Quantum information masking: deterministic versus probabilistic

, can be probabilistically masked by a general unitary-reduction operation if they are linearly independent. The maximal successful probability of probabilistic masking is analyzed and derived for the case of two initial states.

Related papers

Deterministic versus probabilistic quantum information masking

Bo Li, Shuhan Jiang, Xiao-Bin Liang +3 more

We investigate quantum information masking for arbitrary dimensional quantum states. We show that mutually orthogonal quantum states can always be served for deterministic masking of quantum information. We further construct a probabilistic masking machine for linearly independent states. It is shown that a set of $d$ -dimensional states, ${{|{a}_{1}\ensuremath{\rangle}}_{A},|{a}_{2}{\ensuremath{\rangle}}_{A},\ensuremath{\cdots},|{a}_{n}{\ensuremath{\rangle}}_{A}}, n\ensuremath{\le}d$, can be probabilistically masked by a general unitary-reduction operation if they are linearly independent. The maximal successful probability of probabilistic masking is analyzed and derived for the case of two initial states.We investigate quantum information masking for arbitrary dimensional quantum states. We show that mutually orthogonal quantum states can always be served for deterministic masking of quantum information. We further construct a probabilistic masking machine for linearly independent states. It is shown that a set of $d$-dimensional states, ${{|{a}_{1}\ensuremath{\rangle}}_{A},|{a}_{2}{\ensuremath{\rangle}}_{A},\ensuremath{\cdots},|{a}_{n}{\ensuremath{\rangle}}_{A}}, n\ensuremath{\le}d$, can be probabilistically masked by a general unitary-reduction operation if they are linearly independent. The maximal successful probability of probabilistic masking is analyzed and derived for the case of two initial states.

arXiv:1905.00540Physical Review AMay 28, 201929 citations

Quantum information masking in non-Hermitian systems and robustness

Qiao-Qiao Lv, Jin‐Min Liang, Zhi‐Xi Wang +1 more

Abstract By studying quantum information masking (QIM) in non-Hermitian quantum systems, we show that mutually orthogonal quantum states can be deterministically masked, while an arbitrary set of quantum states cannot be masked in non-Hermitian quantum systems. We further demonstrate that a set of linearly independent states which are mutually η -orthogonal can be deterministically masked by a pseudo-unitary operator. Moreover, we study robustness of QIM against noisy environments. The robustness of deterministic and probabilistic QIM under different quantum noise channels is analyzed in detail. Accordingly, we propose and discuss the r -uniform probabilistic QIM in multipartite systems.Abstract By studying quantum information masking (QIM) in non-Hermitian quantum systems, we show that mutually orthogonal quantum states can be deterministically masked, while an arbitrary set of quantum states cannot be masked in non-Hermitian quantum systems. We further demonstrate that a set of linearly independent states which are mutually η -orthogonal can be deterministically masked by a pseudo-unitary operator. Moreover, we study robustness of QIM against noisy environments. The robustness of deterministic and probabilistic QIM under different quantum noise channels is analyzed in detail. Accordingly, we propose and discuss the r -uniform probabilistic QIM in multipartite systems.

