Francesco Anna Mele
@francescoannamele.bsky.social
Quantum Information PhD student at Scuola Normale Superiore of Pisa (Italy)
Honoured to have received the Boeing Quantum Creators Prize at the Chicago Quantum Exchange event today!
This prize recognises early-career researchers who advance quantum information in new directions
This prize recognises early-career researchers who advance quantum information in new directions
November 5, 2025 at 5:18 AM
Honoured to have received the Boeing Quantum Creators Prize at the Chicago Quantum Exchange event today!
This prize recognises early-career researchers who advance quantum information in new directions
This prize recognises early-career researchers who advance quantum information in new directions
Okay, last post on *quantum learning theory with CV systems* (for a few months🫣)
Today's new work tackles another natural and central question in this rapidly developing field: Given an unknown CV state, how to test whether is it Gaussian or not?
arxiv.org/pdf/2510.07305
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Today's new work tackles another natural and central question in this rapidly developing field: Given an unknown CV state, how to test whether is it Gaussian or not?
arxiv.org/pdf/2510.07305
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October 9, 2025 at 10:36 AM
Okay, last post on *quantum learning theory with CV systems* (for a few months🫣)
Today's new work tackles another natural and central question in this rapidly developing field: Given an unknown CV state, how to test whether is it Gaussian or not?
arxiv.org/pdf/2510.07305
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Today's new work tackles another natural and central question in this rapidly developing field: Given an unknown CV state, how to test whether is it Gaussian or not?
arxiv.org/pdf/2510.07305
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The saga of *quantum learning theory with CV systems* never ends!
And indeed, when you look closely at this field, many natural and promising questions arise. For instance:
How to learn CV Gaussian unitaries?
arxiv.org/pdf/2510.05531
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And indeed, when you look closely at this field, many natural and promising questions arise. For instance:
How to learn CV Gaussian unitaries?
arxiv.org/pdf/2510.05531
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October 8, 2025 at 10:36 AM
The saga of *quantum learning theory with CV systems* never ends!
And indeed, when you look closely at this field, many natural and promising questions arise. For instance:
How to learn CV Gaussian unitaries?
arxiv.org/pdf/2510.05531
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And indeed, when you look closely at this field, many natural and promising questions arise. For instance:
How to learn CV Gaussian unitaries?
arxiv.org/pdf/2510.05531
1/
New work on *quantum data hiding*! If you have a quirk for semidefinite/linear programming as an analytical tool for quantum info, this paper might interest you
arxiv.org/pdf/2510.03538
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arxiv.org/pdf/2510.03538
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October 7, 2025 at 10:16 AM
New work on *quantum data hiding*! If you have a quirk for semidefinite/linear programming as an analytical tool for quantum info, this paper might interest you
arxiv.org/pdf/2510.03538
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arxiv.org/pdf/2510.03538
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Excited and honored to be selected as a winner of the Boeing Quantum Creators Prize 🥳
This international award recognizes early-career researchers who are advancing quantum information science and engineering in new directions!
🔗 chicagoquantum.org/2025BQCP
This international award recognizes early-career researchers who are advancing quantum information science and engineering in new directions!
🔗 chicagoquantum.org/2025BQCP
September 26, 2025 at 12:24 PM
Excited and honored to be selected as a winner of the Boeing Quantum Creators Prize 🥳
This international award recognizes early-career researchers who are advancing quantum information science and engineering in new directions!
🔗 chicagoquantum.org/2025BQCP
This international award recognizes early-career researchers who are advancing quantum information science and engineering in new directions!
🔗 chicagoquantum.org/2025BQCP
We also find similar bounds for classical probability distributions:
If two probability distributions are ε-close in TV distance, how close are their mean vectors and their covariance matrices?
This is a natural question, but it has never been explored as far as we known
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If two probability distributions are ε-close in TV distance, how close are their mean vectors and their covariance matrices?
This is a natural question, but it has never been explored as far as we known
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April 29, 2025 at 4:51 PM
We also find similar bounds for classical probability distributions:
If two probability distributions are ε-close in TV distance, how close are their mean vectors and their covariance matrices?
This is a natural question, but it has never been explored as far as we known
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If two probability distributions are ε-close in TV distance, how close are their mean vectors and their covariance matrices?
This is a natural question, but it has never been explored as far as we known
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New bosonic trace distance bounds:
If two (possibly non-Gaussian) states are ε-close in trace distance, how close are their covariance matrices, first moments, and symplectic eigenvalues?
Our new trace distance bounds precisely answer to this question:
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If two (possibly non-Gaussian) states are ε-close in trace distance, how close are their covariance matrices, first moments, and symplectic eigenvalues?
Our new trace distance bounds precisely answer to this question:
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April 29, 2025 at 4:51 PM
New bosonic trace distance bounds:
If two (possibly non-Gaussian) states are ε-close in trace distance, how close are their covariance matrices, first moments, and symplectic eigenvalues?
Our new trace distance bounds precisely answer to this question:
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If two (possibly non-Gaussian) states are ε-close in trace distance, how close are their covariance matrices, first moments, and symplectic eigenvalues?
