Hiding and masking quantum information in complex and real quantum mechanics
arXiv:2010.07843 · doi:10.1103/PhysRevResearch.3.033176
Abstract
Classical information can be completely hidden in the correlations of bipartite quantum systems. However, it is impossible to hide or mask all quantum information according to the no-hiding and no-masking theorems derived recently. Here we show that any set of informationally complete quantum states is neither hidable nor maskable, thereby strengthening the no-hiding and no-masking theorems known before. Then, by virtue of Hurwitz-Radon matrices (representations of the Clifford algebra), we show that information about real quantum states can be completely hidden in the correlations, although the minimum dimension of the composite Hilbert space required increases exponentially with the dimension of the original Hilbert space. Moreover, the set of real quantum states is a maximal maskable set within quantum theory and has a surprising connection with maximally entangled states. These results offer valuable insight on the potential and limit of hiding and masking quantum information, which are of intrinsic interest to a number of active research areas.
arXiv comment9+9.1 pages and 4 figures; published in Phys. Rev. Research
References in corpus (30)
- Quantum entanglement
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Quantum secret sharing
- Entanglement of a Pair of Quantum Bits
- Average Entropy of a Subsystem
- Black holes as mirrors: quantum information in random subsystems
- How to share a quantum secret
- Fast Scramblers
- Symmetric Informationally Complete Quantum Measurements
- Conditions for a class of entanglement transformations
- Universal state inversion and concurrence in arbitrary dimensions
- On mutually unbiased bases
- Noncommuting mixed states cannot be broadcast
- Informational derivation of Quantum Theory
- Quantum Data Hiding
- Experimental Quantum Cloning of Single Photons
- Tight informationally complete quantum measurements
- The SIC Question: History and State of Play
- Quantum information cannot be completely hidden in correlations: implications for the black-hole information paradox
- Operational Resource Theory of Imaginarity
- Quantifying the Imaginarity of Quantum Mechanics
- Limited Holism and Real-Vector-Space Quantum Theory
- Division Algebras and Quantum Theory
- Simulating quantum systems using real Hilbert spaces
- Masking quantum information is impossible
- Quantum State Tomography with Joint SIC POMs and Product SIC POMs
- Entanglement, quantum randomness, and complexity beyond scrambling
- Complete characterization of qubit masking
- Masking Quantum Information on Hyperdisks
- Impossibility of masking a set of quantum states of nonzero measure
Cited by in corpus (27)
- Unitary-invariant witnesses of quantum imaginarity
- Resource Theory of Imaginarity: New Distributed Scenarios
- Imaginarity of Gaussian states
- Quantifying the imaginarity of quantum states via Tsallis relative entropy
- Nonlocal Advantages of Quantum Imaginarity
- Quantifying imaginarity in terms of pure-state imaginarity
- Quantum Information Masking in Non-Hermitian Systems and Robustness
- Quantum information masking of an arbitrary qudit can be realized in multipartite lower dimensional systems
- Coherence and imaginarity of quantum states
- Censorship of Quantum Resources in Quantum Networks
- Expectation value dynamics within real Hilbert space quantum mechanics
- Quantum-imaginarity-based quantum speed limit
- No-masking theorem for observables
- Self-interacting quantum particles and the Dirac delta potential
- Imaginarity measures induced by real part states and the complementarity relations
- Klein-Gordon equation within the real Hilbert space formalism
- Analyzing the free states of one quantum resource theory as resource states of another
- A simple formulation of no-cloning and no-hiding that admits efficient and robust verification
- Experimental Masking of Real Quantum States
- Off-resonant preservation and generation of imaginarity in distributed scenarios
- Deformed angular momentum algebra within the real Hilbert space
- Entanglement is indispensable for masking arbitrary set of quantum states
- The quantum harmonic oscillator and the real Hilbert space
- Measure of set imaginarity
- Generalized imaginary units in quantum mechanics
- Experimental certification of the nonlocal advantages of quantum imaginarity
- Comment on "Masking quantum information is impossible"