Quantum Information and Foundations
How quantum systems store and process information, and what quantum mechanics says about measurement and reality.
arXiv: quant-ph
21 topics
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In quantum theory the order of two operations, or the frame used to describe a system, could itself be in a superposition. The questions are which such situations can exist in nature and how physics looks from the viewpoint of a quantum object.
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Some quantum processes can be copied efficiently on ordinary computers, for example when entanglement stays small or noise washes out the quantum effects. The question is where exactly the line between easy and hard lies.
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Collapse models add a tiny random kick to the Schrodinger equation that makes large superpositions destroy themselves while leaving atoms almost untouched. The kicks also cause faint heating and X-ray emission, which experiments search for.
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Contextuality and Bell nonlocality
7 problemsQuantum measurement results cannot be explained as pre-existing values that are simply revealed: distant particles are correlated too strongly (nonlocality), and a result would have to depend on which other measurements are made alongside it (contextuality). Many quantitative questions about both effects are unsolved.
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Interaction with the surroundings spreads information about a quantum object into its environment, which suppresses visible interference and makes the object look classical. How far this process alone explains the classical world, including which parts of the universe count as separate objects, is unsettled.
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Quantum computers make errors, and error-correcting codes can fix them only if errors are rare enough and not too strongly linked across qubits. How much noise, and of what kind, error correction can tolerate, and whether logical errors keep falling as codes grow, are open.
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Every other force is known to obey quantum rules, but gravity is too weak to test directly. Tabletop experiments aim to see whether gravity between two tiny masses can create entanglement (linked quantum states), which a classical field is argued not to do.
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Quantum PCP and Hamiltonian complexity
6 problemsFinding the lowest energy of a system of many interacting quantum parts is, in the worst case, hard even for a quantum computer. The quantum PCP question asks whether even a rough estimate stays hard, and related questions ask how complex low-energy states must be.
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Atoms and molecules can be in two places at once, but everyday objects never are. Experiments put ever larger objects into superpositions to find whether quantum rules keep holding.
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Measurement problem and the Born rule
6 problemsQuantum theory says an unobserved system evolves smoothly into a blend of possibilities, yet every measurement shows exactly one result, with a probability equal to a squared amplitude. There is no agreement on how the single result arises or why the probabilities take that form.
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Quantum operations spread entanglement through a system while measurements remove it. As the measurement rate rises, the system switches sharply from highly entangled to weakly entangled, a phase transition visible only in the record of individual measurement outcomes.
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Quantum low-density parity-check (LDPC) codes protect many logical qubits using checks that each involve only a few qubits, promising error correction with far fewer physical qubits than standard codes. Using them needs links between distant qubits, fast decoding and a way to compute on the stored qubits.
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Chemistry and materials are made of interacting electrons, which quantum computers can in principle simulate directly. The open question is for which molecules and materials an error-corrected quantum computer would beat the best classical methods, and at what cost.
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Quantum correlations between distant particles are stronger than classical ones but weaker than the no-faster-than-light-signalling rule alone permits. The search is for simple physical principles that give exactly the quantum amount.
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Quantum Shannon theory asks how much information can be sent through a noisy quantum channel and how much pure entanglement can be extracted from noisy shared states. Several basic quantities cannot yet be computed even for the simplest noise models.
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Foundations of quantum thermodynamics
7 problemsThermodynamics was built for engines with countless particles. For a few quantum particles, strongly linked to their surroundings or in superposition, even heat and work need new definitions.
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Each way of building qubits (superconducting circuits, trapped ions, neutral atoms held by laser beams, photons) has error sources set by its own physics. Which of these set a hard lower limit on error rates, and how low each platform can go, is not known.
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A magnetic hard drive keeps a bit for years because flipping it costs energy that heat rarely supplies. The question is whether a quantum bit can be stored the same way, with no active correction, in a material in our three-dimensional world.
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SIC-POVMs and mutually unbiased bases
4 problemsA quantum measurement can be built from a set of equally spaced states, the quantum analogue of a perfectly symmetric arrangement of points on a sphere. Whether such sets exist in every dimension, and how many mutually unbiased bases (measurement bases where knowing one outcome tells nothing about the others) exist in dimension 6, are unsolved.
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Quantum mechanics has no standard clock observable, so questions such as how long a particle takes to tunnel through a barrier, or when it reaches a detector, have several competing answers. Experiments with cold atoms and ultrafast lasers now measure these times.
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Quantum computers have beaten classical supercomputers on contrived sampling tasks. Whether they give large speedups on problems people care about, and how anyone can check an answer no classical computer can reproduce, are open.