arXiv:2203.03864Laser Physics LettersFeb 21, 20228 citations

Masking quantum information encoded in pure and mixed states

Huaixin Cao, Yuxing Du, Zhihua Guo +2 more

Masking of quantum information means that information is hidden from a subsystem and spread over a composite system. Modi et al. proved in [Phys. Rev. Lett. 120, 230501 (2018)] that this is true for some restricted sets of nonorthogonal quantum states and it is not possible for arbitrary quantum states. In this paper, we discuss the problem of masking quantum information encoded in pure and mixed states, respectively. Based on an established necessary and sufficient condition for a set of pure states to be masked by an operator, we find that there exists a set of four states that can not be masked, which implies that to mask unknown pure states is impossible. We construct a masker $S^\sharp$ and obtain its maximal maskable set, leading to an affirmative answer to a conjecture proposed in Modi's paper mentioned above. We also prove that an orthogonal (resp. linearly independent) subset of pure states can be masked by an isometry (resp. injection). Generalizing the case of pure states, we introduce the maskability of a set of mixed states and prove that a commuting subset of mixed states can be masked by an isometry $S^{\diamond}$ while it is impossible to mask all of mixed states by any operator. We also find the maximal maskable sets of mixed states of the isometries ${S^{\sharp}}$ and ${S^{\diamond}}$ , respectively.Masking of quantum information means that information is hidden from a subsystem and spread over a composite system. Modi et al. proved in [Phys. Rev. Lett. 120, 230501 (2018)] that this is true for some restricted sets of nonorthogonal quantum states and it is not possible for arbitrary quantum states. In this paper, we discuss the problem of masking quantum information encoded in pure and mixed states, respectively. Based on an established necessary and sufficient condition for a set of pure states to be masked by an operator, we find that there exists a set of four states that can not be masked, which implies that to mask unknown pure states is impossible. We construct a masker $S^\sharp$ and obtain its maximal maskable set, leading to an affirmative answer to a conjecture proposed in Modi's paper mentioned above. We also prove that an orthogonal (resp. linearly independent) subset of pure states can be masked by an isometry (resp. injection). Generalizing the case of pure states, we introduce the maskability of a set of mixed states and prove that a commuting subset of mixed states can be masked by an isometry $S^{\diamond}$ while it is impossible to mask all of mixed states by any operator. We also find the maximal maskable sets of mixed states of the isometries ${S^{\sharp}}$ and ${S^{\diamond}}$, respectively.

arXiv:2004.14572Apr 30, 20201 citation

$k$ -Uniform states and quantum information masking

Fei Shi, Mao-Sheng Li, Lin Chen +1 more

A pure state of $N$ parties with local dimension $d$ is called a $k$ -uniform state if all the reductions to $k$ parties are maximally mixed. Based on the connections among $k$ -uniform states, orthogonal arrays and linear codes, we give general constructions for $k$ -uniform states. We show that when $d\geq 4k-2$ (resp. $d\geq 2k-1$ ) is a prime power, there exists a $k$ -uniform state for any $N\geq 2k$ (resp. $2k\leq N\leq d+1$ ). Specially, we give the existence of $4,5$ -uniform states for almost every $N$ -qudits. Further, we generalize the concept of quantum information masking in bipartite systems given by [Modi \emph{et al.} {Phys. Rev. Lett. \textbf{120}, 230501 (2018)}] to $k$ -uniform quantum information masking in multipartite systems, and we show that $k$ -uniform states and quantum error-correcting codes can be used for $k$ -uniform quantum information masking.A pure state of $N$ parties with local dimension $d$ is called a $k$-uniform state if all the reductions to $k$ parties are maximally mixed. Based on the connections among $k$-uniform states, orthogonal arrays and linear codes, we give general constructions for $k$-uniform states. We show that when $d\geq 4k-2$ (resp. $d\geq 2k-1$) is a prime power, there exists a $k$-uniform state for any $N\geq 2k$ (resp. $2k\leq N\leq d+1$). Specially, we give the existence of $4,5$-uniform states for almost every $N$-qudits. Further, we generalize the concept of quantum information masking in bipartite systems given by [Modi \emph{et al.} {Phys. Rev. Lett. \textbf{120}, 230501 (2018)}] to $k$-uniform quantum information masking in multipartite systems, and we show that $k$-uniform states and quantum error-correcting codes can be used for $k$-uniform quantum information masking.

