A no-go theorem for superpositions of causal orders
arXiv:2008.06205 · doi:10.22331/q-2022-03-01-663
Abstract
The causal order of events need not be fixed: whether a bus arrives before or after another at a certain stop can depend on other variables -- like traffic. Coherent quantum control of causal order is possible too and is a useful resource for several tasks. However, quantum control implies that a controlling system carries the which-order information -- if the control is traced out, the order of events remains in a probabilistic mixture. Can the order of two events be in a pure superposition, uncorrelated with any other system? Here we show that this is not possible for a broad class of processes: a pure superposition of any pair of Markovian, unitary processes with equal local dimensions and different causal orders is not a valid process, namely it results in non-normalised probabilities when probed with certain operations. The result imposes constraints on novel resources for quantum information processing and on possible processes in a theory of quantum gravity.
arXiv comment6+4 pages, two pictures, final version
References in corpus (44)
- Quantum correlations with no causal order
- Quantum computations without definite causal structure
- Experimental Superposition of Orders of Quantum Gates
- Computational advantage from quantum-controlled ordering of gates
- Operational Markov condition for quantum processes
- Experimental Verification of an Indefinite Causal Order
- Quantum causal modelling
- Enhanced communication with the assistance of indefinite causal order
- Perfect discrimination of no-signalling channels via quantum superposition of causal structures
- Indefinite Causal Order in a Quantum Switch
- Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure
- Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication
- Witnessing causal nonseparability
- A "general boundary" formulation for quantum mechanics and quantum gravity
- A resource theory of superposition
- Causal and causally separable processes
- Experimental transmission of quantum information using a superposition of causal orders
- Experimental Quantum Switching for Exponentially Superior Quantum Communication Complexity
- Quantum superposition of the order of parties as a communication resource
- Bell's Theorem for Temporal Order
- Quantum computation with programmable connections between gates
- Multiple-time states and multiple-time measurements in quantum mechanics
- Resource theory of coherence based on positive-operator-valued measures
- Communicating via ignorance: Increasing communication capacity via superposition of order
- Computational advantage from quantum superposition of multiple temporal orders of photonic gates
- Time-delocalized quantum subsystems and operations: on the existence of processes with indefinite causal structure in quantum mechanics
- Maximal incompatibility of locally classical behavior and global causal order in multi-party scenarios
- A purification postulate for quantum mechanics with indefinite causal order
- The space of logically consistent classical processes without causal order
- Superdensity Operators for Spacetime Quantum Mechanics
- Updating the Born rule
- Operational quantum theory without predefined time
- Quantum communication in a superposition of causal orders
- On the definition and characterisation of multipartite causal (non)separability
- Experimental entanglement of temporal order
- Witnessing quantum memory in non-Markovian processes
- Entanglement, non-Markovianity, and causal non-separability
- Connecting processes with indefinite causal order and multi-time quantum states
- Observer-dependent locality of quantum events
- Consequences of preserving reversibility in quantum superchannels
- Reversible time travel with freedom of choice
- Reversible dynamics with closed time-like curves and freedom of choice
- Quantum Causal Models
- Transmitting quantum information by superposing causal order of mutually unbiased measurements