A de Finetti representation for finite symmetric quantum states

Abstract

Consider a symmetric quantum state on an n-fold product space, that is, the state is invariant under permutations of the n subsystems. We show that, conditioned on the outcomes of an informationally complete measurement applied to a number of subsystems, the state in the remaining subsystems is close to having product form. This immediately generalizes the so-called de Finetti representation to the case of finite symmetric quantum states.

22 pages, LaTeX

References in corpus (8)

• Quantum cryptography: Public key distribution and coin tossing
• Symmetric Informationally Complete Quantum Measurements
• Unknown Quantum States: The Quantum de Finetti Representation
• On SIC-POVMs and MUBs in Dimension 6
• On the Security of Quantum Cryptography Against Collective Attacks
• Informationally complete measurements and groups representation
• A Generic Security Proof for Quantum Key Distribution
• Entanglement purification of unknown quantum states

Cited by in corpus (75)

• Quantum entanglement
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Secure quantum key distribution over 421 km of optical fiber
• Catalytic Coherence
• Symmetry implies independence
• Tight informationally complete quantum measurements
• The SIC Question: History and State of Play
• One-and-a-half quantum de Finetti theorems
• Loss-tolerant quantum cryptography with imperfect sources
• Faithful Squashed Entanglement
• Quantum Conference Key Agreement: A Review
• Computational advantage of quantum random sampling
• A Generalization of Quantum Stein's Lemma
• Schur-Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations
• Secure Multiparty Quantum Computation with (Only) a Strict Honest Majority
• The power of symmetric extensions for entanglement detection
• Broadcast copies reveal the quantumness of correlations
• Quantum key distribution overcoming extreme noise: simultaneous subspace coding using high-dimensional entanglement
• The Bounded Storage Model in The Presence of a Quantum Adversary
• Unconditional security proof of a deterministic quantum key distribution with a two-way quantum channel
• Quantum key distribution based on private states: unconditional security over untrusted channels with zero quantum capacity
• Security proof of a three-state quantum key distribution protocol without rotational symmetry
• Security proof for a simplified BB84-like QKD protocol
• Quantum Cryptography Based Solely on Bell's Theorem
• Device-Independent Quantum Key Distribution with Commuting Measurements
• Towards a realization of device-independent quantum key distribution
• Quantum information becomes classical when distributed to many users
• Exchange Symmetry and Multipartite Entanglement
• Noisy Preprocessing and the Distillation of Private States
• The Lie Algebraic Significance of Symmetric Informationally Complete Measurements
• Optimal Detection of Entanglement in GHZ States
• Quantum de Finetti theorem under fully-one-way adaptive measurements
• Encoding-side-channel-free and measurement-device-independent quantum key distribution
• Semi-Quantum Key Distribution with High Quantum Noise Tolerance
• Product-state Approximations to Quantum Ground States
• Approximating the Set of Separable States Using the Positive Partial Transpose Test
• Detection of Multiparticle Entanglement: Quantifying the Search for Symmetric Extensions
• Semidefinite programming hierarchies for constrained bilinear optimization
• Finite de Finetti theorem for conditional probability distributions describing physical theories
• Non-classical correlations in quantum mechanics and beyond
• Detecting drift of quantum sources: not the de Finetti theorem
• $SU(p,q)$ coherent states and a Gaussian de Finetti theorem
• Extendibility of bosonic Gaussian states
• Finite size mean-field models
• A Finite de Finetti Theorem for Infinite-Dimensional Systems
• Limitations of semidefinite programs for separable states and entangled games
• Beyond islands: A free probabilistic approach
• Ground States of Fermionic lattice Hamiltonians with Permutation Symmetry
• Client-friendly continuous-variable blind and verifiable quantum computing
• A quantum de Finetti theorem in phase space representation
• The black hole information puzzle and the quantum de Finetti theorem
• Efficient quantum key distribution with trines of reference-frame-free qubits
• Large-$d$ phase transitions in holographic mutual information
• Reductions to IID in Device-independent Quantum Information Processing
• Monogamy of entanglement and improved mean-field ansatz for spin lattices
• Security of quantum key distribution using weak coherent states with nonrandom phases
• $k$-extendibility of high-dimensional bipartite quantum states
• Stronger Methods of Making Quantum Interactive Proofs Perfectly Complete
• Théorèmes de de Finetti, limites de champ moyen et condensation de Bose-Einstein
• A fermionic de Finetti theorem
• Projections of Orbital Measures and Quantum Marginal Problems
• Quantum Causal Structure and Quantum Thermodynamics
• Learning Properties of Quantum States Without the I.I.D. Assumption
• Computing finite-dimensional bipartite quantum separability
• Multipartite maximally entangled states in symmetric scenarios
• Deformations of the symmetric subspace of qubit chains
• Tight concentration inequalities for quantum adversarial setups exploiting permutation symmetry
• $su(d)$-squeezing and many-body entanglement geometry in finite-dimensional systems
• De Finetti Theorems for Braided Parafermions
• Monogamy of highly symmetric states
• A de Finetti theorem for quantum causal structures
• Sampling and the complexity of nature
• Device-independent quantum key distribution
• Moment-sos and spectral hierarchies for polynomial optimization on the sphere and quantum de Finetti theorems