Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states

• URL: http://arxiv.org/abs/2311.18323v2
• Date: Thu, 4 Jan 2024 12:17:01 GMT
• Title: Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states
• Authors: Rajeev Gangwar, Tanmoy Pandit, Kaumudibikash Goswami, Siddhartha Das, Manabendra Nath Bera
• Abstract summary: We propose a faithful measure for non-Markovianity of genuine quantum origin called squashed quantum non-Markovianity (sQNM) It is based on the quantum conditional mutual information and is defined by the left-over non-Markovianity after squashing out all non-quantum contributions. We show that the sQNM is monogamous, continuous, convex, additive on tensor-product states, and generally super-additive.
• Score: 0.6990493129893111
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum non-Markovianity in tripartite quantum states $\rho_{ABC}$ represents a correlation between systems $A$ and $C$ when conditioned on the system $B$ and is known to have both classical and quantum contributions. However, a systematic characterization of the latter is missing. To address this, we propose a faithful measure for non-Markovianity of genuine quantum origin called squashed quantum non-Markovianity (sQNM). It is based on the quantum conditional mutual information and is defined by the left-over non-Markovianity after squashing out all non-quantum contributions. It is lower bounded by the squashed entanglement between non-conditioning systems in the reduced state and is delimited by the extendibility of either of the non-conditioning systems. We show that the sQNM is monogamous, asymptotically continuous, convex, additive on tensor-product states, and generally super-additive. We characterize genuine quantum non-Markovianity as a resource via a convex resource theory after identifying free states with vanishing sQNM and free operations that do not increase sQNM in states. We use our resource-theoretic framework to bound the rate of state transformations under free operations and to study state transformation under non-free operations; in particular, we find the quantum communication cost from Bob ($B$) to Alice ($A$) or Charlie ($C$) is lower bounded by the change in sQNM in the states. The sQNM finds operational meaning; in particular, the optimal rate of private communication in a variant of conditional one-time pad protocol is twice the sQNM. Also, the minimum deconstruction cost for a variant of quantum deconstruction protocol is given by twice the sQNM of the state.

Related papers

• Quantum conditional entropies and fully entangled fraction of states with maximally mixed marginals [0.0]
  The fully entangled fraction (FEF) measures the proximity of a quantum state to maximally entangled states. Quantum conditional entropy (QCE) is a measure of correlation in quantum systems. FEF is intricately linked with $k$- copy nonlocality and $k$- copy steerability.
  arXiv  Detail & Related papers  (2024-08-05T06:16:51Z)
• Anomaly in open quantum systems and its implications on mixed-state quantum phases [6.356631694532754]
  We develop a systematic approach to characterize the 't Hooft anomaly in open quantum systems. By representing their symmetry transformation through superoperators, we incorporate them in a unified framework. We find that anomalies of bosonic systems are classified by $Hd+2(Ktimes G,U(1))/Hd+2(G,U(1))$ in $d$ spatial dimensions.
  arXiv  Detail & Related papers  (2024-03-21T16:34:37Z)
• Tight concentration inequalities for quantum adversarial setups exploiting permutation symmetry [0.5242869847419834]
  We show that our one-sided concentration inequalities for a quantum state require the $N$-qudit system to be permutation invariant. We numerically demonstrate the tightness of our bounds in simple quantum information processing tasks.
  arXiv  Detail & Related papers  (2024-03-18T12:20:46Z)
• The Power of Unentangled Quantum Proofs with Non-negative Amplitudes [55.90795112399611]
  We study the power of unentangled quantum proofs with non-negative amplitudes, a class which we denote $textQMA+(2)$. In particular, we design global protocols for small set expansion, unique games, and PCP verification. We show that QMA(2) is equal to $textQMA+(2)$ provided the gap of the latter is a sufficiently large constant.
  arXiv  Detail & Related papers  (2024-02-29T01:35:46Z)
• 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)
• Protecting quantum correlations of negative quantum states using weak measurement under non-Markovian noise [0.0]
  Weak measurement (WM) and quantum measurement reversal (QMR) are crucial in protecting the collapse of quantum states. We study the quantum correlations, maximal fidelity, and fidelity deviation of the two-qubit negative quantum states developed using discrete Wigner functions. Some negative quantum states perform better with WM and QMR than the Bell state for different cases under evolution via noisy quantum channels.
  arXiv  Detail & Related papers  (2023-09-12T11:19:20Z)
• Quantum State Tomography for Matrix Product Density Operators [28.799576051288888]
  Reconstruction of quantum states from experimental measurements is crucial for the verification and benchmarking of quantum devices. Many physical quantum states, such as states generated by noisy, intermediate-scale quantum computers, are usually structured. We establish theoretical guarantees for the stable recovery of MPOs using tools from compressive sensing and the theory of empirical processes.
  arXiv  Detail & Related papers  (2023-06-15T18:23:55Z)
• Experimental demonstration of optimal unambiguous two-out-of-four quantum state elimination [52.77024349608834]
  A core principle of quantum theory is that non-orthogonal quantum states cannot be perfectly distinguished with single-shot measurements. Here we implement a quantum state elimination measurement which unambiguously rules out two of four pure, non-orthogonal quantum states.
  arXiv  Detail & Related papers  (2022-06-30T18:00:01Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)
• Quantum State Interferography [0.0]
  In this letter, we present an interferometric method, in which, any qubit state, whether mixed or pure, can be inferred from the visibility, phase shift and average intensity of an interference pattern using a single shot measurement. We experimentally implement our method with high fidelity using the polarisation degree of freedom of light.
  arXiv  Detail & Related papers  (2020-02-18T09:32:47Z)

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.