of our new formalism is to put states and operators on an equal footing. Finally we discuss the implications of our new approach to quantum mechanics for the problem of the flow of time.

17 pages, 8 figures

References in corpus (8)

• Experimental joint weak measurement on a photon pair as a probe of Hardy's Paradox
• Quantum weak values
• Direct observation of Hardy's paradox by joint weak measurement with an entangled photon pair
• Experimental Realization of the Quantum Box Problem
• Fast light, slow light, and phase singularities: a connection to generalized weak values
• On quantum non-signalling boxes
• Backward Evolving Quantum States
• Nonlocal Measurements in the Time-Symmetric Quantum Mechanics

Cited by in corpus (68)

• Nonperturbative theory of weak pre- and post-selected measurements
• Quantum common causes and quantum causal models
• Past quantum states
• Inferring causal structure: a quantum advantage
• Weak Values are Interference Phenomena
• Reformulating and Reconstructing Quantum Theory
• Quantum Blockchain using entanglement in time
• Weak value beyond conditional expectation value of the pointer readings
• Information theoretic treatment of tripartite systems and quantum channels
• Weak Values with Decoherence
• The Operator Tensor Formulation of Quantum Theory
• Superdensity Operators for Spacetime Quantum Mechanics
• Can a quantum state over time resemble a quantum state at a single time?
• Contextual-value approach to the generalized measurement of observables
• From time-reversal symmetry to quantum Bayes' rules
• Operational quantum theory without predefined time
• Quantum-coherent mixtures of causal relations
• Pre- and post-selected quantum states: density matrices, tomography, and Kraus operators
• Operational General Relativity: Possibilistic, Probabilistic, and Quantum
• Why initial system-environment correlations do not imply the failure of complete positivity: a causal perspective
• Connecting processes with indefinite causal order and multi-time quantum states
• A Unifying Framework for Spatial and Temporal Quantum Correlations
• Entangled Histories
• Quantum instruments as a foundation for both states and observables
• Each instant of time a new Universe
• Homodyne monitoring of post-selected decay
• Entangled Histories vs. the Two-State-Vector Formalism - Towards a Better Understanding of Quantum Temporal Correlations
• Experimental Test of Entangled Histories
• Modular Quantum Computation in a Trapped Ion System
• Characterising the Hierarchy of Multi-time Quantum Processes with Classical Memory
• Causal and compositional structure of unitary transformations
• Quantum correlations in composite systems
• Incompatible measurements on quantum causal networks
• Uniqueness of quantum state over time function
• Quantum space-time marginal problem: global causal structure from local causal information
• Experimental demonstration of input-output indefiniteness in a single quantum device
• Multitime correlation functions in nonclassical stochastic processes
• Unification of spatiotemporal quantum formalisms: mapping between process and pseudo-density matrices via multiple-time states
• Time-dependent quantum correlations in phase space
• Estimating Pre- and Post-Selected Ensembles
• Different instances of time as different quantum modes: quantum states across space-time for continuous variables
• Formalism Locality in Quantum Theory and Quantum Gravity
• Quantum Causal Inference with Extremely Light Touch
• Temporal Observables and Entangled Histories
• A no-go theorem for superpositions of causal orders
• The spatiotemporal doubled density operator: a unified framework for analyzing spatial and temporal quantum processes
• Quantum to classical transitions in causal relations
• Exploring postselection-induced quantum phenomena with time-bidirectional state formalism
• Restrictions on the existence of weak values in quantum mechanics: weak quantum evolution concept
• Exploring the limits of no backward in time signalling
• Time Symmetry in Operational Theories
• Teleportation of Post-Selected Quantum States
• Stories in the two-state vector formalism
• Entanglement of temporal sections as quantum histories and their quantum correlation bounds
• Hierarchy and robustness of multilevel two-time temporal quantum correlations
• Quantum Correlations in Space-Time: Foundations and Applications
• Spacetime Paths as a Whole
• Reality, Causality, and Quantum Theory
• Continuous monitoring measured signals bounded by past and future conditions in enlarged quantum systems
• Tripartite non-classical correlations without backwards in time signalling
• A de Finetti theorem for quantum causal structures
• A perturbation theory for multi-time correlation functions in open quantum systems
• Time-System Entanglement and Special Relativity
• Dynamical self-averaging for a lattice Schrödinger equation with weak random potential
• Theory of Quantum Path Entanglement and Interference with Multiplane Diffraction of Classical Light Sources
• What are temporal correlations
• Prediction-retrodiction measurements for teleportation and conditional state transfer
• Phenomenological quantum mechanics: I. Phenomenology of quantum observables