Our new trace distance bounds precisely answer to this question:
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New decomposition of Gaussian unitaries:
Any n-mode Gaussian unitary can be written, for all k<n/2, as a composition of an n-mode passive Gaussian unitary, a Gaussian unitary that acts only on the first 2k modes, and another Gaussian unitary acting on the last n-k modes.
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Any n-mode Gaussian unitary can be written, for all k<n/2, as a composition of an n-mode passive Gaussian unitary, a Gaussian unitary that acts only on the first 2k modes, and another Gaussian unitary acting on the last n-k modes.
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April 29, 2025 at 4:51 PM
New decomposition of Gaussian unitaries:
Any n-mode Gaussian unitary can be written, for all k<n/2, as a composition of an n-mode passive Gaussian unitary, a Gaussian unitary that acts only on the first 2k modes, and another Gaussian unitary acting on the last n-k modes.
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Any n-mode Gaussian unitary can be written, for all k<n/2, as a composition of an n-mode passive Gaussian unitary, a Gaussian unitary that acts only on the first 2k modes, and another Gaussian unitary acting on the last n-k modes.
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I’d like to advertise two cute technical results of today’s paper that may be of independent interest (I hope):
A new decomposition of Gaussian unitaries and new bosonic trace distance bounds (the saga of bosonic trace distance bounds never ends! 😍)
arxiv.org/abs/2504.19319
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A new decomposition of Gaussian unitaries and new bosonic trace distance bounds (the saga of bosonic trace distance bounds never ends! 😍)
arxiv.org/abs/2504.19319
1/
April 29, 2025 at 4:51 PM
I’d like to advertise two cute technical results of today’s paper that may be of independent interest (I hope):
A new decomposition of Gaussian unitaries and new bosonic trace distance bounds (the saga of bosonic trace distance bounds never ends! 😍)
arxiv.org/abs/2504.19319
1/
A new decomposition of Gaussian unitaries and new bosonic trace distance bounds (the saga of bosonic trace distance bounds never ends! 😍)
arxiv.org/abs/2504.19319
1/
Fortunately, the symplectic rank is a “robust” measure of non-Gaussianity: it cannot decrease under small perturbations in trace distance.
If a state has high symplectic rank, then all states sufficiently close to it (with bounded "energy") have high symplectic rank.
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If a state has high symplectic rank, then all states sufficiently close to it (with bounded "energy") have high symplectic rank.
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April 29, 2025 at 11:52 AM
Fortunately, the symplectic rank is a “robust” measure of non-Gaussianity: it cannot decrease under small perturbations in trace distance.
If a state has high symplectic rank, then all states sufficiently close to it (with bounded "energy") have high symplectic rank.
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If a state has high symplectic rank, then all states sufficiently close to it (with bounded "energy") have high symplectic rank.
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The fourth operational meaning regards the “non-Gaussian circuit complexity”. Indeed, t-doped states (i.e. states prepared by applying to the vacuum arbitrary Gaussian unitaries and t single-mode non-Gaussian gates) have symplectic rank <= 2t.
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April 29, 2025 at 11:52 AM
The fourth operational meaning regards the “non-Gaussian circuit complexity”. Indeed, t-doped states (i.e. states prepared by applying to the vacuum arbitrary Gaussian unitaries and t single-mode non-Gaussian gates) have symplectic rank <= 2t.
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Interestingly, the monotonicity of the symplectic rank also implies that *the resource theory of non-Gaussianity is irreversible*. 😶🌫️
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April 29, 2025 at 11:52 AM
Interestingly, the monotonicity of the symplectic rank also implies that *the resource theory of non-Gaussianity is irreversible*. 😶🌫️
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This monotonicity is powerful for proving no-go theorems.
For example, it immediately implies that no Gaussian protocol can convert a single-mode non-Gaussian state into the tensor product of two non-Gaussian states. Or, more generally, see Corollary 5 below:
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For example, it immediately implies that no Gaussian protocol can convert a single-mode non-Gaussian state into the tensor product of two non-Gaussian states. Or, more generally, see Corollary 5 below:
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April 29, 2025 at 11:52 AM
This monotonicity is powerful for proving no-go theorems.
For example, it immediately implies that no Gaussian protocol can convert a single-mode non-Gaussian state into the tensor product of two non-Gaussian states. Or, more generally, see Corollary 5 below:
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For example, it immediately implies that no Gaussian protocol can convert a single-mode non-Gaussian state into the tensor product of two non-Gaussian states. Or, more generally, see Corollary 5 below:
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Our main theorem establishes that the symplectic rank is a monotone under post-selected Gaussian operations.
In other words, it cannot increase under any Gaussian protocol, even with the ability to post-select on the outcome of Gaussian measurements.
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In other words, it cannot increase under any Gaussian protocol, even with the ability to post-select on the outcome of Gaussian measurements.
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April 29, 2025 at 11:52 AM
Our main theorem establishes that the symplectic rank is a monotone under post-selected Gaussian operations.
