Quantum data hiding with continuous variable systems

Abstract

Suppose we want to benchmark a quantum device held by a remote party, e.g. by testing its ability to carry out challenging quantum measurements outside of a free set of measurements $\mathcal{M}$. A very simple way to do so is to set up a binary state discrimination task that cannot be solved efficiently by means of free measurements. If one can find pairs of orthogonal states that become arbitrarily indistinguishable under measurements in $\mathcal{M}$, in the sense that the error probability in discrimination approaches that of a random guess, one says that there is data hiding against $\mathcal{M}$. Here we investigate data hiding in the context of continuous variable quantum systems. First, we look at the case where $\mathcal{M}=\mathrm{LOCC}$, the set of measurements implementable with local operations and classical communication. While previous studies have placed upper bounds on the maximum efficiency of data hiding in terms of the local dimension and are thus not applicable to continuous variable systems, we establish more general bounds that rely solely on the local mean photon number of the states employed. Along the way, we perform a rigorous quantitative analysis of the error introduced by the non-ideal Braunstein-Kimble quantum teleportation protocol, determining how much squeezing and local detection efficiency is needed in order to teleport an arbitrary multi-mode local state of known mean energy with a prescribed accuracy. Finally, following a seminal proposal by Sabapathy and Winter, we look at data hiding against Gaussian operations assisted by feed-forward of measurement outcomes, providing the first example of a relatively simple scheme that works with a single mode only.

25 pages; v2 has a generally improved presentation and is close to the published version

References in corpus (15)

• Photonic quantum technologies
• The Quantum Chernoff Bound
• Randomizing quantum states: Constructions and applications
• Quantum state discrimination and its applications
• The Chernoff lower bound for symmetric quantum hypothesis testing
• Entanglement Theory and the Second Law of Thermodynamics
• Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-Gaussian near-optimal receivers
• QPSK coherent state discrimination via a hybrid receiver
• Sampling arbitrary photon-added or photon-subtracted squeezed states is in the same complexity class as boson sampling
• A robust quantum receiver for phase shift keyed signals
• Multi-state discrimination below the quantum noise limit at the single-photon level
• Hiding Quantum Data
• Entanglement in channel discrimination with restricted measurements
• Linear-optical processing cannot increase photon efficiency
• Efficiencies of Quantum Optical Detectors

Cited by in corpus (9)

• Linear optics and photodetection achieve near-optimal unambiguous coherent state discrimination
• Optimal tests for continuous-variable quantum teleportation and photodetectors
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
• Continuous-variable quantum state designs: theory and applications
• Separability and entanglement in superpositions of quantum states
• Bosonic data hiding: power of linear vs non-linear optics
• Universal compiling and (No-)Free-Lunch theorems for continuous variable quantum learning
• Information locking and its resource efficient extraction
• Enhanced Uplink Quantum Communication with Satellites via Downlink Channels