Summoning Information in Spacetime, or Where and When Can a Qubit Be?
arXiv:1210.0913 · doi:10.1088/1751-8113/49/17/175304
Abstract
One of the most important properties of quantum information, and the one ultimately responsible for its cryptographic applications, is that it can't be copied. That statement, however, is not completely accurate. While the no-cloning theorem of quantum mechanics prevents quantum information from being copied in space, the reversibility of microscopic physics actually requires that the information be copied in time. In spacetime as a whole, therefore, quantum information is widely replicated but in a restricted fashion. We fully characterize which regions of spacetime can all hold the same quantum information. Because quantum information can be delocalized through quantum error correction and teleportation, it need not follow well-defined trajectories. Instead, replication of the information in any configuration of spacetime regions not leading to violations of causality or the no-cloning principle is allowed. To demonstrate this, we answer the operational question of exactly when the information can be summoned to a set of spacetime points, showing how to do so efficiently using a combination of teleportation and codeword-stabilized quantum codes. This provides a simple and complete description of where and when a qubit can be located in spacetime, revealing a remarkable variety of possibilities.
v1: 5 pages, 1.2 figures per page on average. v2: 2 words and one arrow added. v3: now includes an efficient construction v4: bug fix in construction, new abstract v5, v6: cosmetic changes
References in corpus (15)
- Black holes as mirrors: quantum information in random subsystems
- Relativistic Quantum Teleportation with Superconducting Circuits
- Simplified instantaneous non-local quantum computation with applications to position-based cryptography
- Codeword Stabilized Quantum Codes
- Quantum metrology for relativistic quantum fields
- Quantum Tagging: Authenticating Location via Quantum Information and Relativistic Signalling Constraints
- Sustainable entanglement production from a quantum field
- Unconditionally Secure Bit Commitment with Flying Qudits
- Information transmission without energy exchange
- Processing quantum information with relativistic motion of atoms
- Quantum Tasks in Minkowski Space
- Quantum Communication with an Accelerated Partner
- A Quantum Paradox of Choice: More Freedom Makes Summoning a Quantum State Harder
- A No-summoning theorem in Relativistic Quantum Theory
- Spacetime replication of continuous variable quantum information
Cited by in corpus (23)
- Quantum cryptography: key distribution and beyond
- Causal Structures and Nonlocality in Double Holography
- Random-Receiver Quantum Communication
- Quantum Signaling in Relativistic Motion and Across Acceleration Horizons
- A Quantum Paradox of Choice: More Freedom Makes Summoning a Quantum State Harder
- Multiphoton and side-channel attacks in mistrustful quantum cryptography
- The connected wedge theorem and its consequences
- Relativistic (2,3)-threshold quantum secret sharing
- One-out-of- spacetime-constrained oblivious transfer
- Spacetime replication of continuous variable quantum information
- Space in Monoidal Categories
- S-money: virtual tokens for a relativistic economy
- Continuous-variable ramp quantum secret sharing with Gaussian states and operations
- A Scheme for Performing Strong and Weak Sequential Measurements of Non-commuting Observables
- Unconstrained Summoning for relativistic quantum information processing
- Encrypted Qubits can be Cloned
- Efficient Code for Relativistic Quantum Summoning
- Localizing and excluding quantum information; or, how to share a quantum secret in spacetime
- A Quantum Paradox of Choice and Purported Classical Analogues
- Distributing bipartite quantum systems under timing constraints
- Constraining the doability of relativistic quantum tasks
- Summoning, No-Signaling and Relativistic Bit Commitments
- Comparing Singlet Testing Schemes