arXiv:2009.12497Sep 26, 20203 citations

Complete characterization of qubit masking

Xiao-Bin Liang, Bo Li, Shao-Ming Fei

We study the problem of information masking through nonzero linear operators that distribute information encoded in single qubits to the correlations between two qubits. It is shown that a nonzero linear operator cannot mask any nonzero measure set of qubit states. We prove that the maximal maskable set of states on the Bloch sphere with respect to any masker is the ones on a spherical circle. Any states on a spherical circle on the Bloch sphere are maskable, which also proves the conjecture on maskable qubit states given by Modi et al. [Phys. Rev. Lett. 120, 230501 (2018)]. we provide explicitly operational unitary maskers for all maskable sets. As applications, different protocols for secret sharing are introduced.We study the problem of information masking through nonzero linear operators that distribute information encoded in single qubits to the correlations between two qubits. It is shown that a nonzero linear operator cannot mask any nonzero measure set of qubit states. We prove that the maximal maskable set of states on the Bloch sphere with respect to any masker is the ones on a spherical circle. Any states on a spherical circle on the Bloch sphere are maskable, which also proves the conjecture on maskable qubit states given by Modi et al. [Phys. Rev. Lett. 120, 230501 (2018)]. we provide explicitly operational unitary maskers for all maskable sets. As applications, different protocols for secret sharing are introduced.

arXiv:1909.11244Physical Review ASep 23, 201934 citations

The masking condition for the quantum state in two-dimensional Hilbert space

Mei-yi Wang, Sujuan Zhang, Chen‐Ming Bai +1 more

Abstract This paper focuses on quantum information masking for the quantum state in two-dimensional Hilbert space. We present a system of equations as the condition of quantum information masking. It is shown that quantum information contained in a single qubit state can be masked, if and only if the coefficients of the quantum state satisfy the given system of equations. By observing the characteristics of non-orthogonal maskable quantum states, we obtain a related conclusion, namely, if two non-orthogonal two-qubit quantum states can mask a single qubit state, they have the same number of terms and the same basis. Finally, for maskable orthogonal quantum states, we analyze two special examples and give their images for an intuitive description.Abstract This paper focuses on quantum information masking for the quantum state in two-dimensional Hilbert space. We present a system of equations as the condition of quantum information masking. It is shown that quantum information contained in a single qubit state can be masked, if and only if the coefficients of the quantum state satisfy the given system of equations. By observing the characteristics of non-orthogonal maskable quantum states, we obtain a related conclusion, namely, if two non-orthogonal two-qubit quantum states can mask a single qubit state, they have the same number of terms and the same basis. Finally, for maskable orthogonal quantum states, we analyze two special examples and give their images for an intuitive description.

arXiv:2111.05574Communications in Theoretical PhysicsApr 18, 20224 citations

\{ \vert a_1 \rangle_A, \vert a_2 \rangle_A, \dots, \vert a_n \rangle_A \}

n \leq d

d

-dimensional states, ${{|{a}_{1}\ensuremath{\rangle}}_{A},|{a}_{2}{\ensuremath{\rangle}}_{A},\ensuremath{\cdots},|{a}_{n}{\ensuremath{\rangle}}_{A}}, n\ensuremath{\le}d$, can be probabilistically masked by a general unitary-reduction operation if they are linearly independent. The maximal successful probability of probabilistic masking is analyzed and derived for the case of two initial states.

S^\sharp

and obtain its maximal maskable set, leading to an affirmative answer to a conjecture proposed in Modi's paper mentioned above. We also prove that an orthogonal (resp. linearly independent) subset of pure states can be masked by an isometry (resp. injection). Generalizing the case of pure states, we introduce the maskability of a set of mixed states and prove that a commuting subset of mixed states can be masked by an isometry

S^{\diamond}

while it is impossible to mask all of mixed states by any operator. We also find the maximal maskable sets of mixed states of the isometries

{S^{\sharp}}

and

{S^{\diamond}}

, respectively.

A pure state of

N

parties with local dimension

d

is called a

k

-uniform state if all the reductions to

k

parties are maximally mixed. Based on the connections among

k

-uniform states, orthogonal arrays and linear codes, we give general constructions for

k

-uniform states. We show that when

d\geq 4k-2

(resp.

d\geq 2k-1

) is a prime power, there exists a

k

-uniform state for any

N\geq 2k

(resp.

2k\leq N\leq d+1

). Specially, we give the existence of

4,5

-uniform states for almost every

N

-qudits. Further, we generalize the concept of quantum information masking in bipartite systems given by [Modi \emph{et al.} {Phys. Rev. Lett. \textbf{120}, 230501 (2018)}] to

k

-uniform quantum information masking in multipartite systems, and we show that

k

-uniform states and quantum error-correcting codes can be used for

k

-uniform quantum information masking.