In other words, it cannot increase under any Gaussian protocol, even with the ability to post-select on the outcome of Gaussian measurements.
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In other words, it cannot increase under any Gaussian protocol, even with the ability to post-select on the outcome of Gaussian measurements.
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Equivalently, the symplectic rank is the minimum number of modes onto which all the non-Gaussianity of a state can be compressed by applying a Gaussian unitary to the state.
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April 29, 2025 at 11:52 AM
Equivalently, the symplectic rank is the minimum number of modes onto which all the non-Gaussianity of a state can be compressed by applying a Gaussian unitary to the state.
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The definition of symplectic rank was already given by @gerardoadesso.bsky.social in 2005 (journals.aps.org/prl/abstract...), but its potential remained unexplored.
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April 29, 2025 at 11:52 AM
The definition of symplectic rank was already given by @gerardoadesso.bsky.social in 2005 (journals.aps.org/prl/abstract...), but its potential remained unexplored.
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New bosonic paper out!
Take the covariance matrix of a pure state and count the number of symplectic eigenvalues that are strictly larger than one: this is a powerful non-Gaussian monotone — the *symplectic rank*
arxiv.org/abs/2504.19319
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Take the covariance matrix of a pure state and count the number of symplectic eigenvalues that are strictly larger than one: this is a powerful non-Gaussian monotone — the *symplectic rank*
arxiv.org/abs/2504.19319
1/
April 29, 2025 at 11:52 AM
New bosonic paper out!
Take the covariance matrix of a pure state and count the number of symplectic eigenvalues that are strictly larger than one: this is a powerful non-Gaussian monotone — the *symplectic rank*
arxiv.org/abs/2504.19319
1/
Take the covariance matrix of a pure state and count the number of symplectic eigenvalues that are strictly larger than one: this is a powerful non-Gaussian monotone — the *symplectic rank*
arxiv.org/abs/2504.19319
1/
In our paper, we find a closed formula for the Gaussian ergotropy in terms of ordered *symplectic* eigenvalues, by establishing the following relation:
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March 28, 2025 at 9:58 AM
In our paper, we find a closed formula for the Gaussian ergotropy in terms of ordered *symplectic* eigenvalues, by establishing the following relation:
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However, in many practical situations, we are restricted to use *Gaussian* unitaries only (and hence ergotropy becomes not so meaningful). It thus makes sense to define the *Gaussian ergotropy*:
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March 28, 2025 at 9:58 AM
However, in many practical situations, we are restricted to use *Gaussian* unitaries only (and hence ergotropy becomes not so meaningful). It thus makes sense to define the *Gaussian ergotropy*:
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It is well-known that the ergotropy can be analytically calculated in terms of ordered eigenvalues, by using the following relation:
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March 28, 2025 at 9:58 AM
It is well-known that the ergotropy can be analytically calculated in terms of ordered eigenvalues, by using the following relation:
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Mathematically, the ergotropy is defined as the maximum --- over all the unitaries --- of the difference between the energy of the initial state and the energy of the state after the application of the unitary.
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March 28, 2025 at 9:58 AM
Mathematically, the ergotropy is defined as the maximum --- over all the unitaries --- of the difference between the energy of the initial state and the energy of the state after the application of the unitary.
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New paper out today on "Q Thermo with CV systems"!
What is the maximum energy that you can extract from a quantum state via Gaussian unitaries only?
We solve this problem by establishing a simple, cute formula for the *Gaussian ergotropy*.
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arxiv.org/abs/2503.21748
What is the maximum energy that you can extract from a quantum state via Gaussian unitaries only?
We solve this problem by establishing a simple, cute formula for the *Gaussian ergotropy*.
1/
arxiv.org/abs/2503.21748
March 28, 2025 at 9:58 AM
New paper out today on "Q Thermo with CV systems"!
What is the maximum energy that you can extract from a quantum state via Gaussian unitaries only?
We solve this problem by establishing a simple, cute formula for the *Gaussian ergotropy*.
1/
arxiv.org/abs/2503.21748
What is the maximum energy that you can extract from a quantum state via Gaussian unitaries only?
We solve this problem by establishing a simple, cute formula for the *Gaussian ergotropy*.
1/
arxiv.org/abs/2503.21748
Here, we prove the theorem in the screenshot, which may be of independent interest. Note that this theorem is stronger than the Avram–Parter’s theorem, as the latter can be recovered by taking the limit of infinite n.
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March 18, 2025 at 12:50 PM
Here, we prove the theorem in the screenshot, which may be of independent interest. Note that this theorem is stronger than the Avram–Parter’s theorem, as the latter can be recovered by taking the limit of infinite n.
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To prove our results, we employ a generalisation of the powerful Avram-Parter's theorem. The latter allows one to understand the asymptotic behaviour of the singular values of an important class of matrices --- the Toeplitz matrices (see the screenshot).
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March 18, 2025 at 12:50 PM
To prove our results, we employ a generalisation of the powerful Avram-Parter's theorem. The latter allows one to understand the asymptotic behaviour of the singular values of an important class of matrices --- the Toeplitz matrices (see the screenshot).
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