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Limitations on device independent secure key via squashed non-locality

Marek Winczewski, Tamoghna Das, Karol Horodecki

Published Mar 28, 2019• 5 citations
OpenAlex

Abstract

We initiate a systematic study to provide upper bounds on device-independent key, secure against a non-signaling adversary (NSDI), distilled by a wide class of operations, currently used in both quantum and non-signaling device-independent protocols. These operations consist of a direct measurements on the devices followed by Local Operations and Public Communication (MDLOPC). We employ the idea of squashing on the secrecy monotones, which provide upper bounds on the key rate in secret key agreement (SKA) scenario, and show that secrecy monotones are the upper bounds on NSDI key. As an important instance, an upper bound on NSDI key rate called squashed non-locality, has been constructed. It exhibits several important properties, including convexity, monotonicity, additivity on tensor products, and asymptotic continuity. Using this bound, we identify numerically a domain of two binary inputs and two binary outputs non-local devices for which the non-locality is zero, and therefore one can not distil key from them via MDLOPC operations. These are mixtures of Popescu-Rohrlich (PR) and anti-PR box with the weight of PR box less than $80\%$. This example confirms the intuition that non-locality need not imply secrecy in the non-signaling scenario. The approach is general, describing how to construct other tighter yet possibly less computable upper bounds. Our technique for obtaining upper bounds is based on the non-signaling analog of quantum purification: the complete extension, which yields equivalent security conditions as previously known in the literature.

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Limitations on a device-independent key secure against a nonsignaling adversary via squashed nonlocality

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We initiate a systematic study to provide upper bounds on device-independent keys, secure against a nonsignaling adversary (NSDI). We employ the idea of ``squashing'' on the secrecy monotones and show that squashed secrecy monotones are the upper bounds on the NSDI key. Our technique for obtaining upper bounds is based on the nonsignaling analog of quantum purification: the complete extension. As an important instance of an upper bound, we construct a measure of nonlocality called ``squashed nonlocality.'' Using this bound, we identify numerically a certain domain of two binary inputs and two binary outputs of nonlocal devices for which the squashed nonlocality is zero. Therefore one can not distill a secure key from these nonlocal devices via a considered (standard) class of operations. Showing a connection of our approach to the one in New J. Phys. 8, 126 (2006), we provide, to our knowledge, the tightest known upper bound in the (3,2,2,2) scenario. Moreover, we formulate a security condition, equivalent to known ones, for the considered class of protocols. To achieve this, we introduce a nonsignaling norm that constitutes an analogy to the trace norm used in the security condition of the quantum key distribution.

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In this work, we introduce the multipartite intrinsic non-locality as a resource quantifier for the multipartite scenario of device-independent (DI) conference key agreement. We prove that this quantity is additive, convex, and monotone under a class of free operations called local operations and common randomness. As one of our technical contributions, we establish a chain rule for multipartite mutual information, which we then use to prove that the multipartite intrinsic non-locality is additive. This chain rule may be of independent interest in other contexts. All of these properties of multipartite intrinsic non-locality are helpful in establishing the main result of our paper: multipartite intrinsic non-locality is an upper bound on secret key rate in the general multipartite scenario of DI conference key agreement. We discuss various examples of DI conference key protocols and compare our upper bounds for these protocols with known lower bounds. Finally, we calculate upper bounds on recent experimental realizations of DI quantum key distribution.

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Multipartite Intrinsic Non-Locality and Device-Independent Conference Key Agreement

Aby Philip, Eneet Kaur, Peter Bierhorst +1 more

In this work, we introduce multipartite intrinsic non-locality as a method for quantifying resources in the multipartite scenario of device-independent (DI) conference key agreement. We prove that multipartite intrinsic non-locality is additive, convex, and monotone under a class of free operations called local operations and common randomness. As one of our technical contributions, we establish a chain rule for two variants of multipartite mutual information, which we then use to prove that multipartite intrinsic non-locality is additive. This chain rule may be of independent interest in other contexts. All of these properties of multipartite intrinsic non-locality are helpful in establishing the main result of our paper: multipartite intrinsic non-locality is an upper bound on secret key rate in the general multipartite scenario of DI conference key agreement. We discuss various examples of DI conference key protocols and compare our upper bounds for these protocols with known lower bounds. Finally, we calculate upper bounds on recent experimental realizations of DI quantum key distribution.

