Quantum data hiding with continuous variable systems

• URL: http://arxiv.org/abs/2102.01100v2
• Date: Tue, 14 Dec 2021 22:57:48 GMT
• Title: Quantum data hiding with continuous variable systems
• Authors: Ludovico Lami
• Abstract summary: We investigate data hiding in the context of continuous variable quantum systems. We look at the case where $mathcalM=mathrmLOCC$, the set of measurements implementable with local operations and classical communication. We perform a rigorous quantitative analysis of the error introduced by the non-ideal Braunstein-Kimble quantum teleportation protocol.
• Score: 8.37609145576126
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• The role of shared randomness in quantum state certification with unentangled measurements [36.19846254657676]
  We study quantum state certification using unentangled quantum measurements. $Theta(d2/varepsilon2)$ copies are necessary and sufficient for state certification. We develop a unified lower bound framework for both fixed and randomized measurements.
  arXiv  Detail & Related papers  (2024-01-17T23:44:52Z)
• Discriminating mixed qubit states with collective measurements [0.2621730497733947]
  We propose and experimentally demonstrate a protocol for distinguishing two copies of single qubit states using collective measurements. We implement our measurements on an IBM Q System One device, a superconducting quantum processor.
  arXiv  Detail & Related papers  (2023-02-17T14:02:26Z)
• Validation tests of GBS quantum computers give evidence for quantum advantage with a decoherent target [62.997667081978825]
  We use positive-P phase-space simulations of grouped count probabilities as a fingerprint for verifying multi-mode data. We show how one can disprove faked data, and apply this to a classical count algorithm.
  arXiv  Detail & Related papers  (2022-11-07T12:00:45Z)
• Lower bounds for learning quantum states with single-copy measurements [3.2590610391507444]
  We study the problems of quantum tomography and shadow tomography using measurements performed on individual copies of an unknown $d$-dimensional state. In particular, this rigorously establishes the optimality of the folklore Pauli tomography" algorithm in terms of its complexity.
  arXiv  Detail & Related papers  (2022-07-29T02:26:08Z)
• Quantum state tomography with tensor train cross approximation [84.59270977313619]
  We show that full quantum state tomography can be performed for such a state with a minimal number of measurement settings. Our method requires exponentially fewer state copies than the best known tomography method for unstructured states and local measurements.
  arXiv  Detail & Related papers  (2022-07-13T17:56:28Z)
• Detecting entanglement in arbitrary two-mode Gaussian state: a Stokes-like operator based approach [1.3999481573773072]
  Detection of entanglement in quantum states is one of the most important problems in quantum information processing. We present an interferometric scheme to test the same separability criterion in which the measurements are being done via Stokes-like operators.
  arXiv  Detail & Related papers  (2021-03-24T04:54:35Z)
• Efficient Verification of Anticoncentrated Quantum States [0.38073142980733]
  I present a novel method for estimating the fidelity $F(mu,tau)$ between a preparable quantum state $mu$ and a classically specified target state $tau$. I also present a more sophisticated version of the method, which uses any efficiently preparable and well-characterized quantum state as an importance sampler.
  arXiv  Detail & Related papers  (2020-12-15T18:01:11Z)
• Bose-Einstein condensate soliton qubit states for metrological applications [58.720142291102135]
  We propose novel quantum metrology applications with two soliton qubit states. Phase space analysis, in terms of population imbalance - phase difference variables, is also performed to demonstrate macroscopic quantum self-trapping regimes.
  arXiv  Detail & Related papers  (2020-11-26T09:05:06Z)
• Random quantum circuits anti-concentrate in log depth [118.18170052022323]
  We study the number of gates needed for the distribution over measurement outcomes for typical circuit instances to be anti-concentrated. Our definition of anti-concentration is that the expected collision probability is only a constant factor larger than if the distribution were uniform. In both the case where the gates are nearest-neighbor on a 1D ring and the case where gates are long-range, we show $O(n log(n)) gates are also sufficient.
  arXiv  Detail & Related papers  (2020-11-24T18:44:57Z)
• Gaussian conversion protocols for cubic phase state generation [104.23865519192793]
  Universal quantum computing with continuous variables requires non-Gaussian resources. The cubic phase state is a non-Gaussian state whose experimental implementation has so far remained elusive. We introduce two protocols that allow for the conversion of a non-Gaussian state to a cubic phase state.
  arXiv  Detail & Related papers  (2020-07-07T09:19:49Z)
• Gaussian Process States: A data-driven representation of quantum many-body physics [59.7232780552418]
  We present a novel, non-parametric form for compactly representing entangled many-body quantum states. The state is found to be highly compact, systematically improvable and efficient to sample. It is also proven to be a universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size.
  arXiv  Detail & Related papers  (2020-02-27T15:54:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.