arXiv:2111.02596•Quantum•Jan 19, 2023•10 citations
We initiate a systematic study to provide upper bounds on device-independent key, secure against a non-signaling adversary (NSDI), distilled by a wide class of operations, currently used in both quantum and non-signaling device-independent protocols. These operations consist of a direct measurements on the devices followed by Local Operations and Public Communication (MDLOPC). We employ the idea of squashing on the secrecy monotones, which provide upper bounds on the key rate in secret key agreement (SKA) scenario, and show that secrecy monotones are the upper bounds on NSDI key. As an important instance, an upper bound on NSDI key rate called squashed non-locality, has been constructed. It exhibits several important properties, including convexity, monotonicity, additivity on tensor products, and asymptotic continuity. Using this bound, we identify numerically a domain of two binary inputs and two binary outputs non-local devices for which the non-locality is zero, and therefore one can not distil key from them via MDLOPC operations. These are mixtures of Popescu-Rohrlich (PR) and anti-PR box with the weight of PR box less than 80%80\%80%. This example confirms the intuition that non-locality need not imply secrecy in the non-signaling scenario. The approach is general, describing how to construct other tighter yet possibly less computable upper bounds. Our technique for obtaining upper bounds is based on the non-signaling analog of quantum purification: the complete extension, which yields equivalent security conditions as previously known in the literature.
We initiate a systematic study to provide upper bounds on device-independent keys, secure against a nonsignaling adversary (NSDI). We employ the idea of ``squashing'' on the secrecy monotones and show that squashed secrecy monotones are the upper bounds on the NSDI key. Our technique for obtaining upper bounds is based on the nonsignaling analog of quantum purification: the complete extension. As an important instance of an upper bound, we construct a measure of nonlocality called ``squashed nonlocality.'' Using this bound, we identify numerically a certain domain of two binary inputs and two binary outputs of nonlocal devices for which the squashed nonlocality is zero. Therefore one can not distill a secure key from these nonlocal devices via a considered (standard) class of operations. Showing a connection of our approach to the one in New J. Phys. 8, 126 (2006), we provide, to our knowledge, the tightest known upper bound in the (3,2,2,2) scenario. Moreover, we formulate a security condition, equivalent to known ones, for the considered class of protocols. To achieve this, we introduce a nonsignaling norm that constitutes an analogy to the trace norm used in the security condition of the quantum key distribution.
We provide several general upper bounds on the rate of a key secure against a quantum adversary in the device-independent conference key agreement (DI-CKA) scenario. They include bounds by reduced entanglement measures and those based on multipartite secrecy monotones such as a multipartite squashed entanglement-based measure, which we refer to as reduced c-squashed entanglement. We compare the latter bound with the known lower bound for the protocol of conference key distillation based on the parity Clauser-Horne-Shimony-Holt game. We also show that the gap between the DI-CKA rate and the device-dependent rate is inherited from the bipartite gap between device-independent and device-dependent key rates, giving examples that exhibit the strict gap.
The aim of this thesis is to understand the fundamental limitations on secret key distillation in various settings of quantum key distribution. We first consider quantum steering, which is a resource for one-sided device-independent quantum key distribution. We introduce a conditional mutual information based quantifier for quantum steering, which we call intrinsic steerability. Next, we consider quantum non-locality, which is a resource for device-independent quantum key distribution. In this context, we introduce a quantifier, intrinsic non-locality, which is a monotone in the resource theory of Bell non-locality. Both these quantities are inspired by intrinsic information and squashed entanglement and are based on conditional mutual information. The idea behind these quantifiers is to suppress the correlations that can be explained by a local hidden variable or by an inaccessible quantum system, thus quantifying the remaining intrinsic correlations. We then prove various properties of these two monotones, which includes the following: monotonicity under free operations, additivity under tensor product of objects, convexity, and faithfulness, among others. Next, we prove that intrinsic steerability is an upper bound on the secret-key-agreement capacity of an assemblage, and intrinsic non-locality is an upper bound on the secret-key-agreement capacity of a quantum probability distribution. Thus we prove that these quantities are upper bounds on the achievable key rates in one-sided device-independent and device-independent quantum key distribution protocols. We also calculate these bounds for certain honest devices. The study of these upper bounds is instrumental in understanding the limitations of protocols that can be designed for various settings. These upper bounds inform us that, even if one considers the best possible protocol, there is no possibility of exceeding the upper bounds on key rates without a quantum repeater. The upper bounds introduced in this thesis are an important step for initiating this line of research in one-sided device-independent and in device-independent quantum key distribution.
In this work, we develop upper bounds on key rates for device-independent quantum key distribution (DI-QKD) protocols and devices. We study the reduced cc\mathrm{cc}cc-squashed entanglement and show that it is a convex functional. As a result, we show that the convex hull of the currently known bounds is a tighter upper bound on the device-independent key rates of the standard Clauser-Horne-Shimony-Holt (CHSH)-based protocol. We further provide tighter bounds for DI-QKD key rates achievable by any protocol applied to the CHSH-based device. This bound is based on reduced relative entropy of entanglement optimized over decompositions into local and nonlocal parts. In the dynamical scenario of quantum channels, we obtain upper bounds for device-independent private capacity for the CHSH-based protocols. We show that the device-independent private capacity for the CHSH-based protocols on depolarizing and erasure channels is limited by the secret key capacity of dephasing channels.
In this work, we introduce the multipartite intrinsic non-locality as a resource quantifier for the multipartite scenario of device-independent (DI) conference key agreement. We prove that this quantity is additive, convex, and monotone under a class of free operations called local operations and common randomness. As one of our technical contributions, we establish a chain rule for multipartite mutual information, which we then use to prove that the multipartite intrinsic non-locality is additive. This chain rule may be of independent interest in other contexts. All of these properties of multipartite intrinsic non-locality are helpful in establishing the main result of our paper: multipartite intrinsic non-locality is an upper bound on secret key rate in the general multipartite scenario of DI conference key agreement. We discuss various examples of DI conference key protocols and compare our upper bounds for these protocols with known lower bounds. Finally, we calculate upper bounds on recent experimental realizations of DI quantum key distribution.
In this work, we introduce multipartite intrinsic non-locality as a method for quantifying resources in the multipartite scenario of device-independent (DI) conference key agreement. We prove that multipartite intrinsic non-locality is additive, convex, and monotone under a class of free operations called local operations and common randomness. As one of our technical contributions, we establish a chain rule for two variants of multipartite mutual information, which we then use to prove that multipartite intrinsic non-locality is additive. This chain rule may be of independent interest in other contexts. All of these properties of multipartite intrinsic non-locality are helpful in establishing the main result of our paper: multipartite intrinsic non-locality is an upper bound on secret key rate in the general multipartite scenario of DI conference key agreement. We discuss various examples of DI conference key protocols and compare our upper bounds for these protocols with known lower bounds. Finally, we calculate upper bounds on recent experimental realizations of DI quantum key distribution.